Harvard Psychological Studies, Volume 1 Containing Sixteen Experimental Investigations from the Harvard Psychological Laboratory. (part 3 of 5)
Tables II. and III. show the results of experiments in changing the color of a single image. This was usually a square, sometimes a disc. The time of optical perception was five seconds. After the disappearance of after-images, if there were any, eighteen to twenty-four changes were made in the color of the memory image, occupying from four and a half to six minutes.
The colors were saturated blue, green, yellow and red, and each one was changed into each of the other colors and then restored. The order of change was varied to avoid uniformity of succession. The four colors were shown to the subjects each day before the experiments began, to establish a standard. The time was taken with a stop-watch, and includes the time between the director's word of command, 'green,' etc., and the subject's report, 'now,' or 'green,' etc. It includes, therefore, two reaction times. The subject reported 'now' the instant he secured the desired color, not waiting for the completion of the shape that usually followed.
TABLE II.
CHANGES OF COLOR. SINGLE IMAGE. 72 CHANGES OF EACH COLOR.
[Label 1: Subject.] [Label 2: To Green.] [Label 3: Return to Blue.] [Label 4: To Yellow.] [Label 5: Return to Blue.] [Label 6: To Red.] [Label 7: Return to Blue.] [Label 8: To Blue.] [Label 9: Return to Green.] [Label 10: To Yellow.] [Label 11: Return to Green.] [Label 12: To Red] [Label 13: Return to Green.]
From Blue. From Green. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
B. 1.72 0.50 1.66 0.38 1.81 0.50 1.23 0.56 1.10 0.65 1.33 0.56 G. 1.15 0.60 1.10 0.79 0.89 0.65 1.75 0.87 1.04 0.75 1.35 0.71 H. 4.67 4.25 4.87 4.06 4.81 3.83 5.27 4.50 5.81 4.89 5.37 4.94 I. 2.27 1.25 1.77 1.19 1.83 1.25 2.15 0.93 1.71 1.04 1.92 1.15 J. 1.38 0.81 1.29 0.94 1.29 0.95 1.65 1.08 1.15 0.77 1.60 0.81 K. 2.35 1.71 1.96 1.66 2.10 1.19 2.25 1.25 2.17 1.73 2.44 1.27
Av. 2.26 1.52 2.11 1.50 2.15 1.39 2.41 1.53 2.15 1.65 2.34 1.57
[Label 1: Subject.] [Label 2: To Blue.] [Label 3: Return to Yellow.] [Label 4: To Green.] [Label 5: Return to Yellow.] [Label 6: To Red.] [Label 7: Return to Yellow.] [Label 8: To Blue.] [Label 9: Return to Red.] [Label 10: To Green.] [Label 11: Return to Red.] [Label 12: To Yellow.] [Label 13: Return to Red.]
From Yellow. From Red. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
B. 1.79 1.06 1.35 0.87 1.89 1.10 1.54 0.58 1.71 0.62 1.31 0.71 G. 1.50 1.10 1.48 0.87 1.31 0.88 1.33 0.92 1.35 0.91 0.77 0.58 H. 5.02 4.54 5.73 3.91 6.15 4.17 6.35 3.91 5.89 4.69 5.54 4.37 I. 2.29 1.31 2.54 1.19 2.29 1.27 2.85 1.10 2.50 1.21 1.65 1.31 J. 1.35 0.98 1.35 0.65 1.27 0.88 1.42 1.04 1.31 1.02 1.25 0.85 K. 3.02 1.52 3.21 2.04 2.23 1.79 2.54 1.56 2.66 1.60 2.88 1.81
Av. 2.49 1.76 2.61 1.59 2.52 1.68 2.67 1.51 2.57 1.68 2.23 1.62
TABLE III.
CHANGES TO THE FOUR COLORS.
Average time in seconds. 72 changes from and 72 changes to each color.
[Label 1: To Blue.] [Label 2: Return from Blue.] [Label 3: To Green.] [Label 4: Return from Green.] [Label 5: To Yellow.] [Label 6: Return from Yellow.] [Label 7: To Red.] [Label 8: Return from Red.]
[1] [2] [3] [4] [5] [6] [7] [8] From blue, 2.26 1.52 2.11 1.50 2.12 1.39 " green, 2.38 1.53 2.16 1.64 2.33 1.57 " yellow, 2.49 1.75 2.61 1.59 2.52 1.68 " red, 2.67 1.52 2.58 1.68 2.27 1.62
Average, 2.52 1.60 2.48 1.59 2.17 1.58 2.33 1.55
Changes from a presented color. Returns to a presented color. 216 movements. 216 movements.
From presented yellow, 2.52 To presented yellow, 1.67 " " red, 2.49 " " red, 1.61 " " green, 2.29 " " green, 1.58 " " blue, 2.16 " " blue, 1.47
Average, 2.37 Average, 1.58
Changes to a color from Returns from a color to a presented color. a presented color. 216 movements. 216 movements.
To blue, 2.52 From blue, 1.60 " green, 2.48 " green, 1.59 " red, 2.33 " yellow, 1.58 " yellow, 2.17 " red, 1.55
Average, 2.37 Average, 1.58
The six subjects fall into two groups--three, H., I., and K., taking longer than the other three. As in the previous experiment H. was markedly longer than any of the others.
There were seventeen hundred and twenty-eight changes in all, including returns to the original color. There were two hundred and sixteen changes from each of the four colors as presented, to each of the other three and, of course, the same number of returns to the presented color.
The change to blue from the other presented colors was the most difficult and the change to yellow was the easiest.
The averages (216 exp. each) are,
Sec. To blue, 2.55 " green, 2.48 " red, 2.33 " yellow, 2.17
The returns to the presented colors did not differ greatly from each other, the averages (216 exp. each) being:
Sec. From blue, 1.603 " green, 1.597 " yellow, 1.589 " red, 1.549
From red appears to be the easiest change, and from blue the hardest.
The getting away from a presented blue was the easiest and from a presented yellow the most difficult, as seen by these averages (216 exp. each):
Sec. From yellow, 2.54 " red, 2.49 " green, 2.29 " blue, 2.16
The returns to the presented colors show that it was hardest to get back to the presented yellow, easiest to get back to the presented blue, the averages (216 exp. each), being:
Sec. To yellow, 1.67 " red, 1.61 " green, 1.58 " blue, 1.47
The facts as to blue and yellow shown by these four tables of averages may be expressed also in this way:
If a blue square was shown, it was easier to change the blue memory image into the other colors, and also easier to get back the blue memory image after such changes, than if any other of the three colors was presented.
If another color than blue was shown it was harder to change the memory image of that color to blue than to any of the other colors, and also harder to get back to the memory image of that color from blue than from any of the other three colors.
If a yellow square was shown, it was harder to change the yellow memory image into the other colors, and also harder to get back the yellow memory image after such changes than if any other of the three colors was presented.
If another color than yellow was shown, it was easier to change the memory image of that color to yellow than to any of the three other colors, and also easier to get back to the memory image of that color from the yellow than from any of the other three colors except red.
If we combine all the changes into a color (both changes from another presented color and returns to this color previously presented) we find that changes to green are hardest, to yellow easiest. The averages (for 432 exp. each) are,
Sec. To green, 2.03 " blue, 1.99 " red, 1.97 " yellow, 1.92
The changes away from a color (both from this color previously presented and from this color to the other previously presented colors) show that it was hardest to get away from yellow, easiest to get away from blue, the averages (for 432 exp. each) being:
Sec. From yellow, 2.06 " red, 2.02 " green, 1.94 " blue, 1.88
As for the subjects, all six found yellow the easiest to change into, one finding red equally easy.
SUBJECTIVE.
For seven of the subjects, mental repetition of the name of the color (usually accompanied by articulatory movements) tended to bring up the color, and one other subject occasionally used this method of bringing about a change that was difficult. With D. the color did not come at repetition of the name. G. was assisted by auditory recall of the name. Nine subjects reported a feeling of strain, usually in the eyes as of focusing, occurring especially when there seemed a difficulty in producing the desired change. The tension attended almost exclusively changes of the presented color, not restorations of that color. For D. this strain was considerable, for G. there was also an after-feeling of strain in the head. For G. the image was clearest when the feeling of strain was least, and J. secured the promptest and clearest results when he could most nearly rid himself of anxiety as to the result. K. in one instance (a change from green to yellow) became conscious of the setting of his jaws and motions of feet and body in aid of his attempt. H. frequently had the feeling of physical fatigue.
In most cases the restoration of the presented color was as a complete square, triangle, etc. In changes from the presented color the new color appeared at a corner, or edge, or as a patch at the center. With E. the "color flashed over the whole field and then had to be restricted to the figure." B. "held the outline, emptied of the old color, while it was filled in with the new." D. "had a clear outline, and the new color came in small blotches inside, and effort spread them out to cover the whole figure." For I. the "new color came sliding in from the right side over the old, which, however, disappeared as if it were moving out of focus." With A. the new color usually came from either the lower left-hand or the upper right-hand corner. F. kept a clear outline and the new color came in from the right.
When E. found it difficult to create at the center the desired color, he thought of some object (garment, grass, sky, etc.) of that color and then transferred it to fill in the outline preserved at the center. B. moved the colored figure aside and in its place put one of the desired color, moved the new figure up to the old and there superposed it. With G. the new colors seemed of new material and there was felt to be an accumulation about the center, of old color-material. Then he located the square outside of this imaginary debris and began again. H. found that the colors of his own experiments, in which he used color squares framed in black, came to his mind at the names of the desired colors, and the association soon gave him the figure also. I. located the new colors around the presented one, first all at the right; then green at the left, red at the right, yellow above, when presented blue was at the center; then yellow and green were at the upper left-hand corner, while red came from behind. The new color 'slid in over the old.' It was found easier to secure the desired color when its position was known beforehand. J. also used a similar device. He 'turned towards the places and brought out the required color and filled the central outline with it.' He tried to break up this scheme and got red without going after it but found himself 'at a loss to find the colors.' Later he succeeded so that the required color simply appeared in the outline of the old color at the center. K. turned his eyes to corners of the central outline, then to the center, and found that this aided in developing the desired color from the corners inward. When difficulty arose, he experienced muscular tension in body and legs and jaws.
Five of the subjects considered the change from a presented color to blue the hardest and one found the change to red hardest. Green was placed second in difficulty by one, and blue second by the one who found red the hardest. Three reported the change to yellow the easiest and two the change to red.
The change from red to yellow caused 'an unpleasant sensation' in C. and the new figure 'had a maroon halo.'
A. in returning from green or blue to yellow passed through a gray; so, once, in changing from yellow to green, and once, green to red. With A. blue retinal clouds, which often came, aided changes to blue and hindered at times changes to other colors. B. had a fusion of yellow and red in changing from yellow to red. G. had a tendency to leave uncolored the lower left-hand corner and it 'was wood-colored'; G. had a gray image as the result of fusion of retinal clouds with red memory image. With H. blue always came in as robin's-egg blue, which then had to be changed to the standard blue. In one instant the green memory image seemed to shift into a purple and change to a positive retinal image which interfered with changes to other colors. J. found whistling and humming an aid in relaxing an unnatural state of tension which would hinder the best results. To increase the vividness of the image he would recall the black background on which the colored squares had hung. In one experiment K. became 'desperately tired of yellow,' which was the presented color, so that his 'mind was ready to jump to any color rather than yellow.' The returns to yellow were, in this experiment, slower than the changes from yellow.
The images sometimes changed sizes, being at times smaller, but usually larger than the object. In one experiment of C. the image was four times the size of the object, which was a green square with sides of one inch.
III. MOVEMENTS OF TWO IMAGES IN THE SAME AND IN DIFFERENT DIRECTIONS.
Table IV. gives the results of experiments in the movements of two images, the objects presented being colored squares or discs. Time of perception was five seconds. After the disappearance of after-images, if there were any, eighteen to twenty-four movements with returns to original positions were made, occupying five or six minutes. The colors were saturated blue, green, yellow and red. Four of the movements were such as separated the two images, and in four the two moved uniformly. The first four movements were right and left, left and right, up and down, down and up; the left-hand object followed the first direction indicated. The right-and-left movements involved the crossing of the images. The last four were both to right, to left, up, down. The time was taken with a stop-watch and includes the time between the director's word of command and the subject's report, 'now.' It includes, therefore, two reaction times. The subject reported the instant the colors reached, or appeared at, the suggested positions.
It is to be noticed that H. was very much slower than any of the others in making the movements, both out and back; and that K., while also slower (though much less so than H.) in making the movements outward, was no slower in making the return movements.
TABLE IV.
MOVEMENTS OF TWO IMAGES.
Twenty movements of each kind for each subject. Averages in seconds.
In Opposite Directions.
Subj. L.-R. Ret. R.-L. Ret. U.-D. Ret. D.-U. Ret.
B. 1.82 2.90 2.10 2.27 0.86 0.87 0.73 0.86
G. 3.02 2.86 2.68 2.63 1.98 2.25 1.63 2.01
H. 9.18 10.30 7.50 7.15 5.16 6.90 5.36 5.21
I. 4.17 3.52 3.40 3.37 1.26 1.47 1.23 1.31
J. 2.17 2.90 2.87 2.27 1.05 1.63 1.02 1.13
K. 5.51 6.43 5.16 4.81 1.43 1.48 1.20 1.23
Ave. 4.32 4.82 3.82 3.75 1.96 2.43 1.87 1.96
Average of all movements involving separation (480), 4.18. Returns, 2.06.
In Same Direction.
Subj. R. Ret. L. Ret. U. Ret. D. Ret.
B. 1.31 1.22 1.30 1.11 0.72 0.67 0.72 0.85
G. 2.66 2.35 3.01 2.53 2.00 1.86 2.22 1.86
H. 8.45 7.91 5.66 7.66 6.53 5.95 5.96 6.11
I. 2.57 2.27 2.13 2.05 0.97 1.26 1.00 1.13
J. 1.11 1.16 1.08 11.5 0.68 0.90 0.73 0.71
K. 3.97 3.91 3.60 4.07 1.35 1.50 1.75 1.71
Ave. 3.33 3.14 2.79 3.10 2.04 2.02 2.04 2.06
Average of all movements together (480), 3.09. Returns, 2.04.
NUMERICAL.
There were nineteen hundred and twenty movements in all, including the returns to the original positions.
In the order of difficulty as shown by the time taken, the movements stand as follows, the numbers being the averages in seconds for one hundred and twenty movements of each kind:
1. Right and left (i.e., crossing), 4.82 sec. 2. Left and right, 4.32 " 3. Up and down, 3.82 " 4. Down and up, 3.75 " 5. Both right, 3.33 " 6. Both left, 3.14 " 7. Both down, 3.10 " 8. Both up, 3.04 "
SUBJECTIVE.
In the experiments in which the time was recorded, there was no disappearance of either image except where movements were made successively. In these cases frequently the image which was awaiting its turn vanished until the first image was placed, a time varying from a quarter of a second to three or four seconds. Occasionally the image already placed would vanish, while the other was en route; the subject's attention in both these cases being centered exclusively on the image he desired to move. This was especially the case when the distances to which the images were moved were great, as to the ends of the room or to ceiling and floor. In other experiments, where, after the movements took place, the images were held for a short time, there were disappearances of one image or the other ranging from one quarter of a second to fifteen seconds, most of the absences, however, being under five seconds. The absences were more numerous in the latter half of the five minutes covered by the experiment. Occasionally a noise in the adjoining room or in the street made the images disappear.
The greater ease of vertical as compared with horizontal movements recalls an observation of Ladd,[3] in which the idioretinal light was willed into the shape of a cross. Ladd says: "The vertical bar of the cross seems much easier to produce and to hold steadily in the field." This present observation is also in accord with that described above in the case of movements of a single image.
[3] Ladd, G.T.: 'Direct Control of the Retinal Field,' PSYCH. REV., 1894, L, pp. 351-355.
On several occasions G. reported that the crossing movement was the easiest, and that the return to the original places was not easier than the other movements. In one experiment he reported the field at the center cloudy, so that it was a relief to get away from it. G.'s time records on these occasions did not support his feeling with regard to the return to the original places, but they show that the crossing movements were, in two or three instances, quicker than the 'left-and-right' movement, and the impression of promptness thus made persisted to the end of the experiment. The four movements in which both images moved uniformly were easier than the four in which movements in different directions were involved.
All the subjects were frequently conscious of eye movements, and more frequently conscious of a tendency to eye movement, which was, however, inhibited. That the strain in the eyes was practically constant during all the movements away from the original places, seems evident from the unanimous reports of a sense of relaxing and relief in the eyes, attending the movement of returning to the original places. The distance to which the images were moved was a powerful factor in producing this sense of strain. When the two images were moved and held but a few inches apart there was no sense of strain and no conscious alternation of attention. Practice increased greatly the distance at which the images could be held apart without conscious alternation of attention, but the strain of holding them apart and of inhibiting eye movement increased with the distance.
In the movements for which the time was recorded the distances varied, according to the subject, from six to eighteen inches, and varied at times with each subject. In the experiments without time record, A., B., C., E., F. and H. reported that they were able to move the images apart to ceiling and to floor, or to the opposite ends of the room, and to hold them there both in consciousness at the same time without either alternation of attention or eye movement, a tendency to which was felt but was inhibited. I. held them two feet apart without fluctuation of attention. A. reported: "I tend to turn my body to left or to right when I move the images in either of these directions." C., H. and I. said: "The eyes diverge when one image moves slowly to the right and one to the left." D. found a slight movement of the eyes which could be detected by the fingers placed lightly on the lids, when the attention was alternating between the images. K. had convergence and divergence of the eyes for crossing and separation respectively and he was accustomed to run his eye over the outline of the image. Strain in the scalp muscles was reported by A., B., E., F. and G. The up-and-down movements were universally characterized by a feeling as if one eye tended to move up and the other down. C. unconsciously inclined his head to the left in such movements as if to make the line of the two eyes parallel with the direction of the movement.
E., when holding the images two feet apart, had a strong feeling of difference of accommodation when alternating in observation and so judged the two to be in different planes.
When the movement seemed difficult the strain was greater, and when an image became dim the effort to restore its brightness or its distinctness of outline was accompanied by a feeling of bringing it nearer by accommodation and near focusing. J. found that the two images approached each other when he attempted to secure greater vividness. An analogous instance is that of A.G.C., a subject quoted in 'Mental Imagery of Students,' by French.[4] In calling up the image of a die this subject held up his hand as if it held the die. When there was no sense of strain the hand was fourteen inches from his face, but when effort was made to image all the sides of the die at once he unconsciously moved his hand to within four inches of his eyes. French says in this connection: "Situation depends on the attention involved and the inference is near that this phenomenon may be connected with feelings of convergence and accommodation which so often accompany concentrated visual attention."
[4] French, F.C.: PSYCH. REVIEW, 1902, IX., p. 40.
The movements were assisted by mentally saying, 'this image is here, that image is there,' in the case of D., G., H., I. and K.; or, at times, by articulating the names of the image, or of the color when the image was of a colored object. I. found it easy to hold outlines, but in order to retain colors in the movements of separation, he had to speak the names continually. H. also repeated the names continually, as, for example, 'violet here, orange there.'
A. represented the line of vision as going to each of the two images, which seemed connected by a line, thus making a triangle, and then pictured himself as standing off and seeing himself looking at the images. When the two objects were solid and the images were to be crossed, B. carried one image above or below the other, but when the objects were colored surfaces he conceived them as pure colors so that there was no sense of impenetrability to interfere with their crossing and they glided by each other. In the up-and-down movements he moved one at a time. C. and D. had to construct some support for the images. In most of the experiments H. first moved the images to a greater distance away, somewhat higher up and a little farther apart. In this new position the images appeared smaller and the suggested movements were made more easily. Sometimes in crossing two colored images he observed a partial mixture of the colors. J. found that a sharp movement of the head in the required direction aided materially in moving the images, and when the objects were colored surfaces fastened to the same card he found it necessary either to conceive the card as of rubber or to picture it as cut in two before he could make the movements of the images.
With A., B., C. and D. there were instances of unwilled movements of the images, in the experiments where the movements were not timed. These were much more frequent with D. than with the others, and to check them required prolonged effort. The more common movements of this sort were rotation of the image, change of its position, separation of its parts (if detachable in the object) and change of shape. E. had a return of the two images of a preceding experiment which persisted in staying a few seconds and which were as vivid as the two legitimate occupants of the mental field.
The images were duplicated five times on different days with A., and once each with C., F. and K.
A.'s cases were these. The 'wraith' of a small box whose image was out at the right, appeared above the other image off at the left and it was turned with a corner to the front. Again, at the central position each image was duplicated, the true pair being of full size, bright and distinct, the false pair small, dim and on a more distant plane, i.e., behind the others. One of the extra images persisted against all effort to banish it, for fifty-five seconds. Again, when twelve inches apart each image was similarly duplicated. In the fourth instance the images were at the center of the field. In the fifth, the right image, eight inches from the center, was duplicated, the extra image being still farther away and above. This second image was very dark, dim and vague in outline, and came and went slowly. The right image of C., when seven feet from the center, had a dim double above it. F. had moved the right-hand image (a violet disc) close to the left when a blue disc also appeared above it. Though repeating the word 'violet' he had imaged the violet disc as blue. K. was holding the two images a foot and a half apart when an extra pair appeared at the center. Both pairs persisted for sixty seconds and then the outer pair vanished, and the inner, the false pair, grew brighter.
As was said in the case of a single image, so with double images, the motion could be traced and often was traced when the movements were away from the original positions, but on the return to the original positions the images were not usually seen in transitu. For ten of the subjects, the image moved downward uniformly on an arc whose center was at the eye; and often the right and left movements were likewise on an arc. With E. the ends of the arc for motion right and left were higher also. H., I. and J. reported that all the movements were in the same plane. The upward movement was always to a less distance and the downward movement to a greater distance than the horizontal movements.
In most cases the images were the size of the percepts, in a number of cases smaller, and in a few cases larger. This was determined by comparison between the image and the percept immediately on opening the eyes and seeing the object at the end of the five minutes occupied by the experiment. A similar mode of comparison showed that, in about half of the experiments, the images were at the end of five minutes approximately equal to the percept in clearness and distinctness of outline. A comparison of these results with those obtained in a series of experiments involving passive observation of the image seems to indicate that active manipulation of the image tends to maintain the qualitative fidelity of the image when at its original position. During the progress of the experiments the reports were almost unanimous and constant that at its original position the image was vivid and distinct, but lost in both respects when away from that position, the loss being greater the greater the distance to which it was moved. Frequently there was fluctuation,--a loss of vividness and then a restoration,--which A. frequently found to be rhythmical, while in general it was evident that an increase of effort or of attention was successful in restoring lost vividness and distinctness.
D., after three minutes, read the time in the image of a watch. In superposing green on yellow, in two instances, the yellow shone through, making a mixed color, and again, in moving a green disc and a yellow disc, the green became suffused with yellow, so that the two discs were one yellow and the other greenish-yellow. For C., similarity in the two objects presented tended to make both images less vivid and distinct and to render more difficult their retention and manipulation. When one of the two objects partially overlapped the other it was difficult to separate the two images, and the area of contact was very vague in the image of the under one, and when the scrutiny reached that portion the other image returned to its original overlapping position.
IV. SUPPRESSION OF ONE OF TWO IMAGES.
The next tables (V. and VI.) give the results of experiments in suppressing one of two images, the objects presented being saturated color squares, discs, triangles, etc., placed side by side, one above the other, or a smaller one superposed on a larger. The time of perception was five seconds. After the disappearance of after-images, if there were any, the subject was directed to suppress one of the two memory images, the one to be suppressed being indicated by the director. The subject reported as soon as the indicated image disappeared, and reported any return of the suppressed image and its later disappearance in consequence of his efforts. Also he reported any disappearance and reappearance of the retained image. Five minutes was the limit of the time for the experiments with a few exceptions. The times were recorded, and those given for the first suppression include the time between the director's command and the subject's report 'now' or 'gone,' and include, therefore, two reaction times. The later suppressions include but one reaction time.
TABLE V.
SUMMARY OF ALL SUPPRESSIONS. AVERAGE TIME IN SECONDS.
[Label 1: Image Suppressed] [Label 2: No of Exper.] [Label 3: Time of First Supp.] [Label 4: Time of Ab. of Supp. Im.] [Label 5: No. of Later Supp.] [Label 6: Time of Later Supp.] [Label 7: No. of Ab. of Supp. Im.] [Label 8: Time of Ab. of Supp. Im.] [Label 9: Time of All Supp.] [Label 10: Time of All Absence of Supp. Im.]
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] Right. 46 11.59 82.39 221 8.43 216 35.74 8.94 43.93 Left. 43 11.89 79.34 175 7.79 173 44.86 8.60 51.26 Upper. 22 11.67 49.77 150 6.26 147 29.75 6.95 32.35 Lower. 17 14.23 64 71 7.88 70 46.68 9.11 50.04 Central. 42 18.24 96.93 357 3.90 352 18.13 5.41 26.54 Marginal. 20 14.25 181.57 24 8.93 24 78.08 11.35 125.12 Sundry. 7 8.71 127.21 19 13.34 19 47.27 12.09 68.78 Averages. 13.48 91.25 6.46 32.14 7.60 41.86
TABLE VI
SUPPRESSIONS GROUPED BY SUBJECTS. AVERAGE TIME IN SECONDS.
[Label 1: Subject] [Label 2: No. of Exp.] [Label 3: Time of First Supp.] [Label 4: Time of Ab. of Supp. Im.] [Label 5: No. of Later Supp.] [Label 6: Time of Later Supp.] [Label 7: No. of Ab. of Supp. Im.] [Label 8: Time of Ab. of Supp. Im.] [Label 9: Time of All Supp.] [Label 10: Time of All Ab. of Supp. Im.]
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] A. 11 28.32 11.29 117 14.90 114 10.35 16.05 10.44 B. 29 5.79 270.44 5 0.25 5 138.80 4.98 251.08 C. 18 7.88 43.08 64 3.94 63 67.49 4.81 62.07 D. 14 23.28 190.07 6 31.66 5 204.60 25.80 193.89 F. 10 12.67 86.07 230 1.95 230 67.92 2.40 10.09 G. 21 21.88 20.39 190 9.97 184 19.37 11.15 19.47 H. 21 15.27 73.27 47 10.30 47 84.48 11.84 81.02 I. 26 9.77 53.83 96 5.06 94 61.34 6.06 59.72 J. 26 3.59 32.18 209 1.40 208 31.69 1.64 31.75 K. 21 21.63 71.90 53 14.75 51 70.04 16.70 31.83 Averages. 13.48 91.25 6.46 32.14 7.60 41.86
There were ten subjects in most of the experiments, and the marked differences in the individual records which were evident in the previous experiments did not exist here except in the case of A., for whom alone the time required to obtain the suppression exceeded the time of absence of the suppressed image.
In several experiments the subjects were unable to suppress the indicated image, which in five cases was the image at the center of a disc and in two cases the outer portion of the disc. Further, five failures were by one subject, D., and one each by A. and F. The statistical report here given includes only the results of the successful experiments. Forty-four of the one hundred and ninety-seven were completely successful, as the suppressed image did not return throughout the entire period. The following table shows the grouping of the experiments according to the recurrence of the suppressed image:
Returned 0 times, 44 " 1 " 26 " 2 " 18 " 3 " 25 " 4 " 16 " 5 " 16 " 6 to 10 " 28 " more than 10 times, 24 Total, 197
Seventy-three and three fifths per cent. of all the experiments have five or fewer returns of the suppressed images.
The subjects suppressed the image as soon as possible after each return, the average time taken to accomplish these later suppressions being 6.46 sec., while the average time of absence of the suppressed image was 32.14 sec.
Including the first efforts and the first absences of the suppressed image, the average time required to suppress the image was 7.60 sec., and the average time of absence of the suppressed image was 41.86 sec.
Arranging the subjects according to the average time they required to accomplish a suppression, we have the following order. J. and F. had more recurrences of the suppressed image than any of the other subjects.
J. 1.64 sec. F. 2.40 " C. 4.80 " B. 4.98 " I. 6.06 " G. 11.15 " H. 11.84 " A. 16.05 " K. 16.70 " D. 25.80 "
Arranging them by the average absence of the suppressed image we have this order:
B. 251.08 sec D. 193.89 " H. 81.02 " C. 62.07 " I. 59.72 " K. 31.83 " J. 31.75 " G. 19.47 " A. 10.44 " F. 10.09 "
It is to be remarked, however, that the ability to keep the suppressed image out of the field increased with practice and that A. and F. had less than half the number of experiments that the rest had. D., who had but two thirds as many as most of the other subjects and therefore had less practice in suppressing the image, stands yet second in respect to this ability.
If we compare the subjects with regard to first efforts and first absences only, we obtain the following orders:
According to Ave. Time req. According to Ave. Absence for first Suppression. of Image after first Suppression. J. 3.59 sec. B. 270.44 sec. B. 5.79 " D. 190.07 " C. 7.88 " F. 86.07 " I. 9.77 " H. 73.27 " F. 12.67 " K. 71.90 " H. 15.27 " I. 53.83 " K. 21.63 " C. 43.08 " G. 21.88 " J. 32.18 " D. 23.28 " G. 20.39 " A. 28.32 " A. 11.29 "
Arranging the groups of images suppressed according to the average times of all suppressions and absences we have these orders:
Suppression. Absences. Central Images, 5.41 Marginal Images, 125.12 Upper " 6.95 Sundry " 68.78 Left " 8.60 Left " 51.26 Right " 8.94 Lower " 50.04 Lower " 9.11 Right " 43.93 Marginal " 11.35 Upper " 32.35 Sundry " 12.09 Central " 26.54
SUBJECTIVE.
Most of the subjects imaginatively placed the image to be suppressed behind the screen, in a drawer, in their closed hands, pushed it forward into the remote distance, sliced up, burned up, or pulverized and so destroyed it. B. and D. 'thought it away' directly, without mechanism or device, or got rid of it 'by a pure act of will.' Superposition was tried, frequently with success, but at times the under image shone through. When the objects were colored discs one superposed on the other, the subject spread over the whole surface the color of the image to be retained, but at times this resulted in there being two shades of the upper color, and a yellow above a red changed to an orange. When red was above yellow, the red appeared more highly illuminated. Associations with objects of the color of the retained image were found helpful but tended to modify the original color. Such associations also, at times, by secondary associations brought back the suppressed image. For example, when thinking of buttercups to enforce a yellow image, the picture of grass surrounding the flowers brought back the suppressed green image. Concentration of the attention on the image to be retained and an ignoring of the other was, on the whole, the method usually and successfully followed. This concentration was helped by imagining the image marked off into minute squares which were carefully counted. Numerous other devices of a similar character were used. Objects having many details and those lending themselves readily to suggestions of action (as a china animal) were the most helpful in enabling the subject to concentrate his attention on their image to the exclusion of another. Some subjects conceived themselves as tracing with a pencil the outline and details of the retained image. Frequently, when the two images were originally near each other and one alone was being held by close scrutiny of its parts, when this scrutiny reached the part of the image which was nearest the position of the suppressed image, the suppressed image returned. The original association between the two images was often broken up by change of the position or shape of the one to be suppressed. But devices soon became 'worn out' and new ones had to be resorted to.
Motor impulses played a large part in the process of suppression, such as head and eye movement away from the image to be suppressed, contraction of the muscles of the forehead and scalp, occasional 'setting' of the teeth, pressure together of the hands when they were supposed to be holding the image and of the knees under like circumstances. The eye traced outline and details and the more actively it could be so employed the more successful was the suppression. The sensations of accommodation and of focusing previously referred to were repeated in this series. Enunciation also was very common.
Frequent comparison of the image with the percept was made at the close of experiments and showed the utmost diversity in size, vividness and distinctness. During an experiment when the suppressed image came back, it was rarely more than a mere blur of color; in two or three instances the form came without color. Green was found to be a difficult color to hold. C. had an orange after-image from a retained yellow image, a red image having been suppressed. Between the images of a gray disc and an orange disc, three inches apart, he had a blue disc. J., while suppressing an orange disc and retaining a green disc, noticed that 'when off the fovea the whole green disc became bright orange.' There was always a sense of readiness on the part of the suppressed image to slip back. As C. expressed this, "The thing suppressed exists in the fringe of consciousness." The recurring image usually came back at its original position even when the retained image was being held in a different part of the field. In such cases the retained image at once resumed its original place.
G. and J. were successful in proportion as they freed themselves from the nervous strain of anxiety as to the result.
V. MOVEMENTS OF A SINGLE IMAGE, THE OBJECT HAVING BEEN MOVED DURING THE EXPOSURE.
In an additional series of experiments with five of the same subjects (B., G., H., I. and K.), the object was moved during the five seconds of exposure either right, left, up or down, a distance of about six to eight inches, and back again. In this way the subject was supplied with further material of a pure memory type and it was believed that some addition to our knowledge of the nature of the control of the image might thus be made by securing data contrasting the construction and the more purely reminiscent work of the imagination.
The question proposed is as follows: Does the fact that a certain movement of an object was presented to the optical perception give an advantage in time, or ease, to the mental recall of that object as so moving, over its recall as moving in other directions? The subjective experiences during such recalls may be expected to throw light upon the matter.
The subject, with closed eyes, was requested to move the mental image of the object in the four directions indicated above, returning it after each movement to its original position, and the time of each movement was recorded and, as well, the report of the subject with regard to his subjective experiences. There were sixteen hundred movements in all, eight hundred away from the original position of the image (two hundred in each of the four directions mentioned above) and eight hundred in returning to the original position.
Besides these experiments, other movements of the object during exposure were made, such as inversion, rotation, change from the vertical to the horizontal position and vice versa, rolling, oblique movements and the subjective phenomena were recorded when the subject had repeated with the image the designated movements. In all the experiments the objects were moved by the hand of the conductor of the experiment.
Table VII. gives the time record in seconds of these experiments for each subject under each of the four variations: Movement of the object to right, left, up, down.
TABLE VII.
MOVEMENTS OF A SINGLE IMAGE, THE OBJECT HAVING BEEN MOVED DURING THE TIME OF OPTICAL STIMULATION. AVERAGE TIME IN SECONDS. TEN MOVEMENTS IN EACH DIRECTION FOR EACH SUBJECT.
a. Object moved to right.
Subject R. Return L. Return Up Return Down Return Aver. B. 0.57 0.75 0.62 0.60 0.64 0.35 0.42 0.37 0.62 0.44 G. 0.55 0.60 0.55 0.57 0.57 0.27 0.25 0.27 0.25 0.26 H. 6.95 6.90 6.47 6.40 6.65 5.40 5.55 4.50 5.00 5.11 I. 2.05 2.10 2.05 2.22 2.10 1.15 1.35 1.32 1.57 1.35 K. 2.35 2.97 2.42 2.62 2.59 1.17 1.20 1.17 1.55 1.28 Ave. 2.49 2.66 2.02 2.48 2.52 1.67 1.75 1.53 1.80 1.69
Ave. to right, 2.49 Ave. of other movements, 2.52 Grand average, 2.10
b. Object moved to left. B. 0.72 0.60 0.62 0.60 0.64 0.52 0.40 0.52 0.42 0.47 G. 0.67 0.45 0.55 0.67 0.59 0.42 0.35 0.35 0.37 0.37 H. 8.22 5.95 6.52 6.42 6.78 5.82 4.10 4.37 5.55 4.96 I. 2.40 1.30 2.25 2.72 2.17 1.97 1.22 0.95 1.47 1.40 K. 2.45 2.57 2.25 2.00 2.30 1.70 1.60 1.32 1.35 1.49 Ave. 2.89 2.17 2.44 2.48 2.50 2.09 1.53 1.50 1.83 1.74
Ave. to left, 2.17 Ave. of other movements, 2.60 Grand average, 2.12
c. Object moved up. B. 0.75 0.62 0.42 0.57 0.59 0.32 0.50 0.42 0.37 0.40 G. 0.65 0.57 0.45 0.47 0.54 0.35 0.27 0.25 0.27 0.29 H. 6.77 6.25 6.85 6.15 6.57 5.27 5.55 5.30 5.30 5.35 I. 2.47 2.27 1.85 2.65 2.31 1.25 1.00 0.87 1.10 1.05 K. 3.40 2.72 1.42 2.20 2.44 1.50 1.37 1.27 1.17 1.33 Ave. 2.81 2.49 2.20 2.41 2.48 1.74 1.74 1.62 1.70 1.69
Ave. up, 2.20 Ave. of other movements, 2.57 Grand average, 2.08
d. Object moved down. B. 0.80 0.72 0.70 0.57 0.70 0.42 0.42 0.50 0.42 0.44 G. 0.60 0.60 0.55 0.47 0.55 0.25 0.25 0.27 0.27 0.26 H. 6.77 6.80 6.80 8.77 7.29 5.90 6.35 4.55 5.55 5.59 I. 2.30 2.20 2.22 1.80 2.13 1.30 1.20 1.15 1.42 1.27 K. 3.15 2.75 2.95 2.30 2.79 1.62 1.57 1.12 1.25 1.39 Ave. 2.72 2.61 2.64 2.78 2.69 1.90 1.92 1.52 1.78 1.79
Ave. down, 2.78 Ave. of other movements, 2.66 Grand average, 2.24
NUMERICAL.
As each movement may be compared with three other movements, and as there were five subjects and four variations in the conditions, there are sixty opportunities of comparing the time required to move the image in the direction in which the object was moved with the time taken to move it in the other directions. In 45 instances the time was less, in 3 the same, and in 12 greater.
These twelve instances occurred with two subjects, three (to left) occurring with K. and nine (three each right, up, down) occurring with H. The cause was the same in all twelve instances, both H. and K. reporting that (in these cases) they had great difficulty in obtaining a reasonably vivid and distinct image when directed to move the image in the direction in which the object had been moved. The attempt to move the image resulted in a vague image spread continuously over the entire area that had been covered by the moving object, and the effort to obtain the image at the desired position only was serious and took an appreciably longer time than usual. It is to be noted, also, that the time usually taken by H. is uniformly very much greater than the time taken by the other subjects. Yet, even with these instances included, the average time of all movements of the image in the direction in which the object had been moved is less than the average time of the other movements, the former being 2.41 seconds, the latter, 2.59 seconds.
TABLE VIII.
MOVEMENTS OF A SINGLE IMAGE.
I., OBJECT PREVIOUSLY MOVED; II., OBJECT NOT MOVED.
Average Time Given in Seconds.
Subjects: B. G. H. I II I II I II To right, 0.57 1.30 0.55 1.46 6.95 7.15 Return, 0.35 0.58 0.27 0.92 5.40 4.51 To left, 0.60 1.06 0.45 1.15 5.95 6.42 Return, 0.40 0.73 0.35 0.89 4.10 4.41 Up, 0.42 1.05 0.45 0.99 6.85 5.96 Return, 0.42 0.46 0.25 0.76 5.30 4.36 Down, 0.57 1.10 0.47 0.82 8.77 5.85 Return, 0.42 0.45 0.27 0.06 5.55 4.40 General 0.54 1.13 0.48 1.10 7.13 6.34 Averages, 0.40 0.55 0.28 0.66 5.09 4.42
Subjects: I. K. I II I II To right, 2.05 1.28 2.35 4.80 Return, 1.15 0.67 1.17 2.40 To left, 1.30 1.34 2.57 4.63 Retur, 1.22 0.62 1.60 2.73 Up, 1.85 1.62 1.42 3.29 Return, 0.87 0.86 1.27 1.90 Down, 1.80 1.36 2.30 3.27 Return, 1.42 0.72 1.25 1.56 General 1.75 1.40 2.16 4.00 Averages, 1.16 0.72 1.32 2.15
If the record of H. is omitted from Table VII., _a, c, _and d, and that of K. from VII., b (as these are the records of the twelve exceptions), the former average becomes 1.44 seconds, the latter 1.86 seconds.
The following table affords the means of comparing the time taken in moving the image in the direction in which the object had been moved with the time taken in moving the image in the same direction when there had been no movement of the object. The averages are obtained from the records of Tables VII. and I.
We have here twenty comparisons each of movements away from the original positions and movements back to the original positions:
In the first case, 15 took less time under I., 5 took more time under I.
The 5 cases of more time occurred with two subjects (H., 3 and I., 2).
In the second case, 12 took less time under I., 8 took more time under I.
The 8 cases of more time occurred with three subjects (G., 1; H., 3; I., 4).
If we omit H.'s record and take the general averages for each subject, we find the following advantages in time in form of movements where the object had been moved;
B., 0.59 seconds. G., 0.52 " K., 1.84 "
But I., 0.35 seconds in favor of movements when the object had not been moved.
Combining these results, we have 0.74 sec. as the average gain in time for these four subjects.
SUBJECTIVE.
With one exception (G.), the subjects found Movements I., movements in the direction in which the object had been moved, easier than Movements II. In Movements II. the eye seemed to construct and compel the motion, which was not the case with Movements I., in which the eye followed the motion. The distance to which the image went in Movements I. seemed predetermined, and these movements seemed exact copies of the original movement of the object, being purely reminiscent and reproducing its irregularities when there were any. Also, the image was usually seen in transitu both out and back, which was never the case with Movements II. Eye movement and enunciation were much less frequent and the image was more vivid and distinct in Movements I.
* * * * *
STUDIES IN ÆSTHETIC PROCESSES.
* * * * *
Transcriber's Note:
Rhythmic measures in the first 2 articles of this section are transcribed as follows:
| delineates measure q quarter note q. dotted quarter note e eighth note % quarter rest
Major accent of the measure is indicated by a >, either above or in front of the beat. Minor accent of the measure is indicated by ., used in the same way.
> . | q q q q | or | >q q .q q | represent the same rhythmic pattern.
* * * * *
THE STRUCTURE OF SIMPLE RHYTHM FORMS.
BY ROBERT MACDOUGALL.
I. PROBLEMS AND METHODS OF EXPERIMENTATION.
The investigation of the problems presented by the psychological phenomena of rhythm has of late years occupied much attention and been pushed in a variety of different directions. Some researches have been concerned with an analysis of rhythm as an immediate subjective experience, involving factors of perception, reaction, memory, feeling, and the like; others have had to do with the specific objective conditions under which this experience arises, and the effect of changes in the relations of these factors; still others have sought to coördinate the rhythm experience with more general laws of activity in the organism, as the condition of most effective action, and to affiliate its complex phenomena upon simpler laws of physiological activity and repose; while a fourth group has undertaken a description of that historical process which has resulted in the establishment of artistic rhythm-types, and has sought to formulate the laws of their construction.[1]
[1] Description: (1) Of the psychological factors of the rhythm experience: Angell and Pierce, Ettlinger, Hauptmann, Mentz, Meumann, Stumpf, Wundt, et al. (2) Of its objective conditions and products: Binet et Courtier, Bolton, Ebhardt, Hurst and McKay, Meumann, Schumann, Sievers, et al. (3) Of its physiological accompaniments: Bolton, Brücke, Dogiel, Hausegger, Mach, Mentz, Ribot, Sherrington, Scripture, Smith, et al. (4) Of its historical evolution: Bücher, Moritz, Scherer, et al.
This differentiation has already made such progress as to constitute the general topic a field within which specialization is called for, instead of an attempt to treat the phenomenon as a whole. It is the purpose of this paper to describe a set of experiments having to do with the second of these problems, the constitution of objective rhythm forms. In the determination of such forms it is, of course, impossible to avoid the employment of terms descriptive of the immediate experience of rhythm as a psychological process, or to overlook the constant connection which exists between the two groups of facts. The rhythm form is not objectively definable as a stable type of stimulation existing in and for itself; the discrimination of true and false relations among its elements depends on the immediate report of the consciousness in which it appears. The artistic form is such only in virtue of its arousing in the observer that peculiar quality of feeling expressed in calling the series of sensory stimuli rhythmically pleasing, or equivalent, or perfect. In no other way than as thus dependent on the appeal which their impression makes to the æsthetic consciousness can we conceive of the development and establishment of fixed forms of combination and sequence among those types of sensory stimulation which arouse in us the pleasurable experience of rhythm. The artistic rhythm form cannot be defined as constituted of periods which are 'chronometrically proportionate,' or mathematically simple. It is not such in virtue of any physical relations which may obtain among its constituents, though it may be dependent on such conditions in consequence of the subordination to physical laws of the organic activities of the human individual. The view must be subjectively objective throughout.
The need for simplicity and exactness has led to the very general employment of material as barely sensorial as could be devised for the carrying on of experiments upon rhythm. Rich tones and complex combinations of them are to be avoided, for these qualities are themselves immediate sources of pleasure, and the introduction of them into the material of experimentation inevitably confuses the analysis which the observer is called upon to make of his experience and of the sources of his pleasure in it. Still more objectionable than the presence of such complex musical tones in an investigation of rhythm is the introduction of the symbols of rational speech in concrete poetical forms. This element can be only a hindrance to the perception of pure rhythmical relations, in virtue of the immediate interest which the images called up by the verbal signs possess, and further, in view of the fact that the connections of significant thought impose upon the purely rhythmical formulation of the series of stimulations an unrelated and antagonistic principle of grouping, namely, the logical relations which the various members of the series bear to one another.
The demand for a simplification of the material which supports the rhythm experience, for the purpose of obtaining a more exact control over the conditions of experimentation, has been met by the invention of a variety of devices whereby the sequences of music, song and poetical speech have been replaced by elementary conventional symbols as the vehicle of the rhythmical impression or expression. On the one side there has commonly been substituted for musical tones and rhythmical speech the most simple, sharply limited and controllable sounds possible, namely, those due to the action of a telephone receiver, to the vibrations of a tuning-fork placed before the aperture of a resonator, or to the strokes of metallic hammers falling on their anvils. On the other side, the form of the reproduced rhythm has been clarified by the substitution of the finger for the voice in a series of simple motor reactions beaten out on a more or less resonant medium; by the use--when the voice is employed--of conventional verbal symbols instead of the elements of significant speech; and--where actual verse has been spoken--by a treatment of the words in formal staccato scansion, or by the beating of time throughout the utterance. The last of these methods is a halting between two courses which casts doubt on the results as characteristic of either type of activity. There is no question that the rhythmic forms of recitative poetry differ vastly from those of instrumental music and chanted speech. The measures of spoken verse are elastic and full of changefulness, while those of music and the chant maintain a very decided constancy of relations. The latter present determinable types of grouping and succession, while it is questionable whether the forms of relationship in spoken verse can ever be considered apart from the emotion of the moment. In so far as the rhythmic form which these differing modes of expression embody are to be made the subject of experimental investigation their characteristic structures should be kept intact as objects of analysis in independent experiments, instead of being combined (and modified) in a single process.
The apparatus employed in the course of the present investigation consisted of four different pieces of mechanism, one affording the vehicle of expression throughout the series of reproduced rhythms, the others providing the auditory material of the various rhythms apperceived but not designedly reproduced. The first of these consisted of a shallow Marey tambour, placed horizontally upon a table with its rubber film upwards, and connected by means of rubber-tubing with a pneumographic pen in contact with the revolving drum of a kymograph. A Deprez electric marker, aligned with the pneumographic stylus, afforded a time record in quarter seconds. Upon this tambour, placed within comfortable reach of the reactor's hand, the various rhythm types were beaten out. The impact of the finger-tip on the tense surface of the drum gave forth a faint and pleasing but at the same time clearly discernible and distinctly limited sound, which responded with audible variations of intensity to the differing stresses involved in the process of tapping, and which I have considered preferable to the short, sharp stroke of the Kraepelin mouth-key employed by Ebhardt. The rate of revolution in the drum was so adjusted to the normal range of excursion in the pneumographic pen as to give sharp definition to every change of direction in the curve, which hence allowed of exact measurements of temporal and intensive phases in the successive rhythm groups. These measurements were made to limits of 1.0 mm. in the latter direction and of 0.5 mm. in the former.[2]
[2] Professor Binet's doubt (L'Année Psychologique 1895, p. 204) that the propulsion of air from the elastic chamber and the rebound of the pen might interfere with the significance of the graphic record is more serious in connection with the application of this method to piano playing than here; since its imperfection, as that writer says, was due to the force and extreme rapidity of the reactions in the former case. The present series involved only light tapping and was carried on at a much slower average rate.
The second piece of apparatus consisted of an ordinary metronome adjusted to beat at rates of 60, 90, and 120 strokes per minute. This instrument was used in a set of preliminary experiments designed to test the capacity of the various subjects for keeping time by finger reaction with a regular series of auditory stimulations.
The third piece of apparatus consisted of an arrangement for producing a series of sounds and silences, variable at will in absolute rate, in duration, and, within restricted limits, in intensity, by the interruptions of an electrical current, into the circuit of which had been introduced a telephone receiver and a rheostat. Portions of the periphery of a thin metallic disc were cut away so as to leave at accurately spaced intervals, larger or smaller extents of the original boundary. This toothed wheel was then mounted on the driving-shaft of an Elbs gravity motor and set in motion. Electrical connections and interruptions were made by contact with the edge of a platinum slip placed at an inclination to the disc's tangent, and so as to bear lightly on the passing teeth or surfaces. The changes in form of a mercury globule, consequent on the adhesion of the liquid to the passing teeth, made it impossible to use the latter medium. The absolute rate of succession in the series of sounds was controlled by varying the magnitudes of the driving weights and the resistance of the governing fans of the motor. As the relation of sounds and intervals for any disc was unalterable, a number of such wheels were prepared corresponding to the various numerical groups and temporal sequences examined--one, for example, having the relations expressed in the musical symbol 3/4 | >q e |*; another having that represented in the symbol 4/4 | >q e e |;* and so on. Variations in intensity were obtained by mounting a second series of contacts on the same shaft and in alignment with those already described. The number of these secondary contacts was less than that of the primary connections, their teeth corresponding to every second or third of those. The connections made by these contacts were with a second loop, which also contained within its circuit the telephone receiver by which the sounds were produced. The rheostatic resistances introduced into this second circuit were made to depart more or less from that of the first, according as it was desired to introduce a greater or slighter periodic accent into the series. This mechanism was designed for the purpose of determining the characteristic sequences of long and short elements in the rhythm group.
*Transcriber's Note:
The original article showed "3/4 | q q q |" and "4/4 | q q q q |". Applying the erratum after the article (below) resulted in fewer beats per measure than indicated by the time signature. Other possibilities are "3/4 | >q e q. |" and "4/4 | >q e e q q |".
"ERRATUM:
On page 313, line 23, the musical symbols should be a quarter note, accented, followed by an eighth note; in the following line the symbols should be a quarter note, accented, followed by two eighth notes."
The fourth piece of apparatus consisted essentially of a horizontal steel shaft having rigidly attached to it a series of metallic anvils, fifteen in number, on which, as the shaft revolved, the members of a group of steel hammers could be made to fall in succession from the same or different heights. The various parts of the mechanism and their connections may be readily understood by reference to the illustration in Plate VIII. On the right, supported upon two metal standards and resting in doubly pivoted bearings, appears the anvil-bearing shaft. On a series of shallow grooves cut into this shaft are mounted loose brass collars, two of which are visible on the hither end of the shaft. The anvils, the parts and attachments of which are shown in the smaller objects lying on the table at the base of the apparatus, consist of a cylinder of steel partly immersed in a shallow brass cup and made fast to it by means of a thumb-screw. This cup carries a threaded bolt, by which it may be attached to the main shaft at any position on its circumference by screwing through a hole drilled in the collar. The adjustment of the anvils about the shaft may be changed in a moment by the simple movement of loosening and tightening the thumb-screw constituted by the anvil and its bolt. The device by which the extent of the hammer-fall is controlled consists of cam-shaped sheets of thin wood mounted within parallel grooves on opposite sides of the loose collars and clamped to the anvils by the resistance of two wedge-shaped flanges of metal carried on the anvil bolt and acting against the sides of slots cut into the sheets of wood at opposite sides. The periphery of these sheets of wood--as exhibited by that one lying beside the loose anvils on the table--is in the form of a spiral which unfolds in every case from a point on the uniform level of the anvils, and which, by variations in the grade of ascent, rises in the course of a revolution about its center to the different altitudes required for the fall of the hammers. These heights were scaled in inches and fractions, and the series employed in these experiments was as follows: 1/8, 2/8, 3/8, 5/8, 7/8, 15/8, 24/8 inch. Upon a corresponding pair of standards, seen at the left of the illustration, is mounted a slender steel shaft bearing a series of sections of brass tubing, on which, in rigid sockets, are carried the shafts of a set of hammers corresponding in number and position to the anvils of the main axis. By means of a second shaft borne upon two connected arms and pivoted at the summit of the standards the whole group of hammers may at any moment be raised from contact with the cams of the main shaft and the series of sounds be brought to a close without interrupting the action of the motor or of the remainder of the apparatus. By this means phases of acceleration and retardation in the series, due to initial increase in velocity and its final decrease as the movement ceases, are avoided. The pairs of vertical guides which appear on this gearing-shaft and enclose the handles of the several hammers are designed to prevent injury to the insertions of the hammer shafts in their sockets in case of accidental dislocations of the heads in arranging the apparatus. This mechanism was driven by an electrical motor with an interposed reducing gear.
The intervals between the successive hammer-strokes are controlled in the following way: on the inner face of the group of pulleys mounted on the main shaft of the mechanism (this gang of pulleys appears at the extreme right in the illustration) is made fast a protractor scaled in half degrees. Upon the frame of the standard supporting these pulleys is rigidly screwed an index of metal which passes continuously over the face of the scale as the shaft revolves. The points of attachment (about the shaft) of the cams are determined by bringing the point of fall of each cam in succession into alignment with this fixed index, after the shaft has been turned through the desired arc of its revolution and made fast by means of the thumb-screw seen in the illustration at the near end of the shaft. Thus, if three strokes of uniform intensity are to be given at equal intervals apart and in continuous succession, the points of fall of the hammers will be adjusted at equal angular distances from one another, for example, at 360°, 240°, and 120°; if the temporal relations desired be in the ratios 2:1:1, the arrangement will be 360°, 180°, 90°; if in the ratios 5:4:3, it will be 360°, 210°, 90°; and so on. If double this number of hammers be used in a continuous series the angular distances between the points of fall of the successive hammers will of course be one half of those given above, and if nine, twelve, or fifteen hammers be used they will be proportionately less.
An interruption of any desired relative length may be introduced between repetitions of the series by restricting the distribution of angular distances among the cams to the requisite fraction of the whole revolution. Thus, if an interruption equal to the duration included between the first and last hammer-falls of the series be desired, the indices of position in the three cases described above will become: 360°, 270°, 180°; 360°, 240°, 180°, and 360°, 260°, 180°. In the case of series in which the heights of fall of the various hammers are not uniform, a special adjustment must be superimposed upon the method of distribution just described. The fall of the hammer occupies an appreciable time, the duration of which varies with the distance through which the hammer passes. The result, therefore, of an adjustment of the cams on the basis adopted when the height of fall is uniform for all would appear in a reduction of the interval following the sound produced by a hammer falling from a greater height than the rest, and the amount of this shortening would increase with every addition to the distance through which the hammer must pass in its fall. In these experiments such lags were corrected by determining empirically the angular magnitude of the variation from its calculated position necessary, in the case of each higher member of the series of distances, to make the stroke of the hammer on its anvil simultaneous with that of the shortest fall. These fixed amounts were then added to the indices of position of the several cams in each arrangement of intervals employed in the experiments.
This apparatus answers a variety of needs in practical manipulation very satisfactorily. Changes in adjustment are easily and quickly made, in regard to intensity, interval and absolute rate. If desired, the gradation of intensities here employed may be refined to the threshold of perceptibility, or beyond it.
The possible variations of absolute rate and of relative intervals within the series were vastly more numerous than the practical conditions of experimentation called for. In two directions the adaptability of the mechanism was found to be restricted. The durations of the sounds could not be varied as were the intervals between them, and all questions concerning the results of such changes were therefore put aside; and, secondly, the hammers and anvils, though fashioned from the same stuff and turned to identical shapes and weights, could not be made to ring qualitatively alike; and these differences, though slight, were sufficiently great to become the basis of discrimination between successive sounds and of the recognition upon their recurrence of particular hammer-strokes, thereby constituting new points of unification for the series of sounds. When the objective differences of intensity were marked, these minor qualitative variations were unregarded; but when the stresses introduced were weak, as in a series composed of 3/8-, 2/8-, 2/8-inch hammer-falls, they became sufficiently great to confuse or transform the apparent grouping of the rhythmical series; for a qualitative difference between two sounds, though imperceptible when comparison is made after a single occurrence of each, may readily become the subconscious basis for a unification of the pair into a rhythmical group when several repetitions of them take place.
In such an investigation as this the qualification of the subject-observer should be an important consideration. The susceptibility to pleasurable and painful affection by rhythmical and arrhythmical relations among successive sensory stimuli varies within wide limits from individual to individual. It is of equal importance to know how far consonance exists between the experiences of a variety of individuals. If the objective conditions of the rhythm experience differ significantly from person to person it is useless to seek for rhythm forms, or to speak of the laws of rhythmical sequence. Consensus of opinion among a variety of participators is the only foundation upon which one can base the determination of objective forms of any practical value. It is as necessary to have many subjects as to have good ones. In the investigation here reported on, work extended over the two academic years of 1898-1900. Fourteen persons in all took part, whose ages ranged from twenty-three to thirty-nine years. Of these, five were musically trained, four of whom were also possessed of good rhythmic perception; of the remaining nine, seven were good or fair subjects, two rather poor. All of these had had previous training in experimental science and nine were experienced subjects in psychological work.
II. THE ELEMENTARY CONDITIONS OF THE APPEARANCE OF THE RHYTHM IMPRESSION.
The objective conditions necessary to the arousal of an impression of rhythm are three in number: (a) Recurrence; (b) Accentuation; (c) Rate.
(a) Recurrence.--The element of repetition is essential; the impression of rhythm never arises from the presentation of a single rhythmical unit, however proportioned or perfect. It does appear adequately and at once with the first recurrence of that unit. If the rhythm be a complex one, involving the coördination of primary groups in larger unities, the full apprehension of its form will, of course, arise only when the largest synthetic group which it contains has been completed; but an impression of rhythm, though not of the form finally involved, will have appeared with the first repetition of the simplest rhythmical unit which enters into the composition. It is conceivable that the presentation of a single, unrepeated rhythmical unit, especially if well-defined and familiar, should originate a rhythmical impression; but in such a case the sensory material which supports the impression of rhythm is not contained in the objective series but only suggested by it. The familiar group of sounds initiates a rhythmic process which depends for its existence on the continued repetition, in the form of some subjective accentuation, of the unit originally presented.
The rhythmical form, in all such cases, is adequately and perfectly apprehended through a single expression of the sequence.[3] It lacks nothing for its completion; repetition can add no more to it, and is, indeed, in strict terms, inconceivable; for by its very recurrence it is differentiated from the initial presentation, and combines organically with the latter to produce a more highly synthetic form. And however often this process be repeated, each repetition of the original sequence will have become an element functionally unique and locally unalterable in the last and highest synthesis which the whole series presents.
[3] When the formal key-note is distinctly given, the rhythmical movement arises at once; when it is obscure, the emergence of the movement is gradual. This is a salient difference, as Bolton, Ettlinger and others have pointed out, between subjective rhythms and those objectively supported.
Rhythmical forms are not in themselves rhythms; they must initiate the factor of movement in order that the impression of rhythm shall arise. Rhythmical forms are constantly occurring in our perceptional experience. Wherever a group of homogeneous elements, so related as to exhibit intensive subordination, is presented under certain temporal conditions, potential rhythm forms appear. It is a mere accident whether they are or are not apprehended as actual rhythm forms. If the sequence be repeated--though but once--during the continuance of a single attention attitude, its rhythmical quality will ordinarily be perceived, the rhythmic movement will be started. If the sequence be not thus repeated, the presentation is unlikely to arouse the process and initiate the experience of rhythm, but it is quite capable of so doing. The form of the rhythm is thus wholly independent of the movement, on which the actual impression of rhythm in every case depends; and it may be presented apart from any experience of rhythm.
There is properly no repetition of identical sequences in rhythm. Practically no rhythm to which the æsthetic subject gives expression, or which he apprehends in a series of stimulations, is constituted of the unvaried repetition of a single elementary form, the measures, | >q. q |, or | >q. q q |, for example. Variation, subordination, synthesis, are present in every rhythmical sequence. The regular succession is interrupted by variant groups; points of initiation in the form of redundant syllables, points of finality in the form of syncopated measures, are introduced periodically, making the rhythm form a complex one, the full set of relations involved being represented only by the complete succession of elements contained between any one such point of initiation and its return.
(b) Accentuation.--The second condition for the appearance of the rhythm impression is the periodic accentuation of certain elements in the series of sensory impressions or motor reactions of which that rhythm is composed. The mechanism of such accentuation is indifferent; any type of variation in the accented elements from the rest of the series which induces the characteristic process of rhythmic accentuation--by subjective emphasis, recurrent waves of attention, or what not--suffices to produce an impression of rhythm. It is commonly said that only intensive variations are necessary; but such types of differentiation are not invariably depended on for the production of the rhythmic impression. Indeed, though most frequently the basis of such effects, for sufficient reasons, this type of variation is neither more nor less constant and essential than other forms of departure from the line of indifference, which forms are ordinarily said to be variable and inessential. For the existence of rhythm depends, not on any particular type of periodical variation in the sensory series, but on the recurrent accentuation, under special temporal conditions, of periodic elements within such a series; and any recurrent change in quality--using this term to describe the total group of attributes which constitutes the sensorial character of the elements involved--which suffices to make the element in which it occurs the recipient of such accentuation, will serve as a basis for the production of a rhythmical impression. It is the fact of periodical differentiation, not its particular direction, which is important. Further, as we know, when such types of variation are wholly absent from the series, certain elements may receive periodical accentuation in dependence on phases of the attention process itself, and a subjective but perfectly real and adequate rhythm arise.
In this sense those who interpret rhythm as fundamentally dependent on the maintenance of certain temporal relations are correct. The accentuation must be rhythmically renewed, but the sensory incentives to such renewals are absolutely indifferent, and any given one of the several varieties of change ordinarily incorporated into rhythm may be absent from the series without affecting its perfection as a rhythmical sequence. In piano playing the accentual points of a passage may be given by notes struck in the bass register while unaccented elements are supplied from the upper octaves; in orchestral compositions a like opposition of heavy to light brasses, of cello to violin, of cymbals to triangle, is employed to produce rhythmical effects, the change being one in timbre, combined or uncombined with pitch variations; and in all percussive instruments, such as the drum and cymbals, the rhythmic impression depends solely on intensive variations. The peculiar rhythmic function does not lie in these elements, but in a process to which any one of them indifferently may give rise. When that process is aroused, or that effect produced, the rhythmic impression has been made, no matter what the mechanism may have been.
The single objective condition, then, which is necessary to the appearance of an impression of rhythm is the maintenance of specific temporal relations among the elements of the series of sensations which supports it. It is true that the subjective experience of rhythm involves always two factors, periodicity and accentuation; the latter, however, is very readily, and under certain conditions inevitably, supplied by the apperceptive subject if the former be given, while if the temporal conditions be not fulfilled (and the subject cannot create them) no impression of rhythm is possible. The contributed accent is always a temporally rhythmical one, and if the recurrence of the elements of the objective series opposes the phases of subjective accentuation the rhythm absolutely falls to the ground. Of the two points of view, then, that is the more faithful to the facts which asserts that rhythm is dependent upon the maintenance of fixed temporal intervals. These two elements cannot be discriminated as forming the objective and subjective conditions of rhythm respectively. Both are involved in the subjective experience and both find their realization in objective expressions, definable and measurable.
(c) Rate.--The appearance of the impression of rhythm is intimately dependent on special conditions of duration in the intervals separating the successive elements of the series. There appears in this connection a definite superior limit to the absolute rate at which the elements may succeed one another, beyond which the rapidity cannot be increased without either (a) destroying altogether the perception of rhythm in the series or (b) transforming the structure of the rhythmical sequence by the substitution of composite groups for the single elements of the original series as units of rhythmic construction; and a less clearly marked inferior limit, below which the series of stimulations fails wholly to arouse the impression of rhythm. But the limits imposed by these conditions, again, are coördinated with certain other variables. The values of the thresholds are dependent, in the first place, on the presence or absence of objective accentuation. If such accents be present in the series, the position of the limits is still a function of the intensive preponderance of the accented over the unaccented elements of the group. Further, it is related to the active or passive attitude of the æsthetic subject on whom the rhythmical impression is made, and there appear also important individual variations in the values of the limits.
When the succession falls below a certain rate no impression of rhythm arises. The successive elements appear isolated; each is apprehended as a single impression, and the perception of intensive and temporal relations is gotten by the ordinary process of discrimination involved when any past experience is compared with a present one. In the apprehension of rhythm the case is altogether different. There is no such comparison of a present with a past experience; the whole group of elements constituting the rhythmic unit is present to consciousness as a single experience; the first of its elements has never fallen out of consciousness before the final member appears, and the awareness of intensive differences and temporal segregation is as immediate a fact of sensory apprehension as is the perception of the musical qualities of the sounds themselves.
The absolute value of this lower limit varies from individual to individual. In the experience of some persons the successive members of the series may be separated by intervals as great as one and one half (possibly two) seconds, while yet the impression is distinctly one of rhythm; in that of others the rhythm dies out before half of that interval has been reached. With these subjects the apprehension at this stage is a secondary one, the elements of the successive groups being held together by means of some conventional symbolism, as the imagery of beating bells or swinging pendulums. A certain voluminousness is indispensable to the support of such slow measures. The limit is reached sooner when the series of sounds is given by the fall of hammers on their anvils than when a resonant body like a bell is struck, or a continuous sound is produced upon a pipe or a reed.
In these cases, also, the limit is not sharply defined. The rhythmical impression gradually dies out, and the point at which it disappears may be shifted up or down the line, according as the æsthetic subject is more or less attentive, more or less in the mood to enjoy or create rhythm, more passive or more active in his attitude toward the series of stimulations which supports the rhythmical impression. The attention of the subject counts for much, and this distinction--of involuntary from voluntary rhythmization--which has been made chiefly in connection with the phenomenon of subjective rhythm, runs also through all appreciation of rhythms which depend on actual objective factors. A series of sounds given with such slowness that at one time, when passively heard, it fails to produce any impression of rhythm, may very well support the experience on another occasion, if the subject try to hold a specific rhythm form in mind and to find it in the series of sounds. In such cases attention creates the rhythm which without it would fail to appear. But we must not confuse the nature of this fact and imagine that the perception that the relations of a certain succession fulfil the the form of a rhythmical sequence has created the rhythmical impression for the apperceiving mind. It has done nothing of the kind. In the case referred to the rhythm appears because the rhythmical impression is produced, not because the fact of rhythmical form in the succession is perceived. The capacity of the will is strictly limited in this regard and the observer is as really subject to time conditions in his effortful construction as in his effortless apprehension. The rhythmically constructive attitude does not destroy the existence of limits to the rate at which the series must take place, but only displaces their positions.
A similar displacement occurs if the periodic accentuations within the series be increased or decreased in intensity. The impression of rhythm from a strongly accented series persists longer, as retardation of its rate proceeds, than does that of a weakly accented series; the rhythm of a weakly accented series, longer than that of a uniform succession. The sensation, in the case of a greater intensive accent, is not only stronger but also more persistent than in that of a weaker, so that the members of a series of loud sounds succeeding one another at any given rate appear to follow in more rapid succession than when the sounds are faint. But the threshold at which the intervals between successive sounds become too great to arouse any impression of rhythm does not depend solely on the absolute loudness of the sounds involved; it is a function also of the degree of accentuation which the successive measures possess. The greater the accentuation the more extended is the temporal series which will hold together as a single rhythmic group.
This relation appears also in the changes presented in beaten rhythms, the unit-groups of which undergo a progressive increase in the number of their components. The temporal values of these groups do not remain constant, but manifest a slight increase in total duration as the number of component beats is increased, though this increase is but a fraction of the proportional time-value of the added beats. Parallel with this increase in the time-value of the unit-group goes an increase in the preponderance of the accented element over the intensity of the other members of the group. Just as, therefore, in rhythms that are heard, the greatest temporal values of the simple group are mediated by accents of the highest intensity, so in expressed rhythms those groups having the greatest time-values are marked by the strongest accentuation.
Above the superior limit a rhythm impression may persist, but neither by an increase in the number of elements which the unit group contains, nor by an increase in the rate at which these units follow one another in consciousness. The nature of the unit itself is transformed, and a totally new adjustment is made to the material of apprehension. When the number of impressions exceeds eight or ten a second--subject to individual variations--the rhythmical consciousness is unable longer to follow the individual beats, a period of confusion ensues, until, as the rate continues to increase, the situation is suddenly clarified by the appearance of a new rhythm superimposed on the old, having as its elements the structural units of the preceding rhythm. The rate at which the elements of this new rhythm succeed one another, instead of being more rapid than the old, has become relatively slow, and simple groups replace the previous large and complex ones. Thus, at twelve beats per second the rhythms heard by the subjects in these experiments were of either two, three or four beats, the elements entering into each of these constituent beats being severally three and four in number, as follows:
TABLE I.
> > Simple Trochaic, four beats per second: 1 2 3, 4 5 6; 7 8 9,10 11 12. \___/ \___/ \___/ \______/ > ________ ___________ / \ / \ Dipodic Trochaic, " " " " 1 2 3, 4 5 6; 7 8 9,10 11 12. \__/ \__/ \___/ \________/ >>> Simple Dactylic, three " " " 1 2 3 4, 5 6 7 8, 9 10 11 12. \____/ \____/ \_______/
The only impression of rhythm here received was of a trochaic or dactylic measure, depending upon an accent which characterized a group and not a single beat, and which recurred only twice or thrice a second. Sometimes the subjects were wholly unaware that the elements of the rhythm were not simple, a most significant fact, and frequently the number reported present was one half of the actual number given. During the continuance of such a series the rhythm form changes frequently in the apprehension of the individual subject from one to another of the types described above.
It cannot be too strongly insisted on that the perception of rhythm is an impression, an immediate affection of consciousness depending on a particular kind of sensory experience; it is never a construction, a reflective perception that certain relations of intensity, duration, or what not, do obtain. If the perception of rhythm in a series of impressions were dependent on intellectual analysis and discrimination, the existence of such temporal limits as are actually found would be inconceivable and absurd. So long as the perception of the uniformity or proportion of time-relations were possible, together with the discrimination of the regular recurrence in the series of points of accentuation, the perception of rhythm should persist, however great or small might be the absolute intervals which separated the successive members of the series. If it were the conception of a certain form of relation, instead of the reception of a particular impression, which was involved, we should realize a rhythm which extended over hours or days, or which was comprehended in the fraction of a second, as readily as those which actually affect us.
The rate at which the elements of a series succeed one another affects the constitution of the unit groups of which the rhythmical sequence is composed. The faster the rate, the larger is the number of impressions which enter into each group. The first to appear in subjective rhythm, as the rate is increased from a speed too slow for any impression of rhythm to arise, are invariably groups of two beats; then come three-beat groups, or a synthesis of the two-beat groups into four, with major and minor accents; and finally six-and eight-beat groups appear. When objective accentuation is present a similar series of changes is manifested, the process here depending on a composition of the unit-groups into higher orders, and not involving the serial addition of new elements to the group.
The time relations of such smaller and larger units are dependent on the relative inertia of the mechanism involved. A definite subjective rhythm period undoubtedly appears; but its constancy is not maintained absolutely, either in the process of subjective rhythmization or in the reproduction of ideal forms. Its manifestation is subject to the special conditions imposed on it by such apprehension or expression. The failure to make this distinction is certain to confuse one's conception of the temporal rhythmic unit and its period. The variations of this period present different curves in the two cases of subjective rhythmization and motor expression of definite rhythm forms. In the former the absolute duration of the unit-group suffers progressive decrease as the rate of succession among the stimuli is accelerated; in the latter a series of extensions of its total duration takes place as the number of elements composing the unit is increased. The series of relative values for units of from two to eight constituents which the finger reactions presented in this investigation is given in the following table:
TABLE II.
No. of Elements. Proportional Duration. Two, 1.000 Three, 1.109 Four, 1.817 Five, 1.761 Six, 2.196 Seven, 2.583 Eight, 2.590
This progressive extension of the rhythm period is to be explained by the mechanical conditions imposed on the expression of rhythm by processes of muscular contraction and release. Were it possible freely to increase the rate of such successive innervations, we should expect to find a much greater constancy in the whole period occupied by the series of reactions which composes the unit. The comparatively unsatisfactory quality of these larger series, and the resolution of them into subgroups described elsewhere in this paper, are due to this inability to accommodate the series of motor reactions to the subjective rhythm period.
On the other hand, the temporal value of the unit which appears as the result of subjective rhythmization undergoes a progressive decrease in absolute magnitude as the rate of succession among the undifferentiated stimuli is accelerated. The series of values for units containing from two to eleven constituents is given in the following table:
TABLE III.
No. of Elements. Duration in Seconds. Two, 2.00 Three, 1.75 Four, 1.66 Seven, 1.75 Nine, 1.50 Eleven, 0.97
If the time-value of the simple rhythm group here depended solely on the relation of the successive stimuli to the subjective rhythm period, no progressive diminution should be presented, for in proportion as the absolute value of the separating intervals decreases the true nature of this period should be more clearly manifested. It is scarcely to be doubted that the complexity of its content is likewise a determinant of the temporal value of this period, and that to this factor is to be attributed the changes which are here presented.[4]
[4] Bolton reports a similar decrease in the temporal value of the unit, and gives the following quantitative relations:
Average length of 2-group, 1.590 secs. " " " 3-group, 1.380 " " " " 4-group, 1.228 " " " " 6-group, 1.014 " " " " 8-group, 1.160 "
In subjective rhythmization the number of elements which compose the unit is dependent solely on the relation of the subjective rhythm period to the rate of succession among such elements. In objective rhythm, as has been pointed out, a free treatment of the material is rendered impossible by the determination of specific points of increased stress, in virtue of which a new unit of change appears, namely, the whole period elapsing from any one occurrence of accentuation to its return.
But this is not the sole determinant of the numerical limits of the simple group in such objective rhythms. The structural unit must indeed adhere to the scheme given by the period of the recurrent accentuation; but the point at which simple successions of this figure give place to complex structures (at which | >q. q q_| is replaced by | >q. q q;q. q q|, for example) may conceivably be hastened or retarded by other factors than that of the simple rate of succession. The degrees of segregation and accentuation which characterize the rhythmic unit are elements which may thus affect the higher synthesis. Increase in either of these directions gives greater definition to the rhythmic figure and should tend to preserve the simple group in consciousness. The latter relation was not made the subject of special investigation in this research. The former was taken up at a single point. The sounds were two in number, alternately accented and unaccented, produced by hammer-falls of 7/8 and 1/8 inch respectively. These were given at three rates of succession, and three different degrees of segregation were compared together. In the following table is given, for six subjects, the average number of elements entering into the group-form, simple or complex, under which the rhythm was apprehended:
TABLE IV.
Ratio of Beat-interval Value in Seconds of Average Interval, to Group-interval. 5/12 3/12 2/12 1.000: 1.400 3.5 5.3 9.0 1.000: 1.000 4.0 5.4 9.6 1.000: 0.714 5.2 8.4 10.8
The quantitative relations presented by these figures are consistent throughout. For every rate of speed the average rhythmic group is smallest when the interval separating the successive groups is at its maximum; it is largest when this interval is at its minimum; while in each case a median value is presented by the relation of uniformity among the intervals. In the second as well as the first of the ratios included in the foregoing table the interval which separates adjacent groups is felt to be distinctly longer than that internal to the group; in the third the relative durations of the two intervals are those which support psychological uniformity. In the latter case, in consequence of the freer passage from group to group, the continuity of the rhythmical series is more perfectly preserved than in the former, and the integration of its elements into higher syntheses more extended.
The extension of the numerical limits of the rhythm group in subjective rhythm which appear in consequence of progressive acceleration in the rate of succession is given for a series of six different values of the separating intervals in the following table, the figures of which represent the average for six observers:
TABLE V.
HIGHEST UNITS WHICH APPEAR.
Value of interval in secs.: 12/12 7/12 5/12 3/12 2/12 1/12 No. of el's in rhythm group: 2.5 3.0 4.0 7.0 9.0 11.0 Average duration of group: 2.500 1.750 1.666 1.750 1.500 0.917
SIMPLE UNITS.
No. of els. in simplest group: 2.5 2.3 2.9 3.7 4.7 5.0 Duration of simplest group: 2.50 1.34 1.21 0.92 0.78 0.41
The rate of increase here presented in the number of elements is not sufficiently rapid to counterbalance the acceleration of speed and maintain a constancy in the duration of the group. The greatest value of this period is coördinated with the slowest rate of succession, the lowest with the most rapid. As the speed increases, the duration of the rhythmic unit is shortened. Its average duration for all rates here included is 1.680 sec., or, without the first of the series (one-second intervals, at which only two of the observers received the impression of rhythm), 1.516 sec. These values are not for the simplest combinations, but for the highest synthetical unit which was immediately apprehended in the series of stimulations. This compounding becomes more pronounced as the rate of succession is accelerated, but even at intervals of 5/12 and 7/12 sec. it is the characteristic mode of apprehension.
The number of elements in the simple groups of which these higher units are composed, and their average duration, are also given in the table. These likewise show a progressive increase in number, but of a much slower rate than that manifested by the total synthesis of elements. That is to say, in subjective rhythm as well as in objectively figured series, subordinate rhythmical differences in the material sink out of consciousness less rapidly than the inclusion of fresh elements takes place; in other words, the organic complexity of the rhythmic unit increases with every acceleration in the rate of succession. The duration of these simple structural groups, as may be inferred, decreases with such acceleration, but at a much more rapid rate than is the case with the total reach of rhythmical apprehension, the value of that unit which appears in connection with the highest speed here included being less than half a second. The 'liveliness' of such rapid measures is thus a resultant of several factors. It is not a consequence solely of the more rapid rate at which the individual stimuli succeed one another, but depends also on the shortening of the periods of both these rhythmical units and on the progressive divergence of the simple from the complex group.
The influence of the rate of succession on the rhythmical unit is not confined to its segregation from adjacent groups, but affects the internal configuration of the measure as well. With every acceleration in rate the relative preponderance of the interval following the accented element (in rhythms having initial stress) increases; as the rate is retarded, smaller and smaller degrees of difference in the values of accented and unaccented intervals are discriminated. In this regard the influence of reduction in the absolute value of the separating intervals is analogous to that of increased accentuation within the group. In fast tempos and with high degrees of emphasis the interval following the initial accent is relatively longer, that following the unaccented relatively shorter, than at slow tempos and with weak emphasis. This is but another way of expressing the fact that as the elements of the auditory series succeed one another more and more slowly the impression of rhythm fades out and that as their succession increases in rapidity the impression becomes more and more pronounced. The following table presents these relations in a quantitative form for trochaic rhythm. The figures represent the number of times the second, or group interval, was judged to be greater than, equal to, or less than the first or internal interval of the group. Three rates were compared together, having average intervals of 5/12, 3/12 and 2/12 sec. Six observers took part, but only a small number of judgments was made by each, to which fact is probably to be attributed the irregularities of form which appear in the various curves:
TABLE VI.
Ratio of 1st to 2d 5/12 3/12 2/12 Interval + = - + = - + = - 1.000: 1.057 95.0 0.0 5.0 100.0 0.0 0.0 100.0 0.0 0.0 1.000: 1.000 94.7 5.3 0.0 86.0 10.5 3.5 87.5 12.5 0.0 1.000: 0.895 40.0 60.0 0.0 46.2 49.6 3.3 74.1 18.5 7.4 1.000: 0.846 41.0 50.0 9.0 39.4 54.6 6.0 40.0 52.0 8.0 1.000: 0.800 20.0 60.0 20.0 13.0 70.0 17.0 53.8 46.2 0.0 1.000: 0.756 29.4 23.5 47.1 21.8 43.4 34.8 28.0 72.0 0.0
Av. for all ratios, 53.3 33.1 13.5 51.1 38.0 10.8 63.9 33.5 2.6
Within the limits of its appearance, as the figures just presented indicate, the force, definition and persistency of the rhythmical impression do not continue uniform. At the lowest rates at which rhythm appears the integration of the successive groups is weak and their segregation indistinct. As the rate increases the definition of the rhythmic form grows more precise, group is separated from group by greater apparent intervals, and the accentuation of the groups becomes more pronounced. In subjective rhythmization of an undifferentiated series, likewise, the impression of segregation and periodic accentuation grows more forcible and dominating as the rate increases. The sensitiveness to form and dynamic value in the successive groups also increases up to a certain point in the process of acceleration. As expressed in the capacity to discriminate departures from formal equivalence among the groups, this function reached its maximum, for those concerned in this investigation, at rates varying individually from 0.3 sec. to 0.6 sec. in the value of their intervals.
It is in virtue of its nature as an impression, as opposed to a construction, that every structural unit, and every rhythmical sequence into which it enters, possesses a distinct individual quality, by which it is immediately apprehended and discriminated from other forms, as the face of an acquaintance is remembered and identified without detailed knowledge of the character of any feature it possesses. For what persists from the reception of a rhythm impression and becomes the basis of future recognition and reproduction of it, is not the number of beats in a unit or sequence, nor the absolute or relative intensity of the components of the group; it is the quality of the groups as individuals, and the form of the sequence as a whole. The phrase and verse are as vividly conceived as the unit group; the stanza or the passage is apprehended as immediately and simply as the bar or the measure. Of the number and relation of the individual beats constituting a rhythmical sequence there is no awareness whatever on the part of the æsthetic subject. I say this without qualification. So long as the rhythmical impression endures the analytic unit is lost sight of, the synthetic unit, or group, is apprehended as a simple experience. When the rhythm function is thoroughly established, when the structural form is well integrated or familiar, it becomes well-nigh impossible to return to the analytic attitude and discern the actual temporal and intensive relations which enter into the rhythm. Even the quality of the organic units may lapse from distinct consciousness, and only a feeling of the form of the whole sequence remain. The Gestaltsqualität of the passage or the stanza is thus frequently appreciated and reproduced without an awareness of its sequential relations, though with the keenest sense of what is necessary to, or inconsistent with, its structure; so that the slightest deviation from its form is remarked and the whole sequence accurately reproduced.
In order to isolate and exhibit the tendency toward rhythmization in regularly repeated motor reactions, one should examine series of similar movements made at different rates both as an accompaniment to a recurrent auditory stimulus and as free expressions of the motor impulse independent of such objective control. In the former of these cases the series of stimuli should be undifferentiated in quality as well as uniform in time. The rhythm which appears in such a case will contradict the phases of an objective series which prescribes its form, and the evidence of its existence, presented under such adverse conditions, should be indubitable.
As preliminary to their special work the members of the experimental group were tested in regard to the promptness and regularity of their reactions (by finger flexion) in accompanying a periodically recurrent stimulus given by the beating of a metronome; records were taken also of their capacity to estimate and maintain constant time relations by freely tapping at intervals of one, two and five seconds. Of the latter type of reaction the records show that a temporal grouping of the reactions is presented in every rate of tapping. This, owing to the large absolute intervals, is uniformly in groups of two, the first member of which is of shorter, the second of longer duration. There is likewise an intensive differentiation of the alternate reactions. Thus a double rhythmical treatment appears, but while with intervals of two seconds the phases of temporal and intensive rhythm coincide, at rates of one and five seconds they are opposed, that is, the accentuation falls on the initial reaction which is followed by the shorter interval. This doubtlessly marks the emergence of that tendency to initial accentuation which was subsequently found to prevail in all expression of rhythm.
The types of reaction which these records afford leave no doubt that a fuller investigation of the matter would show the constant presence, in all such forms of activity, of a rhythmical automatization of the series. The special problems which such an investigation should first resolve, relate to the dependence of the amount of rhythmical differentiation on the rate of succession among the reactions; the relation of the form of this reaction series to factors of attention and control; and the significance, in connection with the process of rhythmization, of auditory stimuli produced by and accompanying the reaction series, that is, the comparison of soundless and sounded reactions.
In the second set of experiments the reactor was directed simply to accompany the beating of a metronome by a light tapping with the forefinger on a rubber-surfaced tambour connected with a pneumographic registering pen, with which was aligned an electrical time-marker also actuated by the metronome. Three rates of tapping were adopted, 60, 90 and 120 beats per minute. No specific instructions were given as to direction or keenness of attention on the part of the reactor; the most natural and simple accompaniment was desired. Occasionally, for comparison, the reactor was directed to attend closely to each successive beat as it occurred.
Certain questions as to the applicability of the material here interpreted to the point in question, and as to its relation to the objective conditions of experimentation, must be met at the outset. The first of these is as to the actual uniformity of the metronome series. Objective determination of its temporal regularity is unnecessary (in so far as such a determination looks toward an explanation of the form of tapping by reference to inequality in the metronomic intervals). That the rhythmical phases which appear in the accompaniment are not due to inequality in the stimulation intervals, is shown by the reversal of relations between the metronome and its accompaniment which occur in the midst of a continuous series of taps. To speak roughly, a break occurs every twentieth beat. I do not refer to minor irregularities occurring within the single group but not affecting the form of the rhythmical accompaniment. The latter appeared with surprising rarity, but when found were included in the continuous calculation of averages. But in every score or so of beats a stroke out of series would be interpolated, giving the form | 1 >2 [1] 2 >1 |; the accompaniment being coördinated during the second portion of the whole series with opposite phases of the metronome from those with which its elements were connected in the earlier part. Moreover, the dependence of this grouping of the sounds on subjective attitudes may readily be made to appear. When attention is turned keenly on the process its phases of rhythmical differentiation decline; when the accompaniment becomes mechanical they mount in value. When the observer tries to mark the ticking as accurately as possible, not only does the index of his motor reactions become more constant, but the sounds of the instrument likewise appear more uniform. The observers report also that at one and the same time they are aware of the regularity of the metronome and the rhythmical nature of their tapping, while yet the conviction remains that the accompaniment has been in time with the beats. Furthermore, if the phases of ticking in the metronome were temporarily unlike, the motor accompaniment by a series of observers, if accurate, should reproduce the time-values of the process, and if inaccurate, should present only an increase of the mean variation, without altering the characteristic relations of the two phases. On the other hand, if the series be uniform and subjectively rhythmized by the hearer, there should be expected definite perversions of the objective relations, presenting a series of increasing departures from the original in proportion as the tendency to rhythmize varied from individual to individual.
On the other hand, a rhythm is already presented in the sounds of the metronome, occasioned by the qualitative differentiation of the members of each pair of ticks, a variation which it was impossible to eliminate and which must be borne in mind in estimating the following results.
Five reactors took part in the experiment, the results of which are tabulated in the following pages. The figures are based on series of one hundred reactions for each subject, fifty accompaniments to each swing and return of the metronome pendulum. When taken in series of ten successive pairs of reactions, five repetitions of the series will be given as the basis of each average. The quantitative results are stated in Tables VII.-XIV., which present the proportional values of the time intervals elapsing between the successive reactions of an accompaniment to the strokes of a metronome beating at the rates of 60, 90 and 120 per minute.
TABLE VII.
I. AVERAGES ACCORDING TO REACTORS OF ALL RATES FOR BOTH PHASES.
(a) In Series of Ten Successive Pairs of Beats.
Subject. I II III IV V VI VII VIII IX X
J. 1.000 1.005 1.022 1.053 1.044 1.116 1.058 1.061 1.055 1.052 K. 1.000 1.027 1.057 1.111 1.093 1.086 1.074 1.096 1.093 1.071 N. 1.000 1.032 1.062 0.990 1.009 0.980 1.019 1.040 1.067 1.040
Aver. 1.000 1.021 1.047 1.051 1.049 1.061 1.050 1.066 1.072 1.054
TABLE VIII.
(b) First and Second Halves of the Preceding Combined in Series of Five.
Subject. I II III IV V J. 1.058 1.031 1.041 1.054 1.048 K. 1.043 1.050 1.076 1.102 1.082 N. 0.990 1.025 1.051 1.028 1.024
Aver. 1.030 1.035 1.056 1.061 1.051
TABLE IX.
AVERAGES OF ALL RATES AND SUBJECTS ACCORDING TO PHASES OF METRONOME.
(a) In Series of Ten Successive Reactions in Accompaniment of Each Phase.
Phase. I II III IV V VI VII VIII IX X First, 1.000 1.055 1.102 1.097 1.082 1.066 1.053 1.123 1.120 1.074 Second, 1.000 0.988 0.992 1.007 1.016 1.055 1.015 1.009 1.024 1.001
TABLE X.
(b) First and Second Halves of the Preceding Combined in Series of Five.
Phase. I II III IV V First, 1.033 1.054 1.112 1.108 1.078 Second, 1.027 1.001 1.000 1.015 1.008
TABLE XI.
AVERAGES OF ALL SUBJECTS ACCORDING TO RATES AND PHASES OF METRONOME.
(a) First Phase, Series of Ten Successive Reactions.
Rate. I II III IV V VI VII VIII IX X 60 1.000 1.168 1.239 1.269 1.237 1.209 1.265 1.243 1.237 1.229 90 1.000 1.048 1.063 1.095 1.086 1.069 1.102 1.127 1.168 1.095 120 1.000 1.004 0.942 1.043 1.057 0.978 0.949 1.065 1.065 0.967
TABLE XII.
(b) Second Phase, Series of Ten Successive Reactions.
Rate. I II III IV V VI VII VIII IX X 60 1.000 0.963 0.942 0.947 1.009 0.695 0.993 0.995 1.023 0.996 90 1.000 0.893 0.987 1.018 1.036 1.005 0.995 1.000 0.977 1.000 120 1.000 1.000 0.990 1.048 1.040 1.007 0.986 1.030 1.037 0.962
TABLE XIII.
AVERAGES OF ALL SUBJECTS AND BOTH PHASES OF METRONOME ACCORDING TO RATES.
(a) In Series of Ten.
Rate. I II III IV V VI VII VIII IX X 60 1.000 1.065 1.140 1.108 1.123 0.952 1.129 1.119 1.130 1.112 90 1.000 0.970 1.025 1.056 1.061 1.037 1.048 1.063 1.072 1.047 120 1.000 1.000 0.990 1.048 1.040 1.007 0.986 1.030 1.037 0.962
TABLE XIV.
(b) Above Combined in Series of Five.
Rate. I II III IV V 60 0.976 1.097 1.129 1.119 1.117 90 1.018 1.009 1.044 1.059 1.054 120 1.003 0.993 1.010 1.042 1.001
In the following table (XV.) is presented the average proportional duration of the intervals separating the successive reactions of these subjects to the stimulations given by the alternate swing and return of the pendulum.
TABLE XV.
Subject. Rate: 60. Rate: 90. Rate: 120. B. 0.744 : 1.000 0.870 : 1.000 0.773 : 1.000 J. 0.730 : 1.000 0.737 : 1.000 0.748 : 1.000 K. 0.696 : 1.000 0.728 : 1.000 0.737 : 1.000 N. 0.526 : 1.000 0.844 : 1.000 0.893 : 1.000
The corresponding intensive values, as measured by the excursion of the recording pen, are as follows:
TABLE XVI.
Subject. Rate: 60. Rate: 90. Rate: 120. B. (1.066 : 1.000) 0.918 : 1.000 (1.010 : 1.000) J. 0.938 : 1.000 0.943 : 1.000 0.946 : 1.000 K. 0.970 : 1.000 0.949 : 1.000 (1.034 : 1.000) N. 0.883 : 1.000 0.900 : 1.000 0.950 : 1.000
These figures present a double process of rhythmic differentiation, intensively into stronger and weaker beats, and temporally into longer and shorter intervals. The accentuation of alternate elements has an objective provocative in the qualitative unlikeness of the ticks given by the swing and return of the pendulum. This phase is, however, neither so clearly marked nor so constant as the temporal grouping of the reactions. In three cases the accent swings over to the shorter interval, which, according to the report of the subjects, formed the initial member of the group when such grouping came to subjective notice. This latter tendency appears most pronounced at the fastest rate of reaction, and perhaps indicates a tendency at rapid tempos to prefer trochaic forms of rhythm. In temporal grouping the coördination of results with the succession of rates presents an exception only in the case of one subject (XV. B, Rate 120), and the various observers form a series in which the rhythmizing tendency becomes more and more pronounced.
Combining the reactions of the various subjects, the average for all shows an accentuation of the longer interval, as follows:
TABLE XVII.
Rate. Temp. Diff. Intens. Diff. 60 0.674 : 1.000 0.714 : 1.000 90 0.795 : 1.000 0.927 : 1.000 120 0.788 : 1.000 0.985 : 1.000
The rhythmical differentiation of phases is greatest at the slowest tempo included in the series, namely, one beat per second, and it declines as the rate of succession increases. It is impossible from this curve to say, however, that the subjective rhythmization of uniform material becomes more pronounced in proportion as the intervals between the successive stimulations increase. Below a certain rapidity the series of sounds fails wholly to provoke the rhythmizing tendency; and it is conceivable that a change in the direction of the curve may occur at a point beyond the limits included within these data.
The introduction from time to time of a single extra tap, with the effect of transposing the relations of the motor accompaniment to the phases of the metronome, has been here interpreted as arising from a periodically recurring adjustment of the reaction process to the auditory series which it accompanies, and from which it has gradually diverged. The departure is in the form of a slow retardation, the return is a swift acceleration. The retardation does not always continue until a point is reached at which a beat is dropped from, or an extra one introduced into, the series. In the course of a set of reactions which presents no interpolation of extra-serial beats periodic retardation and acceleration of the tapping take place. This tertiary rhythm, superimposed on the differentiation of simple phases, has, as regards the forms involved in the present experiments, a period of ten single beats or five measures.
From the fact that this rhythm recurs again and again without the introduction of an extra-serial beat it is possible to infer the relation of its alternate phases to the actual rate of the metronome. Since the most rapid succession included was two beats per second, it is hardly conceivable that the reactor lost count of the beats in the course of his tapping. If, therefore, the motor series in general parallels the auditory, the retardations below the actual metronome rate must be compensated by periods of acceleration above it. Regarded in this light it becomes questionable if what has been called the process of readjustment really represents an effort to restore an equilibrium between motor and auditory processes after an involuntary divergence. I believe the contrasting phases are fundamental, and that the changes represent a free, rhythmical accompaniment of the objective periods, which themselves involve no such recurrent differentiation.
Of the existence of higher rhythmic forms evidence will be afforded by a comparison of the total durations of the first and second five-groups included in the decimal series. Difference of some kind is of course to be looked for; equivalence between the groups would only be accidental, and inequality, apart from amount and constancy, is insignificant. In the results here presented the differentiation is, in the first place, of considerable value, the average duration of the first of these groups bearing to the second the relation of 1.000:1.028.
Secondly, this differentiation in the time-values of the respective groups is constant for all the subjects participating. The ratios in their several cases are annexed:
TABLE XVIII.
Subject. Ratio. J. 1.000:1.042 K. 1.000:1.025 N. 1.000:1.010
It is perhaps significant that the extent of this differentiation--and inferably the definition of rhythmical synthesis--corresponds to the reported musical aptitudes of the subjects; J. is musically trained, K. is fond of music but little trained, N. is without musical inclination.
The relations of these larger rhythmical series repeat those of their constituent groups--the first is shorter, the second longer. The two sets of ratios are brought together for comparison in the annexed table:
TABLE XIX.
Subject. Unit-Groups. Five Groups. J. 1.000:1.354 1.000:1.042 K. 1.000:1.388 1.000:1.025 N. 1.000:1.326 1.000:1.010
It is to be noted here, as in the case of beating out specific rhythms, that the index of differentiation is greater in simple than in complex groups, the ratios for all subjects being, in simple groups, 1.000:1.356, and in series of five, 1.000:1.026.
There is thus present in the process of mechanically accompanying a series of regularly recurring auditory stimuli a complex rhythmization in the forms, first, of a differentiation of alternate intervals, and secondly, of a synthesis of these in larger structures, a process here traced to the third degree, but which may very well extend to the composition of still more comprehensive groups. The process of reaction is permeated through and through by rhythmical differentiation of phases, in which the feeling for unity and equivalence must hold fast through really vast periods as the long slow phases swing back and forth, upon which takes place a swift and yet swifter oscillation of rhythmical values as the unit groups become more limited, until the opposition of single elements is reached.
III. THE CHARACTERISTICS OF THE RHYTHMICAL UNIT.
A. The Number of Elements in the Group and its Limits.
The number of elements which the rhythmical group contains is related, in the first place, to the rate of succession among the elements of the sequence. This connection has already been discussed in so far as it bears on the forms of grouping which appear in an undifferentiated series of sounds in consequence of variations in the absolute magnitude of the intervals which separate the successive stimuli. In such a case the number of elements which enter into the unit depends solely on the rate of succession. The unit presents a continuous series of changes from the lowest to the highest number of constituents which the simple group can possibly contain, and the synthesis of elements itself changes from a succession of simple forms to structures involving complex subordination of the third and even fourth degree, without other change in the objective series than variations in tempo.
When objectively defined rhythm types are presented, or expression is given to a rhythm subjectively defined by ideal forms, these simple relations no longer hold. Acceleration or retardation of speed does not unconditionally affect the number of elements which the rhythm group contains. In the rhythmization of an undifferentiated series the recurrence of accentuation depends solely on subjective conditions, the temporal relations of which can be displaced only within the limits of single intervals; for example, if a trochaic rhythm characterizes a given tempo, the rhythm type persists under conditions of progressive acceleration only in so far as the total duration of the two intervals composing the unit approximates more closely to the subjective rhythm period than does that of three such intervals. When, in consequence of the continued reduction of the separating intervals, the latter duration presents the closer approximation, the previous rhythm form is overthrown, accentuation attaches to every third instead of to alternate elements, and a dactylic rhythm replaces the trochaic.
In objective rhythms, on the other hand, the determination of specific points of increased stress makes it impossible thus to shift the accentuation back and forth by increments of single intervals. The unit of displacement becomes the whole period intervening between any two adjacent points of accentuation. The rhythm form in such cases is displaced, not by those of proximately greater units, but only by such as present multiples of its own simple groups. Acceleration of the speed at which a simple trochaic succession is presented results thus, first, in a more rapid trochaic tempo, until the duration of two rhythm groups approaches more nearly to the period of subjective rhythmization, when--the fundamental trochaism persisting--the previous simple succession is replaced by a dipodic structure in which the phases of major and minor accentuation correspond to the elementary opposition of accented and unaccented phases. In the same way a triplicated structure replaces the dipodic as the acceleration still continues; and likewise of the dactylic forms.
We may say, then, that the relations of rate to complexity of structure present the same fundamental phenomena in subjective rhythmization and objectively determined types, the unit of change only differing characteristically in the two cases. The wider range of subjective adjustment in the latter over the former experience is due to the increased positive incentive to a rhythmical organic accompaniment afforded by the periodic reinforcement of the objective stimulus.
An investigation of the limits of simple rhythmical groups is not concerned with the solution of the question as to the extent to which a reactor can carry the process of prolonging the series of elements integrated through subordination to a single dominant accentuation. The nature of such limits is not to be determined by the introspective results of experiments in which the observer has endeavored to hold together the largest possible number of elements in a simple group. When such an attempt is made a wholly artificial set of conditions, and presumably of mechanisms, is introduced, which makes the experiment valueless in solving the present problem. Both the direction and the form of attention are adverse to the detection of rhythmical complications under such conditions. Attention is directed away from the observation of secondary accents and toward the realization of a rhythm form having but two simple phases, the first of which is composed of a single element, while within the latter fall all the rest of the group. Such conditions are the worst possible for the determination of the limits of simple rhythm groups; for the observer is predisposed from the outset to regard the whole group of elements lying within the second phase as undifferentiated. Thus the conditions are such as to postpone the recognition of secondary accents far beyond the point at which they naturally arise.
But further, such an attempt to extend the numerical scope of simple rhythm groups also tends to transform and disguise the mechanism by which secondary stresses are produced, and thereby to create the illusion of an extended simple series which does not exist. For we have no right to assume that the process of periodic accentuation in such a series, identical in function though it be, involves always the same form of differentiation in the rhythmical material. If the primary accentuation be given through a finger reaction, the fixating of that specific form of change will predispose toward an overlooking of secondary emphases depending on minor motor reactions of a different sort. The variety of such substitutional mechanisms is very great, and includes variations in the local relations of the finger reaction, movements of the head, eyes, jaws, throat, tongue, etc., local strains produced by simultaneous innervation of flexor and extensor muscles, counting processes, visual images, and changes in ideal significance and relation of the various members of the group. Any one of these may be seized upon to mediate the synthesis of elements and thus become an unperceived secondary accentuation.
Our problem is to determine at what point formal complication of the rhythmical unit tends naturally to arise. How large may such a group become and still remain fundamentally simple, without reduplication of accentual or temporal differentiation? The determination of such limits must be made on the basis of quantitative comparison of the reactions which enter into larger and smaller rhythmical series, on the one hand, and, on the other, of the types of structure which appear in subjective rhythmization and the apprehension of objective rhythms the forms of which are antecedently unknown to the hearer. The evidence from subjective rhythms is inconclusive. The prevailing types are of two and three beats. Higher forms appear which are introspectively simple, but introspection is absolutely unable to solve the problem as to the possible composite nature of these extended series. The fact that they are confined to even numbers, the multiples of two, and to such odd-numbered series as are multiples of three, without the appearance of the higher primes, indicates the existence in all these groups of secondary accentuation, and the resolution of their forms into structures which are fundamentally complications of units of two and three elements only. The process of positive accentuation which appears in every higher rhythmical series, and underlying its secondary changes exhibits the same reduction of their elementary structure to double and triple groups, has been described elsewhere in this report. Here it is in place to point out certain indirect evidence of the same process of resolution as manifested in the treatment of longer series of elements.
The breaking up of such series into subgroups may not be an explicitly conscious process, while yet its presence is indispensable in giving rhythmical form to the material. One indication of such undiscriminated rhythmical modification is the need of making or avoiding pauses between adjacent rhythmical groups according as the number of their constituents varies. Thus, in rhythms having units of five, seven, and nine beats such a pause was imperative to preserve the rhythmical form, and the attempt to eliminate it was followed by confusion in the series; while in the case of rhythms having units of six, eight, and ten beats such a pause was inadmissible. This is the consistent report of the subjects engaged in the present investigation; it is corroborated by the results of a quantitative comparison of the intervals presented by the various series of reactions. The values of the intervals separating adjacent groups for a series of such higher rhythms are given in Table XX. as proportions of those following the initial, accented reaction.
TABLE XX.
Rhythm. Initial Interval. Final Interval Five-Beat, 1.000 1.386 Six " 1.000 0.919 Seven " 1.000 1.422 Eight " 1.000 1.000 Nine " 1.000 1.732 Ten " 1.000 1.014
The alternate rhythms of this series fall into two distinct groups in virtue of the sharply contrasted values of their final intervals or group pauses. The increased length of this interval in the odd-numbered rhythms is unquestionably due to a subdivision of the so-called unit into two parts, the first of which is formally complete, while the latter is syncopated. In the case of five-beat rhythms, this subdivision is into threes, the first three of the five beats which compose the so-called unit forming the primary subgroup, while the final two beats, together with a pause functionally equivalent to an additional beat and interval, make up the second, the system being such as is expressed in the following notation: | .q. q q; >q. q % |. The pause at the close of the group is indispensable, because on its presence depends the maintenance of equivalence between the successive three-groups. On the other hand, the introduction of a similar pause at the close of a six-beat group is inadmissible, because the subdivision is into three-beat groups, each of which is complete, so that the addition of a final pause would utterly unbalance the first and second members of the composite group, which would then be represented by the following notation: | >q. q q; .q. q q % |; that is, a three-group would alternate with a four-group, the elements of which present the same simple time relations, and the rhythm, in consequence, would be destroyed. The same conditions require or prevent the introduction of a final pause in the case of the remaining rhythm forms.
The progressive increase in the value of the final interval, which will be observed in both the odd-and even-numbered rhythms, is probably to be attributed to a gradual decline in the integration of the successive groups into a well-defined rhythmical sequence.
This subdivision of material into two simple phases penetrates all rhythmical structuring. The fundamental fact in the constitution of the rhythmical unit is the antithesis of two phases which we call the accented and the unaccented. In the three-beat group as in the two-beat, and in all more complex grouping, the primary analysis of material is into these two phases. The number of discriminable elements which enter each phase depends on the whole constitution of the group, for this duality of aspect is carried onward from its point of origin in the primary rhythm group throughout the most complex combination of elements, in which the accented phase may comprise an indefinitely great number of simple elements, thus:
______ __________ ______________ / \ / \ / \ > . > . >> . | q q ; q q |, | q q q; q q q |, | q q q q; q q q q |, etc. \_/ >
An indication of this process of differentiation into major and minor phases appears in the form of rhythm groups containing upwards of four elements. In these the tendency is, as one observer expresses it, 'to consider the first two beats as a group by themselves, with the others trailing off in a monotonous row behind.' As the series of elements thus bound up as a unit is extended, the number of beats which are crowded into the primary subgroup also increases. When the attempt was made to unite eleven or twelve reactions in a single group, the first four beats were thus taken together, with the rest trailing off as before. It is evident that the lowest groups with which attention concerned itself here were composed of four beats, and that the actual form of the (nominally) unitary series of eleven beats was as follows:
_______________________ / \ >> > > | q q q q; q q q q; q q q q |. . . .
The subscripts are added in the notation given above because it is to be doubted if a strictly simple four-beat rhythm is ever met with. Of the four types producible in such rhythm forms by variation in the accentual position, three have been found, in the course of the present investigation, to present a fundamental dichotomy into units of two beats. Only one, that characterized by secondary accentuation, has no such discriminable quality of phases. Of this form two things are to be noted: first, that it is unstable and tends constantly to revert to that with initial stress, with consequent appearance of secondary accentuation; and second, that as a permanent form it presents the relations of a triple rhythm with a grace note prefixed.
The presence of this tendency to break up the four-rhythm into subgroups of two beats explains a variety of peculiarities in the records of this investigation. The four-beat rhythm with final accent is found most pleasant at the close of a rhythmical sequence. The possibility of including it in a continuous series depends on having the final interval of 'just the right length.' If one keeps in mind that a secondary initial accent characterizes this rhythm form, the value required in this final interval is explained by the resolution of the whole group into two units of three beats each, the latter of the two being syncopated. The pause is of 'just the right length' when it is functionally equal to two unaccented elements with their succeeding intervals, as follows: | .q. q q; .q % % |.
Likewise in four-rhythms characterized by initial stress there appears a tendency to accent the final beat of the group, as well as that to accent the third. Such a series of four may therefore break up in either of two ways, into | >q. q; .q q | on a basis of two-beat units, or into | .q. q q; >q % %| on a basis of three-beat units.
The persistence of these simple equivalences appears also in the treatment of syncopated measures and of supplementary or displaced accents. Of the form | >q. q >q. | one reactor says, and his description may stand for all, "This deliberate introduction of a third accent on the last beat is almost impossible for me to keep. The single group is easy enough and rather agreeable, but in a succession of groups the secondarily accented third beat comes against the first of the next group with a very disagreeable effect." This is the case where no pause intervenes between the groups, in which case the rhythm is destroyed by the suppression, in each alternate simple group, of the unaccented phase; thus, | >q. q >q. | alone is pleasant, because it becomes | .q. q; >q % |, but in combination with preceding and succeeding groups it is disagreeable, because it becomes in reality | >q. q; .q % |, etc. A long pause between the groups destroys this disagreeableness, since the lacking phase of the second subgroup is then restored and the rhythm follows its normal course.
The amphibrachic form, | >q q. q |, is more difficult to maintain than either the dactylic or the trochaic, and in a continuous series tends to pass over into one of these, usually the former. 'With sufficient pause,' the reactors report, 'to allow the attitude to die away,' it is easily got. The same inability to maintain this form in consciousness appears when a continuous series of clicks is given, every third of which is louder than the rest. Even when the beginning of the series is made coincident with the initial phase of the amphibrachic group the rhythmic type slips over into the dactylic, in spite of effort. In this, as in the preceding type of reaction, if the interval separating adjacent groups be lengthened, the rhythm is maintained without trouble. The 'dying away' of the attitude lies really in such an arrangement of the intervals as will formally complete a phrase made up of simple two-beat units.
The positive evidence which this investigation affords, points to the existence of factors of composition in all rhythms of more than three beats; and a variety of peculiarities which the results present can be explained--and in my estimation explained only--on the basis of such an assumption. I conclude, therefore, that strictly stated the numerical limit of simple rhythm groups is very soon reached; that only two rhythmical units exist, of two and three beats respectively; that in all longer series a resolution into factors of one of these types takes place; and, finally, that the subordination of higher rhythmical quantities of every grade involves these simple relations, of which, as the scope of the synthesis increases, the opposition of simple alternate phases tends more and more to predominate over triplicated structures.
Variation in the number of elements which enter into the rhythmic unit does not affect the sense of equivalence between successive groups, so long as the numerical increase does not reach a point at which it lessens the definiteness of the unit itself. For the purpose of testing this relation the reactors beat out a series of rhythm forms from 'one-beat' rhythms to those in which the group consisted of seven, eight and nine elements, and in which the units were either identical with one another or were made up of alternately larger and smaller numbers of elements. Two questions were to be answered in each case; the manner in which these various changes affected the sense of rhythmical equivalence in the alternate groups, and the variations in affective quality which these changes introduced into the experience. With the former of these problems we are here concerned. From 'one-beat' to four-beat rhythms the increase in number of constituents in no way affects the sense of rhythmical equivalence. Beyond this point there is a distinct falling off. 'The first part of the rhythm begins to fade away before the end of the second,' says one; and another: 'The series then reverts to a monotonous succession without feeling of rhythm.' This decline marks those groups composed of an odd number of elements much earlier and more strongly than those which contain an even number. The sense of equivalence has fallen off at five and practically disappears at seven beats, while groups of six and eight retain a fairly definite value as units in a rhythmical sequence. This peculiar relation must be due to the subconscious resolution of the larger symmetrical groups into smaller units of three and four constituents respectively.
Likewise the introduction of variations in the figure of the group--that is, in the number of elements which enter into the groups to be compared, the distribution of time values within them, the position of accents, rests, and the like--does not in any way affect the sense of equivalence between the unlike units. Against a group of two, three, four, or even five elements may be balanced a syncopated measure which contains but one constituent, with the sense of full rhythmical equivalence in the functional values of the two types. Indeed, in the case of five-beat rhythms the definition of values is greater when such opposition finds place than when the five-beat group is continuously repeated. This is to be explained doubtlessly by the more definite integration into a higher rhythmical unity which is afforded under the former conditions.
The number and the distribution of elements are factors variable at will, and are so treated in both musical and poetical expression. The condition which cannot be transgressed is the maintenance of strict temporal relations in the succession of total groups which constitute the rhythmical sequence. These relations are, indeed, not invariable for either the single interval or the duration of the whole group, but they are fixed functions of the dynamic values of these elements and units. Two identically figured groups (e.g., | >q. q q | >q. q q | ), no more possess rhythmically substitutionary values than does the opposition of a single beat to an extended series (e.g., | >q. | >q. q q | ), apart from this factor of temporal proportion. Those groups which are identical in figure must also be uniform in duration if they are to enter as substitutionary groups into a rhythmical sequence.[5] When the acatalectic type is alternately departed from and returned to in the course of the rhythmical sequence, the metrical equivalents must present total time-values which, while differing from that of the full measure in direction and degree, in dependence on the whole form of their structure, maintain similar fixed relations to the primary type. The changes which these flexible quantities undergo will here only be indicated. If the substitutionary groups be of different figures, that which comprises the larger number of elements will occupy the greater time, that which contains fewer, the less.
[5] Theoretically and strictly identical; this abstracts from the coördination of such identical groups as major and minor components of a higher rhythmical synthesis, which is really never absent and in virtue of which the temporal values of the groups are also differentiated.
I do not forget the work of other observers, such as Brücke, who finds that dactyls which appear among trochees are of less duration than the latter, nor do I impugn their results. The rhythmical measure cannot be treated as an isolated unit; it must always be considered in its structural relations to the rhythmical sequence of which it forms a part. Every non-conforming measure is unquestionably affected by the prevailing type of the rhythmical sequence in which it occurs. Brücke points out the converse fact that those trochees and iambs are longest which appear in dactylic or other four-measures; but this ignores the complexity of the conditions on which the character of these intrusive types depends. The time-values of such variants are also dependent on the numerical preponderance of the typical form in the whole series. When a single divergent form appears in the sequence the dynamic relations of the two types is different from that which obtains when the numbers of the two approach equality, and the effect of the prevailing form on it is proportionally greater. Secondly, the character of such variants is dependent on the subordinate configuration of the sequence in which they appear, and on their specific functions within such minor rhythmical figures. The relative value of a single dactyl occurring in an iambic pentameter line cannot be predicated of cases in which the two forms alternate with each other throughout the verse. Not only does each type here approximate the other, but each is affected by its structural relation to the proximately higher group which the two alternating measures compose. Thirdly, the quantitative values of these varying forms is related to their logical significance in the verse and the degree of accentuation which they receive. Importance and emphasis increase the duration of the measure; the lack of either shortens it. In this last factor, I believe, lies the explanation of the extreme brevity of dactyls appearing in three-rhythms. When a specific rhythm type is departed from, for the purpose of giving emphasis to a logically or metrically important measure, the change is characteristically in the direction of syncopation. Such forms, as has been said elsewhere, mark nodes of natural accentuation and emphasis. Hence, the dactyl introduced into an iambic or trochaic verse, which, so far as concerns mere number of elements, tends to be extended, may, in virtue of its characteristic lack of accentuation and significance, be contracted below the value of the prevailing three-rhythm. Conversely the trochee introduced into a dactylic sequence, in consequence of its natural accentuation or importance, may exceed in time-value the typical four-rhythm forms among which it appears. The detailed examination of the relation of temporal variations to numerical predominance in the series, to subordinate structural organization, and to logical accentuation, in our common rhythms, is a matter of importance for the general investigation which remains still to be carried out. In so far as the consideration of these factors entered into the experimental work of the present research, such quantitative time relations are given in the following table, the two types in all cases occurring in simple alternation:
TABLE XXI.
Rhythm. 1st Meas. 2d Meas. Rhythm. 1st Meas. 2d Meas.
. > > > > . q q q; q q % 1.000 1.091 q q %; q q q 1.000 1.140 . > > . q q q; q q % 1.000 1.159 q q %; q q q 1.000 1.021 . > > . q q q; q q % 1.000 1.025 q q %; q q q 1.000 1.267 > . . > q q q; q q % 1.000 0.984 q q %; q q q 1.000 1.112 > . . > q q q; q q % 1.000 0.766 q q %; q q q 1.000 1.119
As the disparity in numerical constitution increases, so will also the divergence in time-value of the two groups concerned. When differentiation into major and minor phases is present, the duration of the former will be greater than that of the latter. Hence, in consequence of the combination of these two factors--e.g., in a syncopated measure of unusual emphasis--the characteristic time-values may be inverted, and the briefer duration attach to that unit which comprises the greater number of elements. Intensive values cannot take the place of temporal values in rhythm; the time form is fundamental. Through all variations its equivalences must be adhered to. Stress makes rhythm only when its recurrence is at regular intervals. The number of subordinate factors which combine with the accented element to make the group is quite indifferent. But whether few or many, or whether that element on which stress falls stands alone (as it may), the total time values of the successive groups must be sensibly equivalent. When a secondary element is absent its place must be supplied by a rest of equivalent time-value. If these proper temporal conditions be not observed no device of intensive accentuation will avail to produce the impression of metrical equivalence among the successive groups.
B. The Distribution of Elements Within the Group.
(a) The Distribution of Intensities.
In the analysis of the internal constitution of the rhythmic unit, as in other parts of this work, the investigation follows two distinct lines, involving the relations of rhythm as apprehended, on the one hand, and the relations of rhythm as expressed, on the other; the results in the two cases will be presented separately. A word as to the method of presentation is necessary. The fact that in connection with each experiment a group of questions was answered gives rise to some difficulty in planning the statement of results. It is a simple matter to describe a particular set of experiments and to tell all the facts which were learned from them; but it is not logical, since one observation may have concerned the number of elements in the rhythmic unit, another their internal distribution, and a third their coalescence in a higher unity. On the other hand, the statement of each of these in its own proper connection would necessitate the repetition of some description, however meager, of the conditions of experimentation in connection with each item. For economy's sake, therefore, a compromise has been made between reporting results according to distribution of material and according to distribution of topics. The evidence of higher grouping, for example, which is afforded by variations in duration and phases of intensity in alternate measures, will be found appended to the sections on these respective classes of material.
In all the following sections the hammer-clang apparatus formed the mechanism of experimentation in sensory rhythms, while in reactive rhythms simple finger-tapping was employed.
In comparing the variations in stress which the rhythmical material presents, the average intensities of reaction for the whole group has been computed, as well as the intensities of the single reactions which compose it. This has been done chiefly in view of the unstable intensive configuration of the group and the small amount of material on which the figures are based. The term is relative; in ascertaining the relations of intensity among the several members of the group, at least ten successive repetitions, and in a large part of the work fifty, have been averaged. This is sufficient to give a clear preponderance in the results to those characteristics which are really permanent tendencies in the rhythmical expression. This is especially true in virtue of the fact that throughout these experiments the subject underwent preliminary training until the series of reactions could be easily carried out, before any record of the process was taken. But when such material is analyzed in larger and smaller series of successive groups the number of reactions on which each average is based becomes reduced by one half, three quarters, and so on. In such a case the prevailing intensive relations are liable to be interfered with and transformed by the following factor of variation. When a wrong intensity has accidentally been given to a particular reaction there is observable a tendency to compensate the error by increasing the intensity of the following reaction or reactions. This indicates, perhaps, the presence of a sense of the intensive value of the whole group as a unity, and an attempt to maintain its proper relations unchanged, in spite of the failure to make exact coördination among the components. But such a process of compensation, the disappearance of which is to be looked for in any long series, may transpose the relative values of the accented elements in two adjacent groups when only a small number of reactions is taken into account, and make that seem to receive the major stress which should theoretically receive the minor, and which, moreover, does actually receive such a minor stress when the value of the whole group is regarded, and not solely that member which receives the formal accentuation.
The quantitative analysis of intensive relations begins with triple rhythms, since its original object was to compare the relative stresses of the unaccented elements of the rhythmic group. These values for the three forms separately are given in Table XXII., in which the value of the accented element in each case is represented by unity.
TABLE XXII.
Rhythm. 1st Beat. 2d Beat. 3d Beat.
Dactylic, 1.000 0.436 0.349 Amphibrachic, 0.488 1.000 0.549 Anapæstic, 0.479 0.484 1.000
The dactylic form is characterized by a progressive decline in intensity throughout the series of elements which constitute the group. The rate of decrease, however, is not continuous. There is a marked separation into two grades of intensity, the element receiving accentual stress standing alone, those which possess no accent falling together in a single natural group, as shown in the following ratios: first interval to third, 1.000:0.349; second interval to third, 1.000:0.879. One cannot say, therefore, that in such a rhythmic form there are two quantities present, an accented element and two undifferentiated elements which are unaccented. For the average is not based on a confused series of individual records, but is consistently represented by three out of four subjects, the fourth reversing the relations of the second and third elements, but approximating more closely to equivalence than any other reactor (the proportional values for this subject are 1.000; 0.443; 0.461). Moreover, this reactor was the only musically trained subject of the group, and one in whom the capacity for adhering to the logical instructions of the experiment appears decidedly highest.
In the amphibrachic form the average again shows three degrees of intensity, three out of four subjects conforming to the same type, while the fourth reverses the relative values of the first and third intervals. The initial element is the weakest of the group, and the final of median intensity, the relation for all subjects being in the ratio, 1.000:1.124. The amphibrachic measure begins weakly and ends strongly, and thus approximates, we may say, to the iambic type.
In the anapæstic form the three degrees of intensity are still maintained, three out of four subjects giving consistent results; and the order of relative values is the simple converse of the dactylic. There is presented in each case a single curve; the dactyl moves continuously away from an initial accent in an unbroken decrescendo, the anapæst moves continuously toward a final accent in an unbroken crescendo. But in the anapæstic form as well as in the dactylic there is a clear duality in the arrangement of elements within the group, since the two unaccented beats fall, as before, into one natural group, while the accented element is set apart by its widely differentiated magnitude. The ratios follow: first interval to second, 1.000:1.009; first interval to third, 1.000:2.084.
The values of the three elements when considered irrespective of accentual stress are as follows: First, 1.000; second, 1.001; third, 0.995. No characteristic preponderance due to primacy of position appears as in the case of relative duration. The maximum value is reached in the second element. This is due to the coöperation of two factors, namely, the proximity of the accentual stress, which in no case is separated from this median position by an unaccented element, and the relative difficulty in giving expression to amphibrachic rhythms. The absolute values of the reactions in the three forms is of significance in this connection. Their comparison is rendered possible by the fact that no change in the apparatus was made in the course of the experiments. They have the following values: Dactylic, 10.25; amphibrachic, 12.84; anapæstic, 12.45. The constant tendency, when any difficulty in coördination is met with, is to increase the force of the reactions, in the endeavor to control the formal relations of the successive beats. If such a method of discriminating types be applied to the present material, then the most easily coördinated--the most natural--form is the dactyl; the anapæst stands next; the amphibrach is the most unnatural and difficult to coördinate.
The same method of analysis was next applied to four-beat rhythms. The proportional intensive values of the successive reactions for the series of possible accentual positions are given in the following table:
TABLE XXIII.
Stress. 1st Beat. 2d Beat. 3d Beat. 4th Beat.
Initial, 1.000 0.575 0.407 0.432 Secondary, 0.530 1.000 0.546 0.439 Tertiary, 0.470 0.407 1.000 0.453 Final, 0.492 0.445 0.467 1.000
The first and fourth forms follow similar courses, each marked by initial and final stress; but while this is true throughout in the fourth form, it results in the first form from the preponderance of the final interval in a single individual's record, and therefore cannot be considered typical. The second and third forms are preserved throughout the individual averages. The second form shows a maximum from which the curve descends continuously in either direction; in the third a division of the whole group into pairs is presented, a minor initial accent occurring symmetrically with the primary accent on the third element. This division of the third form into subgroups appears also in its duration aspect. Several inferences may be drawn from this group of relations. The first and second forms only are composed of singly accented groups; in the third and fourth forms there is presented a double accent and hence a composite grouping. This indicates that the position in which the accent falls is an important element in the coördination of the rhythmical unit. When the accent is initial, or occurs early in the group, a larger number of elements can be held together in a simple rhythmic structure than can be coördinated if the accent be final or come late in the series. In this sense the initial position of the accent is the natural one. The first two of these four-beat forms are dactylic in structure, the former with a postscript note added, the latter with a grace note prefixed. In the third and fourth forms the difficulty in coördinating the unaccented initial elements has resulted in the substitution of a dipodic division for the anapæstic structure of triple rhythms with final accent.
The presence of a tendency toward initial accentuation appears when the average intensities of the four reactions are considered irrespective of accentual position. Their proportional values are as follows: First, 1.000; second, 0.999; third, 1.005; fourth, 0.981. Underlying all changes in accentuation there thus appears a resolution of the rhythmic structure into units of two beats, which are primitively trochaic in form.
The influence exerted by the accented element on adjacent members of the group is manifested in these forms more clearly than heretofore when the values of the several elements are arranged in order of their proximity to that accent and irrespective of their positions in the group. Their proportional values are as follows:
TABLE XXIV.
2d Remove. 1st Remove. Accent. 1st Remove. 2d Remove. 0.442 0.526 1.000 0.514 0.442
This reinforcing influence is greater--according to the figures just given--in the case of the element preceding the accent than in that of the reaction which follows it. It may be, therefore, that the position of maximal stress in the preceding table is due to the close average relation in which the third position stands to the accented element. This proximity it of course shares with the second reaction of the group, but the underlying trochaic tendency depreciates the value of the second reaction while it exaggerates that of the third. This reception of the primitive accent the third element of the group indeed shares with the first, and one might on this basis alone have expected the maximal value to be reached in the initial position, were it not for the influence of the accentual stress on adjacent members of the group, which affects the value of the third reaction to an extent greater than the first, in the ratio 1.000:0.571.
The average intensity of the reactions in each of the four forms--all subjects and positions combined--is worthy of note.
TABLE XXV.
Stress. Initial. Secondary. Tertiary. Final. Value, 1.000 1.211 1.119 1.151
The first and third forms, which involve initial accents--in the relation of the secondary as well as primary accent to the subgroups--are both of lower average value than the remaining types, in which the accents are final, a relation which indicates, on the assumption already made, a greater ease and naturalness in the former types. Further, the second form, which according to the subjective reports was found the most difficult of the group to execute--in so far as difficulty may be said to be inherent in forms of motor reaction which were all relatively easy to manipulate--is that which presents the highest intensive value of the whole series.
In the next group of experiments, the subject was required to execute a series of reactions in groups of alternating content, the first to contain two uniform beats, the second to consist of a single reaction. This second beat with the interval following it constitutes a measure which was to be made rhythmically equivalent to the two-beat group with which it alternated. The time-relations of the series were therefore left to the adjustment of the reactor. The intensive relations were separated into two groups; in the first the final reaction was to be kept uniform in strength with those of the preceding group, in the second it was to be accented.
The absolute and relative intensive values for the two forms are given in the following table:
TABLE XXVI.
Rhythm. 1st Beat. 2d Beat. 3d Beat. Value.
Syncopated Measures 13.00 15.12 16.50 Absolute. Unaccented, 1.000 1.175 1.269 Relative.
Syncopated Measures 10.95 11.82 16.11 Absolute. Accented, 1.000 1.079 1.471 Relative.
These averages hold for every individual record, and therefore represent a thoroughly established type. In both forms the reaction of the syncopated measure receives the greatest stress. In the first form, while the stress is relatively less than in the second, it is at the same time absolutely greater. The whole set of values is raised (the ratio of average intensities in the two forms being 1.147:1.000), as it has already been found to be raised in other forms difficult to execute. To this cause the preponderance is undoubtedly to be attributed, as the reports of every subject describe this form as unnatural, in consequence of the restraint it imposes on an impulse to accent the final reaction, i.e., the syncopated measure.
In the next set of experiments the series of reactions involved the alternation of a syncopated measure consisting of a single beat with a full measure of three beats. The same discrimination into accented and unaccented forms in the final measure was made as in the preceding group. The series of absolute and relative values are given in the following table.
TABLE XXVII.
Rhythm. 1st Beat. 2d Beat. 3rd Beat. 4th Beat. Value.
Syncopated Measures 9.77 8.96 9.61 13.78 Absolute. Unaccented, 1.000 0.915 0.983 1.165 Relative.
Syncopated Measures 11.57 11.07 11.53 21.50 Absolute. Accented, 1.000 0.957 0.996 1.858 Relative.
These averages hold for every subject where the syncopated measure receives accentuation, and for two out of three reactors where it is unaccented. The latter individual variation shows a progressive increase in intensity throughout the series.
Here, as in the preceding forms, a well-established type is presented. Not only when accentuation is consciously introduced, but also when the attempt is made--and in so far as the introspection of the reactor goes, successfully made--to maintain a uniformity among the reactions of the full and syncopated measures, the emphasis on the latter is unconsciously increased. In the accented form, as before, there is a clear discrimination into two grades of intensity (ratio of first three elements to final, 1.000:1.888) while in the unaccented no such broad separation exists (ratio of first three elements to final, 1.000:1.156).
The type of succession in each of these forms of reaction is a transformed dactylic, in which group should now be included the simple four-beat rhythm with final accent, which was found to follow the same curve. The group begins with a minor stress in both of the present forms, this stress being greater in the unaccented than in the accented type. This preponderance I believe to be due to the endeavor to repress the natural accent on the syncopated measure. In both forms the intensive value of the second element is less than that of the third, while the intensity of the initial reaction is greater than that of either of these subsequent beats. This form of succession I have called a transformed dactylic. It adheres to the dactylic type in possessing initial accentuation; it departs from the normal dactylic succession in inverting the values of the second and third members of the group. This inversion is not inherent in the rhythmic type. The series of three beats decreasing in intensity represents the natural dactylic; the distortion actually presented is the result of the proximity of each of these groups to a syncopated measure which follows it. This influence I believe to be reducible to more elementary terms. The syncopated measure is used to mark the close of a logical sequence, or to attract the hearer's attention to a striking thought. In both cases it is introduced at significant points in the rhythmical series and represents natural nodes of accentuation. The distortion of adjacent measures is to be attributed to the increase in this elementary factor of stress, rather than to the secondary significance of the syncopation, for apart from any such change in the rhythmical structure we have found that the reactions adjacent to that which receives accentual stress are drawn toward it and increased in relative intensity.
Further quantitative analysis of rhythmical sequences, involving a comparison of the forms of successive measures throughout the higher syntheses of verse, couplet and stanza, will, I believe, confirm this conception of the mutable character of the relations existing between the elements of the rhythmical unit, and the dependence of their quantitative values on fixed points and modes of structural change occurring within the series. An unbroken sequence of dactyls we shall expect to find composed of forms in which a progressive decrease of intensity is presented from beginning to end of the series (unless we should conceive the whole succession of elements in a verse to take shape in dependence on the point of finality toward which it is directed); and when, at any point, a syncopated measure is introduced we shall look for a distortion of this natural form, at least in the case of the immediately preceding measure, by an inversion of the relative values of the second and third elements of the group. This inversion will unquestionably be found to affect the temporal as well as the intensive relations of the unit. We should likewise expect the relations of accented and unaccented elements in the two-beat rhythms to be similarly affected by the occurrence of syncopated measures, and indeed to find that their influence penetrates every order of rhythm and extends to all degrees of synthesis.
To the quantitative analysis of the intensive relations presented by beaten rhythms must be added the evidence afforded by the apprehension of auditory types. When a series of sounds temporally and qualitatively uniform was given by making and breaking an electric circuit in connection with a telephone receiver, the members of a group of six observers without exception rhythmized the stimuli in groups--of two, three and four elements according to rate of succession--having initial accentuation, however frequently the series was repeated. When the series of intervals was temporally differentiated so that every alternate interval, in one case, and every third in another, stood to the remaining interval or intervals in the ratio, 2:1, the members of this same group as uniformly rhythmized the material in measures having final accentuation. In triple groups the amphibrachic form (in regard to temporal relations only, as no accentuation was introduced) was never heard under natural conditions. When the beginning of the series was made to coincide with the initiation of an amphibrachic group, four of those taking part in the investigation succeeded in maintaining this form of apprehension for a time, all but one losing it in the dactylic after a few repetitions; while the remaining two members were unable to hold the amphibrachic form in consciousness at all.
(b) The Distribution of Durations.
The inquiry concerning this topic took the direction, first, of a series of experiments on the influence which the introduction of a louder sound into a series otherwise intensively uniform exerts on the apparent form of the series within which it occurs. Such a group of experiments forms the natural preliminary to an investigation of the relation of accentuation to the form of the rhythm group. The apparatus employed was the fourth in the series already described. The sounds which composed the series were six in number; of these, five were produced by the fall of the hammer through a distance of 2/8 inch; the sixth, louder sound, by a fall through 7/8 inch. In those cases in which the intensity of this louder sound was itself varied there was added a third height of fall of two inches. The succession of sounds was given, in different experiments, at rates of 2.5, 2.2, and 1.8 sec. for the whole series. The durations of the intervals following and (in one or two cases) preceding the louder sound were changed; all the others remained constant. A longer interval intervened between the close and beginning of the series than between pairs of successive sounds. After hearing the series the subject reported the relations which appeared to him to obtain among its successive elements. As a single hearing very commonly produced but a confused impression, due to what was reported as a condition of unpreparedness which made it impossible for the hearer to form any distinct judgment of such relations, and so defeated the object of the experiment, the method adopted was to repeat each series before asking for judgment. The first succession of sounds then formed both a signal for the appearance of the second repetition and a reinforcement of the apperception of its material.
In order to define the direction of attention on the part of the observer it was made known that the factors to be compared were the durations of the intervals adjacent to the louder sound in relation to the remaining intervals of the series, and that all other temporal and intensive values were maintained unchanged from experiment to experiment. In no instance, on the other hand, did any subject know the direction or nature of the variation in those quantities concerning which he was to give judgment. In all, five subjects shared in the investigation, C., E., F., H. and N. Of these C only had musical training. In the tables and diagrams the interval preceding the louder sound is indicated by the letter B, that following it by the letter A. Totals--judgment or errors--are indicated by the letter T, and errors by the letter E. The sign '+' indicates that the interval against which it stands is judged to be greater than the remaining intervals of the series, the sign '=' that it is judged equal, and the sign '-' that it is judged less.
The first series of changes consisted in the introduction of variations in the duration of the interval following the loud sound, in the form of successive increments. This loud sound was at the third position in the series. All intensive relations and the duration of the interval preceding the louder sound remained unchanged. The results of the experiment are presented in the following table.
TABLE XXVIII.
Ratio of A to B A Errors Total Per cent. Other Intervals. + = - + = - B A T judgts. of errors
1.000 : 0.625 2 2 2 4 2 0 4 2 6 12 50 1.000 : 0.666 4 2 0 1 3 2 4 5 9 12 75 1.009 : 0.714 5 3 0 2 2 4 5 6 11 16 69 1.000 : 0.770 5 4 0 1 1 7 5 8 13 18 72 1.000 : 0.833 1 5 0 0 0 6 1 6 7 12 50
Totals, 17 16 2 8 8 19 19 27 46 70
The value of the interval following the louder sound is correctly reported eight times out of thirty; that preceding it is correctly reported sixteen times out of thirty. The influence which such a change in intensive value introduced at a single point in a series of sounds exerts on the apparent relation of its adjacent intervals to those of the remainder of the series is not equally distributed between that which precedes and that which follows it, but affects the latter more frequently than the former in a ratio (allowing latitude for future correction) of 2:1. In the case of interval A the error is one of underestimation in twenty-seven cases; in none is it an error of overestimation. In the case of interval B the error is one of overestimation in seventeen instances, of underestimation in two. The influence of the introduction of such a louder sound, therefore, is to cause a decrease in the apparent duration of the interval which follows it, and an increase in that of the interval which precedes it. The illusion is more pronounced and invariable in the case of the interval following the louder sound than of that preceding it, the proportion of such characteristic misinterpretations to the whole number of judgments in the two cases being, for A, 77 per cent.; for B, 54 per cent. The effect on interval A is very strong. In the second group, where the ratio of this interval to the others of the series is 3:2, it is still judged to be equal to these others in 50 per cent. of the cases, and less in 35 per cent. Further, these figures do not give exhaustive expression to the whole number of errors which may be represented in the judgments recorded, since no account is taken of greater and less but only of change of sign; and an interval might be underestimated and still be reported greater than the remaining intervals of the series in a group of experiments in which the relation of the interval in question to these remaining intervals ranged from the neighborhood of equivalent values to that in which one was double the other. If in a rough way a quantitative valuation of errors be introduced by making a transference from any one sign to that adjacent to it (e.g., - to =, or = to +) equal to one, and that from one extreme sign to the other equal to two, the difference in the influence exerted on the two intervals will become still more evident, since the errors will then have the total (quantitative) values of A 46, and B 19, or ratio of 1.000:0.413.
Next, the position of the louder sound in the series of six was changed, all other conditions being maintained uniform throughout the set of experiments. The series of intervals bore the following relative values: A, 0.900; B, 1.100; all other intervals, 1.000. The louder sound was produced by a fall of 0.875 inch; all others by a fall of 0.250 inch. The louder sound occurred successively in the first, second, third, fourth and fifth positions of the series. In the first of these forms it must of course be remembered that no interval B exists. The results of the experiment are shown in the following table:
TABLE XXIX.
Position Apparent Values. Errors. % of Errors Ditto in B A B A T in tot. judg. quant. Series + = - + = - B A B A 1 2 6 6 0 12 12 85.7 85.7 2 2 8 2 1 7 4 10 11 21 83.3 91.6 73.3 91.6 3 1 9 3 1 8 3 10 11 21 76.9 91.6 71.9 91.6 4 1 8 4 2 6 5 9 11 20 69.2 84.6 52.8 84.6 5 0 12 0 0 4 8 12 12 24 100.0 100.0 60.0 100.0 Totals, 4 37 9 6 31 26 41 57 98 82.3 90.7 64.5 90.7
Total judgments, 113; Errors (B = 31), A = 57.
The relatively meager results set forth in the preceding section are corroborated in the present set of experiments. That such a variation of intensity introduced into an otherwise undifferentiated auditory series, while it affects the time-values of both preceding and following intervals, has a much greater influence on the latter than on the former, is as apparent here as in the previous test. The number of errors, irrespective of extent, for the two intervals are: B, 82.3 per cent, of total judgments; A, 90.7 per cent. When the mean and extreme sign displacements are estimated on the quantitative basis given above these percentages become B, 64.5; A, 90.7, respectively--a ratio of 0.711:1.000.
The direction of error, likewise, is the same as in the preceding section. Since the actual values of the two intervals here are throughout of extreme sign--one always greater, the other always less--only errors which lie in a single direction are discriminable. Illusions lying in this direction will be clearly exhibited, since the differences of interval introduced are in every case above the threshold of discrimination when the disturbing element of variations in intensity has been removed and the series of sounds made intensively uniform. In case of a tendency to underestimate B or overestimate A, errors would not be shown. This problem, however, is not to be met here, as the results show; for there is recorded a proportion of 82.3 per cent. of errors in judgment of interval B, and of 90.7 per cent. in judgment of interval A, all the former being errors of overestimation, all of the latter of underestimation.
The influence of position in the series on the effect exerted by such a change of intensity in a single member can be stated only tentatively. The number of experiments with the louder sound in position five was smaller than in the other cases, and the relation which there appears cannot be absolutely maintained. It may be also that the number of intervals following that concerning which judgment is to be given, and with which that interval may be compared, has an influence on the accuracy of the judgment made. If we abstract from this last set of results, the tendency which appears is toward an increase in accuracy of perception of comparative durations from the beginning to the end of the series, a tendency which appears more markedly in the relations of the interval preceding the louder sound than in those of the interval which follows it. This conclusion is based on the succession of values which the proportion of errors to total judgments presents, as in the annexed table.
TABLE XXX.
Percentage of Errors for Each Position.
Interval. I II III IV V B. 83.3 76.9 69.2 (100) Irrespective A. 85.7 91.6 91.6 84.6 (100) of extent. B. 73.3 71.9 53.8 (60) Estimated A. 85.7 91.6 91.6 84.6 (100) quantitatively.
Next, the relation of the amount of increase in intensity introduced at a single position in such a series to the amount of error thereby occasioned in the apprehension of the adjacent intervals was taken up. Two sets of experiments were carried out, in each of which five of the sounds were of equal intensity, while one, occurring in the midst of the series, was louder; but in one of the sets this louder sound was occasioned by a fall of the hammer through a distance of 0.875 inch, while in the other the distance traversed was 2.00 inches. In both cases the extent of fall in the remaining hammers was uniformly 0.25 inch. The results are given in the following table:
TABLE XXXI.
Interval B.¹ Interval A. Ratio of Interval 0.875 in. 2.00 in. 0.875 in. 2.00 in. B to Interval A. + = - + = - + = - + = - 1.000 : 1.000 0 6 0 0 4 2 0 5 1 0 0 6 0.909 : 1.000 2 4 0 0 4 2 0 2 4 2 2 2 0.833 : 1.000 0 6 0 0 4 2 4 0 2 1 3 2 0.770 : 1.000 0 6 0 2 2 2 2 4 0 4 0 2 0.714 : 1.000 0 6 0 1 5 0 6 0 0 2 2 2 Totals, 2 28 3 19 8 12 11 7 9 7 14 T.E., T.J., 2 30 11 30 13 30 21 30 and per cent., 6.6% 36.6% 60.0% 70.0%
¹Interval B in these experiments is of the same duration as all others but that following the louder sound; hence, judgments in the second column are correct.
Again the markedly greater influence of increased intensity on the interval following than on that preceding it appears, the percentage of errors being, for B (both intensities), 21.6 per cent.; for A, 56.6 per cent. Also, in these latter experiments the direction of error is more definite in the case of interval A than in that of interval B.
The influence of changes in intensity on the amount of error produced is striking. Two intensities only were used for comparison, but the results of subsequent work in various other aspects of the general investigation show that this correlation holds for all ranges of intensities tested, and that the amount of underestimation of the interval following a louder sound introduced into an otherwise uniform series is a function of the excess of the former over the latter. The law holds, but not with equal rigor, of the interval preceding the louder sound. So far as these records go, the influence of such an increase of intensity is more marked in the case of interval B than in that of interval A. It is to be noted, however, that the absolute percentage of errors in the case of A is several times greater than in that of B. I conclude that A is much more sensitive than B to such influences, and that there is here presented, in passing from intensity I. to intensity II., the rise of conditions under which the influence of the louder sound on B is first distinctly felt--that is, the appearance of a threshold--and that the rate of change manifested might not hold for higher intensities.
Lastly, the rate at which the sounds of the series succeeded one another was varied, in order to determine the relation which the amount of influence exerted bore to the absolute value of the intervals which it affected. Three rates were adopted, the whole series of sounds occupying respectively 2.50 secs., 2.20 secs, and 1.80 secs. The results are summed in the following table:
TABLE XXXII.
Rate: 2.5 secs. Rate: 2.2 secs. Rate: 1.8 secs.
Ratio of Interval B B A B A B A to Interval A. + = - + = - + = - + = - + = - + = -
1.000 : 1.000 2 8 0 0 8 2 0 8 2 0 2 8 0 4 0 0 2 2 0.917 : 1.000 0 8 2 4 6 0 3 8 0 0 8 3 2 2 0 0 2 2 0.846 : 1.000 1 9 0 5 4 1 3 8 0 3 7 1 6 5 0 1 8 2 0.786 : 1.000 1 10 0 11 0 0 6 6 0 7 3 4 6 2 2 2 6 2 0.733 : 1.000 4 2 0 4 0 2 4 6 0 8 0 2 0.687 : 1.000 5 3 1 6 1 2 2 6 0 7 0 1
Totals 4 35 2 20 18 3 21 35 3 20 21 20 20 25 2 18 18 11*
*Transcriber's Note: Original "1".
These results are converted into percentages of the total number of judgments in the following table:
TABLE XXXIII.
Rate of B A Success. + = - Errors. + = - Errors. 2.5 secs 10 85 5 15 49 44 7 51 2.2 " 36 59 5 41 33 34 33 67 1.8 " 43 53 4 47 38 38 24 62
In the case of interval A the direction of the curve of error changes in passing from Rate II. to Rate III. In the case of interval B the increase is continuous.
This increase in the percentage of error is, further, distinctly in the direction of an accentuation of the overestimation of the interval B, as is shown in the percentage of cases in which this interval appeared greater than the rest of the series for each of the three rates.
If the three rates be combined in the one set of results, the difference in the effects produced on the interval following the louder sound and on that which precedes it becomes again apparent. This is done in the table below.
TABLE XXXIV.
B A B A Ratio + = - + = - T.E. T.J. % T.E. T.J. % I. 2 20 2 0 12 12 2 24 8.5 12 24 50.0 II. 5 18 2 4 16 5 5 25 20.0 21 25 84.4 III. 10 22 0 9 19 4 10 32 31.0 23 32 72.0 IV. 13 18 2 20 9 8 13 33 39.0 17 37 46.0 V. 8 8 0 12 0 4 8 16 50.0 4 16 25.0 VI. 7 9 1 13 1 3 7 17 41.0 4 17 24.0
The overestimation of the interval before the louder sound also tends to increase in extent with the actual increase in duration of the interval following that sound over the other intervals of the series.
Thus, the form which the sensible time-relations of such a limited series of sounds present is found to be intimately dependent on the intensive preponderance of certain elements within it, on the degree of increased stress which such elements receive, on their local position in the series, and on the rate at which the stimulations succeed one another. The knowledge of these facts prepares us for the whole series of relations manifested in the special quantitative investigations reported in the sections which follow. In the first of these is presented the time-relations obtaining among the successive reactions of the various rhythm types discussed in the preceding division of this part, the section, namely, on the distribution of intensities.
In the first group of reactions the series was not to be consciously accented, nor to be divided into groups by the introduction of pauses. The reactor was required only to conceive it as a succession of two-beat groups continuously repeated, the way in which the groups should be defined, whether by counting or otherwise, being left to his own discretion. The experimental group was composed of five subjects.
The following table presents the quantitative results of an analysis of the material in series of ten successive pairs of reactions, upon the basis of unity as the value of the first element.
TABLE XXXV.
Quantities. I II III IV V VI VII VIII IX X Whole Meas., 1.000 0.894 1.035 0.912 1.000 0.877 1.070 0.877 1.070 0.841 First Inter., 1.000 1.142 1.071 1.142 1.000 1.285 1.000 1.214 1.000 1.214 Second Inter., 1.000 0.837 1.023 0.860 1.000 0.744 1.093 0.767 1.093 0.790
Within the limits of the calculation no progressive change appears, either of acceleration or of retardation, whether in general or on the part of individual reactors. In narrower ranges the inconstancy of the periods is very marked, and their variations of clearly defined rhythmical character. The duration of the total measures of two beats is throughout alternately longer and shorter, the average of their values presenting a ratio of 1.000:0.847. The order of this arrangement, namely, that the longer period precedes the shorter in the larger group, is drawn from the fact that measurements consistently began with the initial reaction of the series.
An analysis of the constituent intervals of the unit group, as shown in the second and third lines of the table, reveals the existence of a complex subordinate rhythm. The two components of the rhythmical group do not increase and decrease concomitantly in temporal value in composing the alternate long and short measures of the fluent rhythm. The movement involves a double compensating rhythmical change, in which the two elements are simultaneously in opposite phases to each other. A measure which presents a major first interval contains always a minor second; one introduced by a minor first concludes with a major second. The ratios of these two series of periodic variations must themselves manifestly be different. Their values are, for the first interval of the measure, 1.000:1.214; and for the second interval, 1.000:0.764. The greater rhythmical differentiation marks the second of the two intervals; on the variations of this second interval, therefore, depends the appearance of that larger rhythm which characterizes the series. The ratios of these primary intervals are less consistently maintained than are those of the rhythmical measures built out of them. It will be noted that in both intervals there is a tendency for the value of the difference between those of alternate groups to increase as the tapping progresses. This change I have interpreted as indicative of a progressive definition in the process of rhythmization, depending on an increase in coördination and differentiation of the reactions as the series advances.
A simple stress on alternate elements was next introduced in the series, forming a simple trochaic measure repeated without interruption. The quantitative results follow, arranged as in the preceding experiment.
TABLE XXXVI.
Quantity. I II III IV V VI VII VIII IX X Measure, 1.000 1.035 1.070 1.035 1.087 1.070 1.071 1.052 1.070 1.070 1st Int., 1.000 1.000 1.111 1.000 1.055 1.111 1.166 1.111 1.111 1.111 2d Int., 1.000 1.025 1.051 1.051 1.102 1.051 1.025 1.025 1.051 1.051
Here again there is no progressive acceleration or retardation. The rhythmical differentiation of alternate measures is very slight--the average ratio of the first to the second being 1.000:0.993--but is of the same type as in the preceding. The excess in the amount of this differentiation presented by the first type of reaction over the second may be due to the presence of a tendency to impart rhythmical character to such a series of reactions, which, prohibited in one form--the intensive accent--finds expression through the substitution for this of a temporal form of differentiation.
In this trochaic rhythm the phases of variation in the constituent intervals of the measure are concomitant, and their indices of differentiation almost identical with each other. Their values are, for the first, 1.000:0.979; and for the second, 1.000:0.995. The higher index is that of the first interval, that, namely, which follows the accented beat of the measure, and indicates that the rhythmical change is due chiefly to a differentiation in the element which receives the stress.
In iambic measures similarly beaten out there is likewise no acceleration nor retardation apparent in the progress of the tapping. The temporal differentiation of alternate measures is of the same extent as in the preceding group, namely, 1.000:0.991. the proportional quantitative values of the measure and its constituent intervals, taken in series of ten successive repetitions, are as follow:
TABLE XXXVII.
Quantity I II III IV V VI VII VIII IX X Measure, 1.000 0.979 1.000 0.979 1.020 0.979 0.979 1.020 0.979 0.979 1st Int., 1.000 0.941 0.941 1.000 1.000 0.941 8.082 0.941 0.941 0.941 2d Int., 1.000 1.000 1.032 0.967 1.032 1.000 1.000 1.032 1.000 0.967
The alternation of greater and less duration in the rhythm groups is due to a variation in the time-value of the second interval only, the index of average change in the first member being zero. That is, the greater index of instability again attaches to that element which receives the stress. Though this holds true throughout these experiments, the amount of difference here is misleading, since on account of the smaller absolute value of the first interval the proportional amount of change within it which passes unrecorded is greater than in the case of the second interval.
In general, the larger temporal variations of the trochaic and iambic rhythm forms are too slight to be significant when taken individually. The evidence of rhythmical treatment in such a series of reactions, which is strongly marked in the unaccented form, nevertheless receives reinforcement from these inconsiderable but harmonious results.
The proportional values of the variations in alternate measures for accented and unaccented elements are given in the following table, in which the figures for the trochaic and iambic forms are combined:
TABLE XXXVIII.
Interval I II III IV V VI VII VIII IX X Accented, 1.000 1.000 1.083 1.000 1.041 1.000 1.083 1.000 1.041 1.000 Unacc. 1.000 1.000 1.000 1.035 1.071 1.000 0.964 1.000 1.000 1.000
It is perhaps worthy of note that in this table a still higher rhythmical synthesis of regular form appears in the accented elements if the figures be taken in series of four consecutive pairs of reactions.
In the group of triple rhythms next taken up--the dactylic, the amphibrachic and the anapæstic--each type presents an increase in the duration of the unit group between the beginning and end of the series, but without any regular curve connecting these terms. Neither the average results nor those of the individual subjects show anywhere a decrease of duration in the progress of the tapping. The proportional results for each of the three rhythm forms, and their averages, are given in the following table.
TABLE XXXIX.
Rhythm. I II III IV V VI VII VIII IX X Datyl., 1.000 1.062 1.062 1.087 1.087 1.075 1.125 1.112 1.125 1.112 Amphib., 1.000 1.000 1.000 1.069 1.085 1.046 1.046 1.046 1.046 1.035 Anapæs., 1.000 1.012 1.023 1.012 1.037 1.037 1.023 1.059 1.023 1.084
Average, 1.000 1.024 1.036 1.060 1.060 1.060 1.072 1.072 1.072 1.084
When all types and subjects are thus combined the summation of these inconstant retardations presents sharply differentiated terms and a curve uninverted at any point.
A separate analysis of the components of the rhythmical group shows, for the dactylic form, an important increase in duration in only one of the three intervals, namely, that following the element which receives accentual stress. The proportional values for these intervals follow.
TABLE XL.
Interval. I II III IV V VI VII VIII IX X First, 1.000 1.153 1.153 1.153 1.153 1.231 1.193 1.193 1.231 1.231 Second, 1.000 0.917 0.917 1.000 0.917 0.917 0.917 0.917 0.917 0.917 Third 1.000 1.000 1.033 1.066 1.055 1.066 1.133 1.066 1.066 1.066
Since the progressive variation does not penetrate the whole measure, but affects only a single constituent having a strongly marked functional character, the process of change becomes unlike that of true retardation. In such a case, if the increase in duration be confined to a single element and parallel the changes in a simultaneous variant of a different order, we should regard them as functionally connected, and therefore interpret the successively greater periods of time occupied by the rhythmical measures as constituting no real slowing of the tempo. The measure of relative tempo in such a case consists in the ratios of the successive durations of the rhythmical units after the subtraction of that element of increase due to this extraneous source. Here, since the increase is confined to that member of the group which receives accentual stress, and since the increase of accentuation is typically accompanied by an extension of the following interval, the changes presented do fulfil the conditions of a progressively increased accentuation of the rhythm group, and to this origin I think it is undoubtedly to be attributed. It is to be noted that the final interval also undergoes a slight increase, while the median suffers a similarly slight decrease in duration as the series progresses.
In the amphibrachic form the changes manifested by the constituents of the unit group are more obscure. No progressive retardation of the accented element is apparent. In the initial and final intervals the difference in duration between the first and last members of the series is small and appears early in the process. If we assume the general application of the laws of change presented in the preceding section, there should be here two influences concerned in the determination of the relations presented, the factors, namely, of position and accent. The falling of the accentual stress on the median interval eliminates one of the two factors of progressive reduction in that element and replaces it by a factor of increase, thereby doing away with the curve of change; while at the same time it decreases the changes which occur in the bounding intervals of the group by removing the accent from the first and by the proximate position of its own accent tending to reduce the last interval.
Under this same assumption there should be expected in the anapæstic form of rhythm an exaggeration of the progressive increase in the final interval, together with a further reduction in the duration of the initial; since from the falling of the accent on the final interval two factors of increase combine, while in the initial, which immediately follows the accented interval in the series, a positive factor of reduction appears. This is actually the type of change presented by the quantitative relations, which are given as proportional values in the following table.
TABLE XLI.
Interval. I II III IV V VI VII VIII IX X First, 1.000 0.950 1.000 0.950 1.000 0.950 1.000 1.000 1.000 1.050 Second, 1.000 1.100 1.000 1.050 1.100 1.000 1.000 1.050 1.100 1.000 Third, 1.000 1.073 1.073 1.024 1.024 1.122 1.098 1.098 1.098 1.146
Between its first and last terms the first interval shows a departure slightly less than that of the previous rhythm from the rate of change which characterizes the dactylic type; but if the average values of the whole series of intervals be taken in each of the three cases, the progressive reduction will be seen clearly to continue in passing from the second to the third form. The figures annexed give these averages as proportions of the first interval in the series.
TABLE XLII.
1st Av. of Rhythm. Interv. all others. Dactylic, 1.000 : 1.188 Amphibrachic, 1.000 : 1.019 Anapæstic, 1.000 : 1.000
The relations of the various intervals in the three forms are put together here for comparison:
TABLE XLIII.
Rhythm. 1st Interval. 2d Interval. 3d Interval. Dactylic, 1.000 : 1.231 1.000 : 1.000 1.000 : 1.066 Amphibrachic, 1.000 : 1.045 1.000 : 1.000 1.000 : 1.054 Anapæstic, 1.000 : 1.050 1.000 : 1.000 1.000 : 1.146
An analysis of the factors of accentual stress and of position in the rhythmical group in isolation from each other, confirms the assumptions already made as to their influence in defining the form of the rhythmic unit. Table XLIV. exhibits the series of temporal changes taking place in accented and unaccented intervals, respectively, for the three forms combined, and therefore independent of position in the group.
TABLE XLIV.
Interval. I II III IV V VI VII VIII IX X Accented. 1.000 1.064 1.064 1.064 1.064 1.094 1.094 1.064 1.094 1.129 Unaccented, 1.000 1.000 1.000 1.080 1.040 1.040 1.040 1.040 1.040 1.040
Similarly, in Table XLV. are given the proportional values of the series of intervals in order of their position in the group and independent of accentual stress:
TABLE XLV.
Interval. I II III IV V VI VII VIII IX X First, 1.000 1.043 1.087 1.043 1.087 1.043 1.043 1.121 1.043 1.121 Second, 1.000 1.000 1.000 1.043 1.000 0.956 1.000 0.956 1.000 0.956 Third, 1.000 1.028 1.028 1.055 1.028 1.083 1.083 1.083 1.083 1.083
The former table makes clear the predominance of the increase in the accented element over the average of all unaccented elements of the series; the latter shows the independence of increase in the initial and final, and of decrease in the median interval, of any relation to the position of the accentual stress. Both the intensive accentuation and the demarcation of successive groups thus appear to be factors of definition in the rhythmic unit. Those types which are either marked by a more forcible accent or separated by longer pauses are more distinctly apprehended and more easily held together than those in which the accent is weaker or the pause relatively less. It would follow that the general set of changes which these series of reactions present are factors of a process of definition in the rhythmical treatment of the tapping, and are not due to any progressive change in the elementary time relations of the series.
The figures for measures of four beats are incomplete. They show an increase in the average duration of the group from first to last of the series in three out of the four forms, namely, those having initial, secondary and final stress.
Of the relative amounts contributed by the several elements to the total progressive variation of the measures in the first form, the least marks those intervals which follow unaccented beats, the greatest those which follow accented beats; among the latter, that shows the greater increase which receives the primary accent, that on which falls the secondary, subconscious accent shows the less; and of the two subgroups which contain these accents that in which the major accent occurs contributes much more largely to the progressive change than does that which contains the minor.
When the phases of accented and unaccented elements are compared, irrespective of their position in the rhythmic group, the same functional differences are found to exist as in the case of triple rhythms. Their quantitative relations are given in the following table.
TABLE XLVI.
Phase. I II III IV V VI VII VIII IX X Accented. 1.000 1.103 1.069 1.172 1.241 1.139 1.206 1.310 1.241 1.310 Unacc., 1.000 1.083 1.128 1.169 1.159 1.208 1.169 1.250 1.169 1.169
The cause of the apparent retardation lies, as before, in a change occurring primarily in the accented elements of the rhythm, and this progressive differentiation, it is inferable from the results cited above, affects adjacent unaccented elements as well, the whole constituting a process more naturally interpretable as a functional accompaniment of progressive definition in the rhythmical treatment of the material than as a mark of primary temporal retardation.
The contribution of the several intervals according to position in the series and irrespective of accentual stress is given in the table following.
TABLE XLVII.
Interval. I II III IV V VI VII VIII IX X First, 1.000 1.136 1.136 1.182 1.227 1.227 1.227 1.273 1.318 1.318 Second, 1.000 1.042 1.042 1.125 1.166 1.042 1.042 1.083 1.083 1.166 Third, 1.000 1.150 1.250 1.250 1.250 1.250 1.400 1.400 1.450 1.450 Fourth, 1.000 1.059 1.059 1.147 1.179 1.147 1.179 1.294 1.206 1.179
A rhythmical alternation is here presented, the contributions of the first and third elements being far in advance of those of the second and fourth. The values of the minor pair are almost equal; of the major the third exceeds the first. Under the assumption already made this would indicate the existence at these points of nodes of natural accentuation, of which the second marks the maximum reached in the present series.
The determination of relative time-values for accented and unaccented intervals was next sought by indirect experimentation, in which the affective aspect of the experience was eliminated from consideration, and account was taken only of the perception of quantitative variations in the duration of the successive intervals. Proceeding from the well-known observation that if every alternate element of a temporally uniform auditory series receive increased stress, the whole series will coalesce into successive groups of two elements in which the louder sound precedes and the weaker follows, while the interval which succeeds the unaccented sound, and which therefore separates adjacent groups, will appear of greater duration than that which follows the accented element, the investigation sought by employing the method of right and wrong cases with a series of changing time-values for the two intervals to determine the quantitative proportion of the two durations necessary to produce the impression of temporal uniformity in the series.
Two rhythm forms only were tested, the trochaic and dactylic, since without an actual prolongation of considerable value in the interval following the louder sound, at the outset, no apprehension of the series as iambic or anapæstic could be brought about. The stimuli were given by mechanism number 4, the distance of fall being 2/8 and 7/8 inch respectively for unaccented and accented sounds. The series of changes included extreme proportional values of 0.714 and 1.769 in duration of the two intervals. Six persons took part in the investigation. In the following table is given the percentage of cases in which the interval following the unaccented element was judged respectively greater than, equal to, or less than that which followed the accented element, for each of the series of ratios presented by the time-values of the intervals in trochaic rhythm.
TABLE XLIX.
Ration of Unaccented to Unaccented Interval Judged to be Accented Interval. + = - 1.000 : 1.769 0.0 per cent. 100.0 per cent 0.0 per cent. 1.000 : 1.571 12.5 " 50.0 " 37.5 " 1.000 : 1.400 22.0 " 56.0 " 22.0 " 1.000 : 1.222 16.0 " 84.0 " 1.000 : 1.118 26.0 " 74.0 " 1.000 : 1.000 61.6 " 38.4 " 1.000 : 0.895 100.0 " 1.000 : 0.800 88.8 " 11.2 " 1.000 : 0.714 100.0 "
The anomalous percentage which appears in the first horizontal row needs explanation. The limit of possible differentiation in the time-values of accented and unaccented intervals in a rhythmical group is characteristically manifested, not by the rise of a perception of the greater duration of the interval following the accented element, but through an inversion of the rhythmical figure, the original trochee disappearing and giving place to an iambic form of grouping, the dactyl being replaced by an anapæst. In the case in question the inversion had taken place for all subjects but one, in whom the original trochaic form, together with its typical distribution of intervals, remained unchanged even with such a great actual disparity as is here involved.
For this group of observers and for the series of intensities taken account of in the present experiment, the distribution of time-values necessary to support psychological uniformity lies near to the ratio 1.400:1.000 for accented and unaccented intervals respectively, since here the distribution of errors in judgment is arranged symmetrically about the indifference point. Overestimation of the interval following the louder sound appears by no means invariable. Under conditions of objective uniformity the judgment of equality was given in 38.4 per cent, of all cases. This cannot be baldly interpreted as a persistence of the capacity for correct estimation of the time values of the two intervals in the presence of an appreciation of the series as a rhythmical group. The rhythmic integration of the stimuli is weakest when the intervals separating them are uniform, and since the question asked of the observer was invariably as to the apparent relative duration of the two intervals, it may well be conceived that the hearers lapsed from a rhythmical apprehension of the stimuli in these cases, and regarded the successive intervals in isolation from one another. The illusions of judgment which appear in these experiences are essentially dependent on an apprehension of the series of sounds in the form of rhythmical groups. So long as that attitude obtains it is absolutely impossible to make impartial comparison of the duration of successive intervals. The group is a unit which cannot be analyzed while it continues to be apprehended as part of a rhythmical sequence. We should expect to find, were observation possible, a solution of continuity in the rhythmical apprehension in every case in which these distortions of the normal rhythm form are forced on the attention. This solution appears tardily. If the observer be required to estimate critically the values of the successive intervals, the attention from the outset is turned away from the rhythmical grouping and directed on each interval as it appears. When this attitude prevails very small differences in duration are recognized (e.g., those of 1.000:1.118, and 1.000:0.895). But when this is not the case, the changes of relative duration, if not too great for the limits of adaptation, are absorbed by the rhythmical formula and pass unobserved, while variations which overstep these limits appear in consciousness only as the emergence of a new rhythmic figure. Such inversions are not wholly restricted by the necessity of maintaining the coincidence of accentuation with objective stress. With the relatively great differences involved in the present set of experiments, the rhythmical forms which appeared ignored often the objective accentuation of single groups and of longer series. Thus, if the second interval of a dactyl were lengthened the unaccented element which preceded it received accentuation, while the actual stress on the first sound of the group passed unobserved; and in a complex series of twelve hammer-strokes the whole system of accentuation might be transposed in the hearer's consciousness by variations in the duration of certain intervals, or even by simple increase or decrease in the rate of succession.[6]
[6] Bolton found one subject apperceiving in four-beat groups a series of sounds in which increased stress fell only on every sixth.
In the experiments on dactylic rhythm the changes introduced affected the initial and final intervals only, the one being diminished in proportion as the other was increased, so that the total duration of the group remained constant. The figures, arranged as in the preceding table, are given in Table L.
The percentage given in the case of the highest ratio is based on the reports of two subjects only, one of them the exceptional observer commented on in connection with two-beat rhythms; for all other participants the anapæstic form had already replaced the dactylic. The distribution of values which supports psychological uniformity in this rhythmic figure lies between the ratios 1.166, 1.000, 0.800, and 1.250, 1.000, 0.755, since in this region the proportion of errors in judgment on either side becomes inverted. The two rhythmic forms, therefore, present no important differences[7] in the relations which support psychological uniformity. A comparison in detail of the distribution of judgments in the two cases reveals a higher percentage of plus and minus, and a lower percentage of equality judgments throughout the changes of relation in the dactylic form than in the trochaic. This appears to indicate a greater rhythmical integration in the former case than in the latter. On the one hand, the illusion of isolation from adjacent groups is greater at every point at which the intervening interval is actually reduced below the value of either of the internal intervals in the dactylic than in the trochaic rhythm; and on the other, the sensitiveness to differences in the whole series is less in the case of the trochee than in that of the dactyl, if we may take the higher percentage of cases in which no discrimination has been made in the former rhythm as a negative index of such sensibility.
[7] The ratios of initial to final intervals in the two cases are, for trochaic measures, 1.400:1.000, and for dactylic, 1.400(to 1.666):1.000.
TABLE L.
Ration of Unaccented Unaccented Interval Judged to be to Accented Interval. + = - 1.000 : 2.428 100.0 per cent 1.000 : 2.000 20.0 per cent. 33.3 per cent 46.7 " 1.000 : 1.666 33.2 " 23.9 " 42.9 " 1.000 : 1.400 39.0 " 46.0 " 15.0 " 1.000 : 1.182 60.0 " 37.2 " 2.8 " 1.000 : 1.000 85.4 " 12.2 " 2.4 " 1.000 : 0.846 89.2 " 10.8 " 1.000 : 0.714 100.0 " 1.000 : 0.660 96.0 " 4.0 "
The increase in the number of inverted forms which occur is coördinated percentually in the following table with the successive increments of difference between the accented and unaccented intervals of the group:
TABLE LI.
Rhythm. 2.428 2.000 1.769 1.666 1.571 1.400 1.222 1.182 1.118 1.000 Trochaic, 93.7 74.0 44.2 25.0 25.0 2.9 Datylic, 93.6 54.0 39.4 18.4
These figures are corroborative of the preceding conclusions. The dactylic figure is maintained in the presence of much greater differences in the relative durations of accented and unaccented intervals than is the trochaic. In the latter, inversions not only appear earlier in the series, but become the (practically) exclusive mode of apprehension at a point where not fifty per cent, of the dactyls have suffered transformation. At a certain definite stage in the process the tendencies toward the two forms of apprehension balance each other, so that with the slightest change in direction of attention the rhythmical figure inverts and reverts to the original form indifferently. These points are defined, in the case of the two rhythms here reported on, by the following (or intermediate) ratios: Trochaic-Iambic, (1.400-1.571): 1.000; Dactylic-Anapæstic, (1.666-2.000): 1.000.
The temporal conditions of such equilibrium are a strict function of the degree of accentuation which the rhythm group presents. The location of the indifference point must, therefore be independently determined for each intensive value through which the accented element may pass. Its changes are given for five such increments in the following table, in which the values of the various intervals are represented as proportions of the absolute magnitudes which appear in the first, or undifferentiated series.
TABLE LII.
Intensive Form. 1st Interval. 2d Interval. 3d Interval. 1/8 1/8 1/8 1.000 1.000 1.000 3/8 1/8 1/8 1.042 1.010 0.948 7/8 1/8 1/8 1.142 1.021 0.862 15/8 1/8 1/8 1.146 1.042 0.808 24/8 1/8 1/8 1.291 1.000 0.708
IV. THE COMBINATION OF RHYTHMICAL GROUPS IN HIGHER SYNTHESES AND THEIR EQUIVALENCES.
In the elaboration of higher rhythmical forms the combination of formally identical groups is rather the rule than the exception, since in poetical structures the definition of the metrical form and the maintenance of its proper relations depend on a clear preponderance of its own particular unit-type over local variants. In the experimental investigation of composite rhythm forms the temporal relations of structures presenting such likeness in their constituent groups were first taken up. In the conduct of the research those differences of intensity which are actually expressed and apprehended in the utterance of a rhythmic sequence were uniformly employed. While there is no doubt that a succession of perfectly identical forms would, under the requisite temporal conditions, be apprehended as presenting major and minor phases of accentuation, yet in the expression of rhythmic relations the subordination of accents is consistently observed, and all our ordinary apprehension of rhythm, therefore, is supported by an objective configuration which fulfils already the form of our own subjective interpretation.
The temporal relations of these major and minor phases cannot be considered apart from the index of their respective accentuations. As the distribution of elements within the simple group fluctuates with the changes in intensive accentuation, so does the form of temporal succession in larger structures depend on the relations of intensity in their primary and secondary accentuations. The quantitative values hereafter given apply, therefore, only to those specific intensities involved in the experiment. Two types were chosen, the trochee and the dactyl. The series of sounds was given by successive hammer-falls of 7/8 and 1/8 inch for the major, and 3/8 and 1/8 inch for the minor phase. The distribution of time-values within each group was made on the basis of previous experimentation to determine those relations which support psychological uniformity. These internal relations were maintained unchanged throughout the series of ratios which the durations of the two groups presented. Four subjects took part in the experiment. The quantitative results in the composition of trochaic forms are given in the following tables (LIII., LIV.), the figures of which present, in the form of percentages of total judgments, the apprehension of sensible equality or disparity in the two groups.
In the earlier set of experiments the series of ratios diverged in both directions from unity; in the later it departed in one only, since every divergence in the opposite direction had, in the previous experiments, been remarked at once by the observer. In this second set the series of differences is more finely graded than in the former; otherwise the two sets of figures may be considered identical. Using the equilibrium of errors as an index of sensible equality, the two trochaic groups are perceptually uniform when the temporal ratio of major and minor lies between 1.000:0.757 and 1.000:0.779.
TABLE LIII.
Ratio of Duration 2d Group Judged to be of 1st Group to 2d. + = - 1.000 : 1.250 100 per cent. 1.000 : 1.116 100 " 1.000 : 1.057 100 " 1.000 : 1.000 100 " 1.000 : 0.895 68 " 22 per cent. 1.000 : 0.800 25 " 75 " 1.000 : 0.714 100 per cent.
TABLE LIV.
Ratio of Duration 2d Group Judged to be of 1st Group to 2d. + = - 1.000 : 1.000 100.0 per cent. 1.000 : 0.973 87.5 " 12.5 per cent. 1.000 : 0.870 66.6 " 33.3 " 1.000 : 0.823 33.3 " 22.2 " 44.4 per cent. 1.000 : 0.777 50.0 " 50.0 " 1.000 : 0.735 33.3 " 33.3 " 33.3 " 1.000 : 0.694 33.3 " 66.6 "
In the dactylic form, as in the second trochaic series, ratios varying from unity in one direction only were employed. The results follow:
TABLE LV.
Ratio of Duration Second Group Judged to be of 1st Group to 2d. + = - 1.000 : 1.000 100.0 per cent. 1.000 : 0.946 62.5 " 37.5 per cent. 1.000 : 0.915 33.3 " 66.6 " 1.000 : 0.895 8.3 " 33.3 " 58.3 per cent. 1.000 : 0.800 40.0 " 60.0 "
As in the preceding case, when relations of equality obtained between the two subgroups, the secondary period in every instance appeared longer than the primary. This prolongation was uniformly reported as displeasing. The distribution of values which here support psychological uniformity lies between 1.000:0.915 and 1.000:0.895, that is to say, the difference of phases is less marked than in the case of the simpler trochaic composite. This is a structural principle which penetrates all rhythmical forms. The difference in the case of both of these composites is less than in the opposition of phases within the simple group, in which for identical intensities and (practically) the same group of observers these presented the ratio 1.000:0.714. It is evident that the relative differentiation of accented and unaccented intervals due to specific variations in intensity is greater than is that of successive groups characterized by similar differences of accentual stress; and if still more extensive groups were compared it would unquestionably be found that a further approximation to equality had taken place.
In the integration of rhythmical groups this subordination of the intensive accents which characterize them is not the sole mechanism of higher synthesis with which we are presented. Another mode is the antithesis of rhythmical quantities through verse catalepsis. Such variation of the rhythmical figure can take place in two directions and in two only: by an increase in the number of constituents, giving what may be called redundancy to the measure, and by a decrease in their number, or syncopation. Each of these forms of departure from the typical figure fulfils a specific rhythmic function which determines its temporal and intensive characters, and its local position in the rhythmical sequence.
(a) Redundant Measures.--The position of such a measure is uniformly initial. On rare occasions individual observers reported an inversion of this order in the earlier portion of the series,[8] but in no case were subjectively formulated series concluded in this way; and when the objective succession ended with the redundant measure the experience was rhythmically displeasing. In accentual stress the redundant measure is of secondary rank, the chief intensity falling upon the shorter, typical groups. Variation from the type does not, therefore, unconditionally indicate a point of accentual stress, though the two are commonly connected.
[8] This was probably due to beginning the series of stimulations with the typical measure. Such beginning was always made by chance.
In regard to the relative duration of the redundant measure the subjective reports indicate a large variability. The dactylic form appears to be slightly longer than the trochaics among which it appears; but not infrequently it is shorter.[9] These variations are probably connected with differences in stress due to the relation which the measure bears to the accentual initiation of the whole series; for this accent apparently may fall either within the redundant measure itself or on the first element of the succeeding ___ _____ >/ \ > | | > > group, thus: | q q q; q q; |, or | e e e q q; q q |. \_/
[9] The only form taken up was the occurrence of dactylic measures in trochaic series.
Two rhythm forms were analyzed, the trochaic and the dactylic, the series of sounds being given by hammer-falls of 7/8 and 1/8 inch for accented and unaccented elements respectively. In each experiment full and syncopated measures alternated regularly with each other in continuous succession, giving the forms
> > > > | q. q; q % | and | q. q q; q. % % |. \_____/ \____________/
The initiation of the series was in every case determined by chance. Six observers took part in the work with trochaic forms, five in that with dactylic. The quantitative results are given in the following tables, in each of which the relations of duration, position and stress are included.
TABLE LVI.
TROCHAIC FORM. Apparent Accentuation Ratio of 1st Second Group Judged to be 2d Group of Second Group. to 2d Group. + = - Final + = - 1.000:1.000 55.5% 44.4% 100% 71.5% 28.5% 1.000:0.946 83.3 16.6% 100 30.0 70.0 1.000:0.895 66.6 11.1 22.2 100 30.0 60.0 10.0% 1.000:0.846 16.6 41.6 41.6 100 40.0 60.0 1.000:0.800 16.6 41.6 41.6 100 40.0 60.0 1.000:0.756 49.9 24.9 24.9 100 40.0 60.0 1.000:0.714 16.6 41.6 41.6 100 20.0 80.0
TABLE LVII.
DACTYLIC FORM. Apparent Accentuation Ratio of 1st Second Group Judged to be 2d Group of Second Group. to 2d Group. + = - Final + = - 1.000:1.000 100.0% 100% 40.0% 60.0% 1.000:0.946 83.3% 16.6% 100 40.0 60.0 1.000:0.895 66.6 33.3 100 20.0 80.0 1.000:0.846 37.5 62.5 100 40.0 60.0 1.000:0.800 100.0 100 40.0 60.0
The syncopated measure, like the redundant, bears to the acatalectic group specific relations of duration, accentual stress, and position in the rhythmical sequence. In position it is final. This relation is independent of the factor of duration, on which the order of elements in the simple measure depends. Even the excessive shortening which occurs in the trochaic form, when the full measure has a duration almost one and one half times as great as the syncopated, brings about no inversion of the order.
In duration the syncopated group is a shortened measure. The amount of reduction necessary to preserve rhythmical proportion with the rest of the sequence is greater in the trochaic than in the dactylic form, as in the relation of accented to unaccented elements in the simple measure it is greater than in the case of the trochaic, a principle of structure which has already been pointed out.
There is similar evidence in beaten rhythms to show that when a full measure is elided, the pause which replaces it is of less value than the duration of a syncopated measure. When trochaic rhythms were beaten out with a distinct pause after each measure, the relative values of the two intervals were 1.000:2.046. Such a pause cannot be equivalent to a suppressed beat and its interval; I regard it as functionally equal to a whole measure. If that value be allowed for the second interval which it possesses in the same rhythm type when no pause is introduced, namely, 1.000:0.920, the first two intervals will have a value--in terms of linear measurement--of 1.93 + 1.77 or 3.70. The value of the suppressed measure would therefore be 2.15, a ratio of acatalectic to elided group of 1.000:0.581.
Iambic rhythm beaten out without separating pauses presents the following ratio between first and second intervals, 1.000:1.054; on the introduction of a pause between the measures the ratio becomes 1.000:2.131. The assignment of these proportional values gives 1.68 + 1.77, or 3.45, as the duration of the first two intervals, and 1.81 for the pause, a ratio of 1.00:0.524.
In continuous dactylic tapping, the values of the successive intervals are 1.000; 0.756; 0.927; with a separating pause their relations are 1.000; 0.692; 1.346. These being analyzed as before, the elided measure will have the relative value of 0.419. This shows a decline in the proportional duration of the elision as the total value of the measure elided increases. There can be little question that this principle applies also to the value of elisions of higher rhythmic structures as well.
In intensity the syncopated measure is a point of increased accentual stress. This relation is not constantly maintained in the trochaic form, in which at one ratio the accent appears reduced;[10] in the dactylic form divergences are all in the direction of an apparent increase in accentuation. In rhythms beaten out the form of succession > . > > was always prescribed (e.g., | q. q; q_% | or | q. %; q. q|, but not \______/ \________/ either at the subjects' preference), so that no material was there afforded for a determination of the primacy of particular figures; but the results must of course show any tendency which exists toward an increased accentuation of the syncopated measure. It needs but a cursory reference to the statements of these results in Pt. III., B, of this paper, to observe how constant and pronounced this tendency is.[11]
[10] This result is clearly irregular, and is probably due to the effect of accidental variations on a meager series of judgments. The number of these was three for each observer, making eighteen judgments in all the basis of each percentage in the table.
[11] The subjective notes of the observers frequently refer to this as an explicitly conscious process, the nature of the rhythmical sequence requiring a greater stress at that point than elsewhere. Extracts are appended:
Trochaic Syncopation.--"There is almost a necessity for an accent on the last beat." "... an almost imperative tendency to emphasize the final syllable beyond the rest." "The two taps were followed by a pause and then a tap with increased pressure." "This was not satisfactory with any adjustment of time relations so long as the stress of all three beats was the same. In attempting to make them all equal I almost involuntarily fell into the habit of emphasizing the final one."
Dactylic Syncopation.--"In this series it was easy to lay stress on the last (beat) ... this is the natural grouping; I unconsciously make such." "... of these the heavy one (accented syncopation) was much more satisfactory." "It was constantly my tendency to increase the strength of the last tap." "In this it is natural for me to make the final stroke heavy. To make the second group balance the first by equalizing the time alone is less satisfactory than by introducing elements of both time and force." "I felt that the latter part of the rhythm (unaccented syncopation) was lacking in force. Something seemed continually to be dropped at the end of each group."
The reactors frequently repeated the full measure several times before introducing the syncopated measure, which thus brought a series to its close. It will probably be found that in the actual construction of poetic measures the syncopated or partially syncopated foot is systematically introduced coincidently with points of rhythmical or logical pause.
Conclusive evidence of the integration of simple rhythm forms in higher structures is presented by the process of increasing definition which every rhythmical sequence manifests between its inception and its close. This process is manifested equally in the facts of sensory apprehension and those of motor reproduction of rhythm forms. On the one hand, there is a progressive refinement in the discrimination of variations from temporal uniformity as the series of stimulations advances; and correspondingly, the sequence of motor reactions presents a clearly marked increase in coördination taking place parallel with its progress. A rhythmical form is thus given to the whole succession of simple measures which are included within the limits of the larger series, a form which is no less definite than that exhibited by the intensive and temporal relations of the rhythmical unit, and which, there can be little doubt, is even more important than the latter in determining the character of the rhythm experience as a whole.
The presentation of experimental results bearing on this point will follow the lines already laid down. Only that part of the material which is derived from the apprehension of sensory rhythm forms can be applied to the determination of this formal curve for the ordinary metrical types and their complications. The facts of progressive coördination presented by beaten rhythms are based on the repetition of simple forms only. The completion of the evidence requires a quantitative analysis of the temporal relations presented by the whole sequence of integrated measures which compose the common verse forms: dimeter, trimeter, etc. This matter was not taken up in the present investigation.
The perception of variations in the measures of an iambic pentameter line was first taken up. The series of sounds was produced by the fall of hammer, the distances traversed being, for the accented elements 0.875 inch, and for the unaccented, 0.250 inch. The series was followed by a pause equal to one and a half measures, and was repeated before judgment was made. The time occupied by the series of sounds was 2.62 seconds. The intervals between the successive sounds were adjusted on the basis of previous experimentation concerning the most acceptable relations between the durations of accented and unaccented intervals. Their values were in the ratio 1.000:0.714 for accented and unaccented respectively. The variations were introduced in a single element, namely, the interval following the accented beat of the group, which, in this form of rhythm, is also the inter-group interval. This interval was changed by successive increments of one seventh its original value, or one twelfth the duration of the whole measure. Four such additions were made, the final value of the interval standing to its original duration in the ratio 1.000:0.636. The same series of changes in the duration of the accented interval was made successively in each measure of the pentameter series. In all these experiments the subjects were in ignorance of the character and position of the changes introduced. The results appear in the annexed table.
TABLE LVIII.
Position in Series. Percentage Values. Ratios. I II III IV I II III IV 1.000 : 1.000 0 0 0 0 0 0 0 0 1.000 : 0.874 4 4 4 7 40 40 40 70 1.000 : 0.777 6 6 8 10 60 60 80 100 1.000 : 0.700 6 6 10 10 60 60 100 100 1.000 : 0.636 6 6 10 10 60 60 100 100
In the five horizontal rows on the left of the table are set down the number of times, out of a total of ten judgments, the interval in question was perceived to be greater than the like interval in other groups, under the original relation of uniformity and for the four successive increments. On the right these numbers are given as percentages of the whole number of judgments. These figures show an increase of discriminative sensibility for such changes as the series advances. The percentage of correct discrimination, as it stands in the table, is the same for the first and second positions in the line, but this coincidence is to be attributed to accident, in consequence of the relatively small number of judgments on which the results are based, rather than to a functional indifference in the two positions. I conclude that fuller experiments would show a curve of continuous increase in the number of correct judgments for the whole series of measures here included. If we number the series of ratios given above from one to five, the thresholds of perceptible change for this series of positions, expressed in terms of this numerical series, would be: I., 4.1; II., 4.1; III., 3.9; IV., 3.6.
Secondly, in a series of five trochaic measures, the intervals separating the groups--which in this case follow the unaccented beat--were successively lengthened by increments identical with those employed in the preceding set of experiments. The results are presented in the table below, arranged similarly to the previous one.
TABLE LIX.
Position in Series. Percentage Values. Ratios. I II III IV I II III IV 1.000 : 1.000 0 0 0 0 0.0 10.0 0.0 0.0 1.000 : 0.874 1 1 3 4 16.5 16.5 50.0 60.0 1.000 : 0.777 4 4 5 6 66.0 66.0 83.0 100.0 1.000 : 0.700 6 6 6 6 100.0 100.0 100.0 100.0 1.000 : 0.636 6 6 6 6 100.0 100.0 100.0 100.0
These results are essentially identical with those of the preceding section. The sensitiveness to small differences in duration within the rhythmical series becomes continuously greater as that series proceeds. The thresholds of perceptible change in terms of the numerical series of ratios (as in preceding paragraph) are as follows: I., 4.0; II., 4.0; III., 3.7; IV., 3.6.
Finally, the intensity of the preceding sound was increased as well as the duration of the interval separating it from the following stroke. The measure employed was the trochaic, the interval suffering change was that following the accented beat--in this case, therefore, the intra-group interval. The relations obtaining among the unchanged measures were, as to duration of accented and unaccented elements, 1.000:0.714; as to intensity, 0.875:0.250 inch. Instead of a series, as in the preceding experiments, only one change in each direction was introduced, namely, an increase in duration of a single accented element of the series from 1.000 to 1.285, and an increase of the same element in intensity from 0.875 to 1.875 inch fall. The results are given in the annexed table:
TABLE LX.
Duration. Stress. Position Interval Following Louder in Series. Judged to be Increased Stress. + = - Times Noted. Not Noted. I. 8 per cent. 92 per cent. 0 per cent. 40 per cent. 60 per cent II. 42 " 50 " 8 " 42 " 58 " III. 57 " 36 " 7 " 54 " 46 " IV. 67 " 26 " 7 " 62 " 38 " V. 30 " 40 " 40 " 60 " 40 "
The figures show that in regard to the discrimination of changes in duration occurring in intervals internal to the rhythm group, as well as in the case of intervals separating adjacent groups, there is a progressive increase in sensibility to variations as the succession of sounds advances. This increased sensitiveness is here complicated with another element, the tendency to underestimate the duration of the interval following a louder sound introduced into a series. The influence of this second factor cannot be analyzed in detail, since the amount of underestimation is not recorded unless it be sufficient to displace the sign of the interval; but if such a quantitative method be applied as has already been described, the results show a continuous decrease in the amount of underestimation of this interval from the first position to the fourth, or penultimate, which presents the following relative values: 92, 66, 50, 40. A phase of rapid increase in the amount of underestimation appears in the fifth or final position, represented on the above scale of relative values by 120. This falling off at the end of the series, which appeared also in previous experiments, can be attributed only to an interference with the functions which the several measures bear in the process of comparison, and indicates that the accuracy of judgment is dependent on a comparison of the measure or element in question with those which follow as well as with those which precede it.
The results presented in the preceding section form the statement of but one half the evidence of higher rhythmical synthesis afforded by the material of the present investigation. We turn now to the second set of results. It deals, in general, with the quantitative relations of rhythmic forms which find expression through finger reactions. Portions of this evidence have already been presented, through motives of economy, in connection with the discussion of the phases of differentiation in intensity and duration which such beaten rhythms manifest. The burden of it, however, is contained in the results of an analysis, form by form, of the proportional mean variations which characterize these types of rhythmic expression. This method has been applied to a study (a) of the characters of the constituent intervals of the unit, in their relation to accentuation and position; (b) of the simple group which these elements compose; and (c) of the forms of higher synthesis manifested by the variations in successive groups. The first of these relations concerns, indeed, only the internal organization of the simple group, and has no direct bearing on the combination of such groups in higher syntheses; but, again for the sake of economy, the items are included with the rest of the material.
The application of such a method, as in all treatment of material by mean variations, involves much labor,[12] and on that account alone the lack of its employment to any considerable extent in previous investigations may be excused; but to this method, as it seems to me, must the final appeal be made, as an indisputable means by which all questions concerning the refined features of rhythmical organization, the definition of units and the determination of the forms in which they enter into larger rhythmic quantities, are to be settled.
[12] In connection with this work some 48,000 individual measurements were made (for the transcription of which I am indebted to the patient assistance of my wife). Half of these were measurements of the intensity of the successive reactions; the other half, of the intervals which separated them. The former series has been employed in obtaining the averages which appear in the section on the distribution of intensities; the latter in that on the distribution of durations. The determination of mean variations was made in connection with the second series only (24,000). These quantities were combined in series of single groups, and in series of two, four, eight and ten groups, and for each of these groupings severally the mean variation of the series was computed.
Of all the possible forms of rhythmic apprehension or expression, the material for such a statistical inquiry is most readily obtainable in the form of a series of finger reactions, and to such material the application of the method in the present investigation has been restricted.
In the first experiment of this group the reactor was asked to tap out a series in which temporal, but not intensive variations were introduced; the strokes were to be of uniform strength but separated into groups of two beats. No directions as to length of pause between the successive groups were given, but the whole form of the groups was to be kept absolutely constant. The reports of the subjects were uniformly to the effect that no accent had been introduced. At a cursory examination no intensive grouping was apparent. These records were the earliest analyzed, when only time relations were in mind, and no measurements were made of variations in strength. Only the mean variations of the intervals, therefore, will here be taken up.
A word first as to the relative value of the two intervals and its significance. The form of a rhythmical series is determined in every part by subordination to principles of strict temporal arrangement. Every suppression of elements in such a series, every rest and syncopated measure has as positive and well-defined a function as have the successive reactions and their normal intervals. If such a pause is made as we find introduced in the present case, its value must be a fixed function of the system of durations of which it forms a part, whether it replace an element in a rhythmical unit, or a subgroup in a higher rhythmical quantity. In general, the value of such a rest is less than the duration of a corresponding full measure or interval. For example, the syncopated forms | >q % | and | >q % %| are demonstrably of shorter average duration than the corresponding measures| >q q | and | >q q q|; and the pause occurring at the close of a syncopated line--such as that in the middle of a catalectic trochaic tetrameter--should be found of less value than that of the regular foot.
In the present instance two reactions are made, a pause follows, then the reactions take place again, and so on. The intervals separating successive groups of reactions thus result from the coalescence of two periods, the interval which would regularly follow the reaction and the additional pause at its close. The value of the latter I interpret as functionally equivalent to a group of two beats and not to a single interval; that is, the rhythm beaten out is essentially quadruple, the second member of each composite group being suppressed, as follows: > | q q; % % |. \______/
To estimate the proper value of such a rest the average relative duration of first and second intervals was taken in a continuous series of two-beat measures, in which the first member was accented sufficiently to define the rhythmical groups. The ratio was 1.000:0.760. In the present instance the values of the simple initial interval and the composite interval which follows it are, in terms of the linear measurement, 1.55 mm. and 3.96 mm. Assuming the above ratio to hold, the duration of a period which included the second beat-interval and a group-rest should be 1.16 + 1.55 + 1.16 = 3.87 mm. This is slightly less than the actual value of the period, whereas it should be greater. It must be remembered, however, that the disparity between the two intervals increases with initial accentuation, and in consequence the proportional amounts here added for the second interval (1.16 to 1.55) should be greater. This interval is not rhythmically 'dead' or insensitive. The index of mean variation in all reactors is greater for the first than for the second interval (or interval + pause) in the ratio 1.000:0.436, that is, the value of the latter is more clearly defined than that of the former, and the reactor doubly sensitive to variations occurring within it.
An analysis of the variations of these intervals separately in series of four groups reveals a secondary reciprocal rhythm, in which the changes in value of the mean variation at any moment are in opposite directions in the two intervals. These values in percentages of the total duration of the periods are given in the following table.
TABLE LXI.
Interval. 1st Group. 2d. Group. 3d Group. 4th Group. First, 15.4 per cent. 26.4 per cent. 13.8 per cent. 30.3 per cent. Second, 12.4 " 7.0 " 9.6 " 7.5 "
Without measurement of their intensive values, interpretation of these variations is speculative. They indicate that the pairs of beats are combined in higher groups of four; that the differences of mean variation in the first interval are functions of an alternating major and minor accentuation, the former occurring in the second and fourth, the latter in the first and third; and that the inversely varying values of the mean variation in the second interval are functions of the division into minor and major groups, the reduced values of the second and fourth of these intervals being characteristic of the greater sensitiveness to variations occurring in the group pause than to changes occurring within the group.
The fixity of the group is markedly greater than that of the simple interval. In the one case in which the mean variation of the group is greater than that of the elementary period the material involved was meager (five instead of ten repetitions) and the discrepancy therefore insignificant.
The difference in the mean variation of the first and second intervals respectively rises to an individual maximum of 3.000:1.000, and averages for all subjects 2.290:1.000; the fixity, that is to say, of the inter-group interval in this form of tapping is more than twice as great as that of the intra-group interval. The fixity of the larger rhythmical quantities is greater than that of the smaller, whether the relation be between the elementary interval and the unit group, or between the synthetic unit and its higher composite. The average mean variation of the beat intervals exceeds that of the whole group in the relation of 1.953:1.000. The differentiation of larger and smaller groups is less clear. When the material is taken in groups of eight successive beats the mean variation is less in the case of every subject than when taken in fours, in the ratio 1.000:1.521. The comparative values for groups of two and four beats is reversed in two thirds of the cases, yet so that an average for all subjects gives the ratio 1.000:1.066 between groups of four and two beats. The whole series of values arranged on the basis of unity for the mean variation of the beat interval is given in Table LXII.
TABLE LXII.
Proportional. Single Beat. 2-Beat Group. 4-Beat Group. 8-Beat Group. M.V. 1.000 0.512 0.480 0.320
The persons taking part in the investigation were next required to make a series of reactions composed of unit groups of two beats, in each of which the first member received accentuation, a simple trochaic rhythm. In this type the relation of intra-group to inter-group interval remains unchanged. In all subjects but one the mean variation of the first interval exceeds that of the second in the average ratio 1.722:1.000. The amount of difference is less than in the preceding type of reaction. In the former there is presented not an intensively uniform series, but an irregularly rhythmical grouping of intensities, in dependence on the well-defined parallel types of temporal differentiation; in the latter such intensive differentiation is fundamental and constant in its form. Assuming the character of the second interval to remain unchanged, there is in the intensive fixity of the initial accented element, on the one hand, and the alternate assertion of the impulse to accentuation and repression of it in the attempt to preserve uniformity, on the other, an occasion for the difference in the relation of the mean variation of this interval to that of the following in the two cases. It is to be expected that there should be less irregularity in a series of reactions each of which represents an attempt to produce a definite and constant rhythmical accent, than in a series in which such an accent is spasmodically given and repressed.
For a like reason, the difference in value between the mean variations of the elementary interval and the unit group should be less in the case of the positive rhythm form than in that of a series which combines a definite temporal segregation with an attempt to maintain intensive uniformity. The mean variation of the interval is still of greater value than that of the unit group, but stands to it in the reduced ratio 1.000:0.969.
The relations of higher groups present certain departures from the preceding type. In three cases out of five the unit has a greater > . fixity than its immediate compound ( | q. q; q q |), with an average \_______/ ratio of 0.969:1.072. The original relation, however, is reëstablished in the case of the next higher multiple, the eight-beat group, the whole series of values, arranged on the basis of unity for the simple interval, being as follows:
TABLE LXIII.
Proportional Single Beat 2-Beat Group 4-Beat Group 8-Beat Group M.V. 1.000 0.969 1.072 0.859
An analysis of the material in successive pairs of two-beat groups revealed a pronounced rhythm in the values of the mean variations of the first and second members of the pair respectively, the fixity of the second group being much greater than that of the first, the mean variation having a ratio for all subjects of 0.801:1.000. The interpretation of this rhythmical variation, as in the preceding reaction series, must be speculative in the absence of quantitative measurement of intensive changes, but is still not left in doubt. The rhythmic material is combined in larger syntheses than the groups of two beats, alternately accented and unaccented, which were avowedly in mind. This secondary grouping appears in at least a measure of four beats, into which the unit group enters as the elementary interval entered into the composition of that unit. In this larger group the initial period, or element of stress, is characterized by a greater mean variation than the unaccented period which follows it. There are present in this first interval two factors of instability: the factor of accent, that element which receives the stress, being in general characterized by a greater mean variation than the unaccented; and the factor of position, the initial member of a rhythmical group, independent of accentuation, being marked by a like excess of mean variation over those which follow it. The interpretation of the latter fact lies in the direction of a development of uniformity in the motor habit, which is partially interrupted and reëstablished with the ending and beginning of each successive group, large or small, in the series of reactions.
Further, when the material is arranged with four unit groups in each series, the same relation is found to hold between the first period composed of two unit groups and the second like period, as obtained within these pairs themselves. The mean variation of the first period of four beats is greater than that of the second in the case of all subjects but one, with an average ratio for all subjects of 1.000:0.745. The analysis was not carried further; there is, however, nothing which points to a limitation of the process of synthesis to groups of this magnitude; rather, to judge from the close approximation in definition of the two orders manifested here, there is suggested the probability that it is carried into still higher groupings.
In the next rhythmical type analyzed--the iambic form--that relation of the first to the second interval holds which was found to obtain in the preceding forms. The excess of mean variation in the former over the latter presents the ratio 1.274: 1.000. In amount it is less than in either of the previous types (2.290:1.000 and 1.722:1.000). For here, though both elements have constant relations as accented or unaccented members of the group, the factor of stress has been transferred from the initial to the final beat. Instead, therefore, of combining in a single member, the factors of inconstancy due to stress and to position are distributed between the two elements, and tend to neutralize each other. That the preponderance of irregularity is still with the initial interval leads to the inference that position is a greater factor of inconstancy than accentuation.
Also, the group presents here, as in the preceding forms, a greater fixity than does the individual interval. This relation holds for all subjects but one, the average mean variations of the simple interval and of the unit group having the ratio 1.000:0.824.
In larger groupings irregularities in the relations of higher and lower again occur, and again the greater constancy obtains between the first and second orders of higher grouping (in which for only one subject has the lower group a greater fixity than the higher, and the averages for all subjects in the two cases are in the ratio 1.149:0.951), and the lesser constancy between the unit group and the first higher (in which two subjects manifested like relations with those just given, while three present inverted relations). The whole series of relations, on the basis of unity for the mean variation of the simple interval, is given in Table LXIV.
TABLE LXIV.
Proportional. Single Beat. 2-Beat Group. 4-Beat Group. 8-Beat Group M.V. 1.000 0.824 1.149 0.951
There is also presented here, as in the preceding forms, a synthesis of the material into groups of four and eight beats, with similar differences in the fixity of the first and last periods in each. A single subject, in the case of each order of grouping, diverges from the type. The ratio of difference in the mean variations of the first and second members of the groups is, for series of four beats, 1.000:0.657, and for series of eight beats, 1.000:0.770. This indicates a diminishing definition of rhythmical quantities as the synthesis proceeds, but a diminution which follows too gradual a curve to indicate the disappearance of synthesis at the proximate step in the process.
Three-beat rhythms were next taken up and the same method of analysis carried out in connection with each of the three accentual forms, initial, median, and final stress. In these types of rhythm the intra-group intervals are more than one in number; for the purpose of comparison with the final, or inter-group interval, the average of the first and second intervals has been taken in each case.
The results agree with those of the preceding types. The mean variation of the interval separating the groups is less throughout than that of the average group-interval. The ratios for the various rhythm types are as follows:
TABLE LXV.
Rhythm Form. Initial Stress. Median Stress. Final Stress. Ratios, 1.000 : 0.758 1.000 : 0.527 1.000 : 0.658
This relation, true of the average intra-group interval, is also true of each interval separately. Among these ratios the greatest departure from unity appears in the second form which all subjects found most difficult to reproduce, and in which the tendency to revert to the first form constantly reasserts itself. The difference in value of the mean variations is least in the first form, that with initial accent, and of intermediate magnitude in the third form when the accent is final. The contrary might be expected, since in the first form--as in the second also--the factors of stress and initial position are both represented in the average of the first two intervals, while in the third form the factor of stress affects the final interval and should, on the assumption already made concerning its significance as a disturbing element, tend to increase the mean variation of that interval, and, therefore, to reduce to its lowest degree the index of difference between the two phases. That it does so tend is evident from a comparison of the proportional mean variations of this interval in the three forms, which are in order: initial stress, 4.65 per cent.; median stress, 4.70 per cent., and final stress, 7.15 per cent. That the consequent reduction also follows is shown by the individual records, of which, out of four, three give an average value for this relation, in forms having final stress, of 1.000:0.968, the least of the group of three; while the fourth subject departs from this type in having the mean variation of the initial interval very great, while that of the final interval is reduced to zero.
If, as has been assumed, the magnitude of the average mean variation may be taken as an index of the fixity or definition of the rhythm form, the first of these three types, the ordinary dactylic is the most clearly defined; the second, or amphibrachic, stands next, and the third, the anapæstic, has least fixity; for in regard to the final interval, to the average of the first and second and also to each of these earlier intervals separately, the amount of mean variation increases in the order of the accents as follows:
TABLE LXVI.
Interval. Initial Stress. Median Stress. Final Stress. First, 5.82 per cent. 9.95 per cent. 11.95 per cent. Second, 6.45 " 7.87 " 9.77 " Third, 4.65 " 4.70 " 7.15 "
In these triple rhythms, as in the two-beat forms, the simple interval is more variable than the unit group, and the lower group likewise more unstable than the higher. The series of proportional values for the three forms is given in the table annexed:
TABLE LXVII.
Rhythm Form. Single Interval. 3-Beat Group. 6-Beat Group. Initial Stress, 1.000 1.214 1.037 Median " 1.000 0.422 0.319 Final " 1.000 0.686 0.524
A comparison of the second and third columns of the table shows an excess of mean variation of the smaller group over that of the larger in each of the three forms. It is true also of the individual subjects except in two instances, in each of which the two indices are equal. This proportion is broken in the relation of the primary interval to the unit group in the dactylic rhythm form. A similar diversity of the individual records occurred in the two-beat rhythms.
The same indication of higher groupings appears here as in the case of previous rhythms. Rhythmical variations are presented in the amount of the mean variations for alternate groups of three beats. Chronologically in the records, as well as in dependence on theoretical interpretation, the first member of each higher group is characterized by the greater instability. The amounts of this difference in coördination between the first and last halves in series of six beats is set down for the three rhythm forms in the following table:
TABLE LXVIII.
Stress. First Half. Second Half Initial, 1.000 0.794¹ Median, 1.000 0.668 Final, 1.000 0.770
¹These figures are made up from the records of three out of four subjects. In the exceptional results of the fourth subject no mean variation appears in the first half and 6.3 per cent, in the second, making the average for the whole group 1.000:1.023.
There is still other evidence of higher rhythmical grouping than these oscillations in the amount of the mean variation of alternate groups. Exactness of coördination between the individual intervals of successive groups might undergo development without affecting the relative uniformity of such total groups themselves. But, throughout these results, an increase in coördination between the periods of the whole group takes place in passing from the first to the second member of a composite group. The relation here is not, however, so uniform as in the preceding case. The series of proportional values is given on page 403.
TABLE LXIX.
Stress. First Half. Second Half. Initial, 1.000 0.846¹ Median, 1.000 1.064 Final, 1.000 0.742
¹ Here also the records of three subjects only are involved, the results of the same reactor as in the preceding cases being discarded. Including this, the ratio becomes 1.000:1.016.
The index of mean variation for the individual elements of the group also shows a progressive decrease from first to last as follows:
TABLE LXX.
Stress. Interval I. Interval II. Interval III. Initial, 5.82 per cent. 6.45 per cent. 4.65 per cent. Median, 9.95 " 7.87 " 4.70 " Final, 11.95 " 9.77 " 7.15 "
The relation holds in all cases except that of I. to II. in the rhythm with initial stress. From this table may be gathered the predominance of primacy of position as a factor of disturbance over that of stress. Indeed, in this group of reactions the index of variation for the accented element, all forms combined, falls below that of the unaccented in the ratio 6.95 per cent. : 7.91 per cent.
In rhythms of four beats, as in those of three, the estimation of values is made on the basis of an average of the mean variations for the three intra-group intervals, which is then compared with the final or inter-group interval. As in those previous forms, sensitiveness to variations in duration is greater throughout in the case of the latter than in that of the former. The proportional values of their several mean variations are given in the annexed table:
TABLE LXXI.
Interval. Initial Stress. Secondary Stress. Tertiary Stress. Final Stress. Intra-group, 1.000 1.000 1.000 1.000 Inter-group, 0.941 0.775 0.725 0.713
This relation, true of the average of all intra-group intervals, is not, as in the preceding forms, true of each of the three constituent intervals in every case. In the second and fourth forms, those marked by secondary and final stress, it holds for each member of the group of intervals; in the first form it fails for the second and third intervals, while in the third form it fails for the last of the three.
The proportional amount of this difference in mean variation continuously increases from beginning to end of the series of rhythmical forms. This cannot be interpreted as directly indicative of a corresponding change in the definition which the four forms possess. The absolute values of the several mean variations must simultaneously be taken into account. First, then, in regard to the final pause there is presented the following series of values:
TABLE LXXII.
Stress. Initial. Secondary. Tertiary. Final. M.V. 6.57 per cent. 9.50 per cent. 4.90 per cent. 15.70 per cent.
A very striking rhythmical alternation in the magnitude of the mean variation thus occurs according as the accents fall on the first member of the subgroups when its amount is smaller or on the second member when it is larger. Further, the cases noted above, the second and fourth forms, in which each of the intra-group intervals is severally of greater mean variation than the final pause, are just those in which the index of mean variation in the final pause itself is at a maximum.
The average mean variations of the earlier intervals thus present changes which are analogous to and synchronous with those of the final pause. Their values in proportion to the whole duration of the intervals are as follows[13]:
[13] In the second line of figures has been added the series of values of the average mean variation for all four intervals of the group.
TABLE LXXIII.
Stress. Initial. Secondary. Tertiary. Final. M.V. 6.98 per cent. 12.25 per cent. 6.57 per cent. 22.0 per cent. M.V. 6.87 " 11.56 " 6.15 " 20.45 "
Those rhythmical forms having their accentual stress initial, or on the initial elements of the subgroups, are marked by a sensitiveness almost twice as great as those in which the stress is final, or on the final elements of the subgroups.
Finally, if we take the whole series of intervals severally, we shall find that this rhythmical variation holds true of each element individually as it does of their average. The whole series of values is given in the table annexed.
TABLE LXXIV.
Stress. Interval. Initial. Secondary. Tertiary. Final.
First, 9.57 per cent. 13.23 per cent. 9.00 per cent. 11.45 per cent. Second, 5.53 " 10.60 " 8.70 " 9.00 " Third, 5.83 " 12.93 " 2.00 " 12.90 " Fourth, 6.57 " 9.50 " 4.90 " 7.85 "
It is an obvious inference from these facts that the position of the accent in a rhythmical group is of very great significance in relation to the character of the rhythmical movement. The initial accent gives incomparably greater coördination and perfection to the forms of uttered (produced) rhythm than does the final. It is in this sense the natural position of the accent, because on the success and fluency of this coördination the æsthetic value of the rhythm depends.
In general, though not so unequivocally, the four-beat rhythms show a progressive increase of stability in passing from the simple interval to the group, and from the smaller group to the larger. The series of values for the four accentual positions follows.
TABLE LXXV.
Stress. Single Interval. 4-Beat Group. 2-Beat Group. Initial, 7.27 per cent. 8.20 per cent. 8.17 per cent. Secondary, 11.60 " 9.60 " 6.25 " Tertiary, 3.20 " 3.40 " 2.25 " Final, 10.22 " 6.30 " 6.00 " Average, 8.07 " 6.87 " 5.67 "
Here, as in the preceding rhythmical forms, the most constant relation is that of smaller and larger groups, in which no exception occurs to the excess of mean variation in the former over the latter. The cases in which this relation is reversed are found, as before, in comparing the simple interval with the duration of the unit group; and the exceptional instances are just those, namely the first and third forms, in which the mean variation of this uncompounded interval is itself at a minimum. This means that the simple interval presents a more mobile character than that of the group; and while in general it is less stable than the latter, it is also the first to show the influence of increased coördination. Training affects more readily the single element than the composite measure, and in the most highly coördinated forms of rhythm the simple interval is itself the most perfectly integrated unit in the system of reactions.
Here, as in the preceding rhythmical forms, evidence of higher grouping appears in the alternate increase and decrease of mean variation as we pass from the first to the second subgroup when the material is arranged in series of eight beats. The proportional values of the indices are given in the following table:
TABLE LXXVI.
Subgroups Init. Stress Sec. Stress Tert. Stress Fin. Stress 1st Four, 1.000 1.000 1.000 1.000 2d Four, 0.950 0.762 0.984 0.790
The first member of the larger group, in the case of every rhythm form here in question, is less exactly coördinated than the second, the interpretation of which fact need not here be repeated. Several additional points, however, are to be noted. The differences in stability of coördination which are encountered as one passes from the first to the last of the four rhythm forms, extends, when the reactions are analyzed in series of eight beats, to both members of the compound group, but not in equal ratios. The mean variation of the second and fourth forms is greater, both in the first and second subgroups, than that of the corresponding subgroups of the first and third forms; but this increase is greatest in the first member of the composite group. That is, as the group grows more unstable it does so mainly through an increase in variation of its initial member; or, in other words, the difference in variability of the beat intervals of the first and last subgroups reaches its maximum in those rhythmic types in which the indices of mean variation for these intervals are themselves at their maxima.
This process of coördination, with its indication of a higher rhythmical synthesis, appears also in the transformations in the value of the mean variations in duration of the total groups, when the material is treated in series of eight beats, as in table LXXVII.
TABLE LXXVII.
Subgroups. Init. Stress. Sec. Stress. Tert. Stress. Final Stress. 1st Four, 1.000 1.000 1.000 1.000 2d Four, 0.773 0.768 0.943 0.579
The total initial group, therefore, as well as each of its constituent intervals, is less stable than the second.
Within the unit group itself the values of the mean variation show here, as in the preceding forms, a progressive increase in sensitiveness to temporal variations from first to last of the component intervals. The proportional values for the four intervals in order are, 1.000, 0.786, 0.771, 0.666. The distribution of these relative values, however, is not uniform for all four rhythmical forms, but falls into two separate types in dependence on the position of the accents as initial or final, following the discrimination already made. The figures for the four forms separately are as follows:
TABLE LXXVIII.
Stress. 1st Interval. 2d Interval. 3d Interval. 4th Interval.
Initial, 9.57 per cent. 5.53 per cent. 5.83 per cent. 6.57 per cent. Secondary, 13.23 " 10.60 " 12.93 " 9.50 " Tertiary, 9.00 " 8.70 " 2.00 " 4.90 " Final, 11.45 " 9.00 " 12.60 " 7.85 "
In the first type (Rhythms I. and III.) appear a descending curve followed by an ascending; in the second type (Rhythms II. and IV.) a second descending curve follows the first. The changes in the first type are not coördinated with a similar curve of variation in the intensive magnitude of the beats. It is to be noted here that the smallest mean variation presented in this whole set of results is found in that element of the first form which receives the stress, an exception to the general rule. The variations in the contrasted type have their maxima at those points on which the group initiation-- primary or secondary--falls, namely, the first and third.
As in preceding rhythmical forms, while the separation of accentual stress from primacy in the series tends to increase the mean variation of that element on which this stress falls and to raise the index of mean variation for the whole group, yet the mean variation of the initial element is also raised, and to a still greater degree, reinforcing the evidence that primacy of position is a more important factor of instability than the introduction of accentual stress.
In the investigation of mean variations for units (if we may call them such) of more than four beats only a modicum of material has been worked up, since the types of relation already discovered are of too definite a character to leave any doubt as to their significance in the expression of rhythm. The results of these further experiments confirm the conclusions of the earlier experiments at every point.
These higher series were treated in two ways. In the first the reactor beat out a rhythm consisting in the simple succession of groups of reactions, each of which contained one and only one accent. These units in each case were marked by initial stress, and were composed of five, six, seven, eight and ten beats respectively. The results are given in the following table, which contains the series of mean variations in duration both for single intervals and for total groups.
TABLE LXXIX.
No. Med. Unac'td of Beats. Acc'td Beat. Beats. Final Beat. Average. Group. Five, 12.2% 6.8% 7.1% 7.9% 6.3% Six, 9.2 10.6 6.9 9.7 8.3 Seven, 7.1 5.2 7.9 5.8 3.6 Eight, 12.4 9.5 8.8 9.7 8.0 Ten, 7.5 6.6 7.3 6.8
The averages for the combined, median, unaccented intervals are given separately from those of the final interval, for the reason that the mean variation of the latter is greater in three cases out of five than that of the former, a relation which apparently contradicts what has already been said concerning the sensitiveness to variations which marks the intervals separating rhythmical groups. The reason for this final increase in variation appears when the relative intensities of the series of reactions are considered. They are given in Table LXXX.
TABLE LXXX.
No. of Beats. Acc. Beat. Av. Unacc. Final. Pre-final. Five, 1.000 0.543 0.518 0.500 Six, 1.000 0.623 0.608 0.592 Seven, 1.000 0.515 0.544 0.437 Eight, 1.000 0.929 0.949 0.863 Ten, 1.000 0.621 0.640 0.545
In every case the final element is marked by an increase over that which precedes it (see last two columns of table) of the average value for all rhythms of 1.000:0.900; an increase which raises it above the average value of the whole series of preceding unaccented beats in three cases out of five. To this final accentuation the increase in variation is to be attributed. Yet despite the additional element of disturbance due to this increased final stress the average value of the mean variation for this final interval is lower than that of the median unaccented intervals in the ratio (all rhythms combined) of 0.992:1.000.
Turning, then, to Table LXXIX., there is presented, firstly, an excess of variation in the accented element over that of the average unaccented elements in every case but one (the six-beat rhythm in which the values are nearly identical), which for the whole series of rhythms has a value of 1.000:0.794. Secondly, in every completed case (part of the figures in the last rhythm are inadvertently lacking), the average mean variation of the single interval preponderates over that of the total group.
The second form of rhythmical tapping, in which the longer series were beaten out as pairs of equal subgroups, was added in order to determine the quantitative relations of the mean variations for alternate subgroups when such groups were purposely intended, instead of appearing in the form of unconscious modifications of the rhythmical treatment, as heretofore. At the same time the results present an additional set of figures embodying the relations here in question. They are as follows:
TABLE LXXXI. Intervals. Groups. Number Av. 1st 2d 1st 2d of Beats. Acc. Unacc. Half. Half. Half. Half. Average Totals Six, 27.9% 20.9% 23.4% 23.0% 14.6% 13.3% 13.9% 13.8% Eight, 16.6 14.8 13.2 17.3 6.2 3.3 4.7 2.7 Ten, 7.9 2.6 3.4 4.0 5.9 5.2 5.5 3.1
No exception here occurs to the characteristic predominance in instability of the accented element. As regards simple intervals, the relation of first and second groups is reversed, the reason for which I do not know. It may be connected with the rapid speed at which the series of reactions was made, and its consequent raising of the threshold of perceptible variation, proportional to the value of the whole interval, to which is also due the higher absolute value of the variations which appear in both tables.
These inversions disappear when we compare the relative stability of the first and second subgroups, in which the excess of variation in the former over the latter is not only constant but great, presenting the ratio for all three rhythms of 1.000:0.816. The characteristic relation of lower to higher rhythmical syntheses also is here preserved in regard to the two subgroups and the total which they compose.
The points here determined are but a few of the problems regarding the structure of larger rhythmical sequences which are pressing for examination. Of those proximate to the matter here under consideration, the material for an analysis of the mean variation in intensity of a series of rhythmical reactions is contained in the measurements taken in the course of the present work, and this may at a future time be presented. The temporal variations having once been established it becomes a minor point.
Such conclusions, however, are only preliminary to an investigation of the characteristic structure of the ordinary metrical forms, and to these attention should next be turned. The configuration of the common meters should be worked out both in relation to the whole formal sequence, and to the occurrence within the series of characteristic variations. There can be no question that each metrical structure, the iambic trimeter or dactylic tetrameter line, for example, composes a definite rhythmical melody within which each measure is shortened or prolonged, subdued or emphasized, according to its position and connections in the series of relations which constitute the rhythmical sequence.
These several metrical forms should be explored and the characters of each measure in the series quantitatively determined. Such an investigation would include an ascertainment of the proportional time-value of each successive measure, its average force, and its sensitiveness to variations, temporal and intensive. It should include an examination of the configuration of the single measure and the changes in distribution of accents and intervals which it undergoes as the rhythmical series advances. For the rhythm group must not be conceived as a simple unchanging form; both intensively and temporally it is moulded by its function in the whole sequence, the earlier iambic of a heroic measure being unlike the later, the dactyl which precedes a measure of finality different from that which introduces the series. Such a set of determinations will give the pure characteristic curves of our common poetical meters.
But these meters are no more simple forms than are their constituent measures. At every point their structure is subject to modification by factors which appear in the rhythmic utterance in virtue of its use as a medium for the free expression of thought and emotion; and the manner in which the characteristic form is altered by these factors of variation must be studied. Of these variations the more important are the effects of the introduction of variants--of spondees among dactyls, of anapæsts among iambics, and the like--and the occurrence of points of origin, emphasis, interruption, and finality in special accentuations, syncopated measures, cæsural pauses and elisions. These factors influence the structure both of those measures within which they appear and of those adjacent to them. The nature and extent of this wave of disturbance and its relation to the configuration of the whole sequence call for examination.
Finally, this process of investigation should be applied to the larger structures of the couplet and stanza, that the characteristic differences in the pair or series of verses involved may be determined. These characters include the whole time occupied by each verse of the stanza, the relative values of acatalectic and catalectic verses occurring within the same stanza structure, differences in rhythmical melody between the latter forms, the variations of average intensity in the accentual elements of such lines, and a determination of the values of rests of higher and lower degrees--mid-line, verse, and couplet pauses--which appear in the various stanza forms, and their relation to other structural elements.
* * * * *
RHYTHM AND RHYME.
BY R.H. STETSON.
I. INTRODUCTION.
The psychological theory of rhythm has its beginnings in the work of Herbart,[1] who inaugurated the treatment of rhythm as a species of time perception and suggested an explanation of its emotional effects. While Herbart had simply pointed out the effect of a whole rhythmic series in giving rise to an emotion of expectation, delay, or haste, Lotze[2] applied the principle severally to each unit group (each foot) in the rhythm, and made the emotional effect of rhythm depend on these alternate feelings of strain, expectation, and satisfaction produced by every repetition of the unit group. Vierordt[3] did the first experimental work on rhythm, determining the period of greatest regularity in the tapping of rhythms. But the first important experiments were carried on by von Brücke.[4] By tapping out rhythms on a kymograph, he determined the well-known 'Taktgleichheit' of the feet in scanned verse, and noted a number of facts about the time relations of the different unit groups. Mach[5] added to the previous knowledge about rhythm certain observations on the subjective accentuation of an objectively uniform series, and specially he noted that the process is involuntary. With a much clearer understanding of the facts of rhythm than his predecessors had had, he really provided the foundation for the theories which follow. His most important contribution, for some time overlooked, was his emphasis of the essentially motor nature of the phenomena of rhythm, and his motor theory therefor.
[1] Herbart, J.F.: 'Psychol. Untersuchungen' (Sämmt. Werk, herausgeg. von Hartenstein), Leipzig, 1850-2, Bd. VII., S. 291 ff.
[2] Lotze, R.H.: 'Geschichte der Æsthetik,' München, 1863, S. 487 ff.
[3] Vierordt, K.: 'Untersuchungen über d. Zeitsinn,' Tübingen, 1868.
[4] von Brücke, E.W.: 'Die physiol. Grundlagen d. neuhochdeutschen Verskunst,' Wien, 1871.
[5] Mach, Ernst: 'Unters. ü. d. Zeitsinn d. Ohres,' _Wiener Sitz. Ber., mathem. naturw. Classe_, 1865, Bd. 51, II., S. 133. Beiträge zur Physiol. d. Sinnesorgane, S. 104 ff.
Many of the recent theories of rhythm are based on Wundt's analysis. The work of Wundt and Dietze,[6] was concerned with rhythmic series; but it may be noted that the 'span of consciousness' and the 'synthetic activity of consciousness' were the subjects actually under investigation. Rhythm was considered as a special temporal form of this 'psychic synthesis.' There are three different elements in a sound series, declared these writers, which contribute to this synthesis: qualitative changes, intensive changes and melodic changes. Of these the intensive changes are the most important. Every increase in intensity, that is, every beat ('Hebung') is followed by a decrease, and the next increase which follows is recognized as a repetition of the preceding beat and as the forerunner of the beat which is to follow. From this comes the synthetic power of the rhythm. Just as the simple unit groups are built up by this synthesizing power, so they in turn are combined into larger phrases and periods. The motor factor has little place in Wundt's own discussion,[7] the 'mental activity' is the all-important thing. Bolton[8] also made a very important contribution to the experimental knowledge of rhythm. His work was based entirely on Wundt's theory. His method of experimentation was accurate and his observations copious. The arrangement of his apparatus, however, led him to emphasize objective uniformity as a condition of rhythmic grouping; so that Meumann's criticism of his application of this principle to poetry is quite just. Nevertheless Bolton established the essential facts of subjective accentuation and apparent temporal displacement. It is noteworthy that he laid great emphasis on the motor aspect of rhythm, and made many careful observations on the 'motor accompaniment.' While inclining strongly to a motor interpretation he did not attempt to cut loose from the Wundtian 'apperceptive process' as the primary factor.
[6] Wundt, W.: 'Physiol. Psych.,' 4te Aufl., Leipzig, 1893, Bd. II., S. 83.
[7] Wundt, W.: 'Physiol. Psych.,' 4te Aufl., Leipzig, 1893, II., S. 89 ff.
[8] Bolton, T.L.: Amer. Jour. of Psych., 1894, VI., p. 145 et seq.
The most elaborate consideration of rhythm yet published is that of Meumann.[9] He avowedly worked out and defended the theory of Wundt. The only important difference is the larger place which he gave to the 'motor accompaniment,' although he was always careful to emphasize its secondary and derived character. He insisted that the 'mental activity' is always primary, and that without it there can be no rhythmization; and he opposed vigorously the motor inclinations of Mach and Bolton. It is certainly unfortunate that rhythm has always fallen into the hands of the investigators of the 'attention,' or the 'span of consciousness,' or the 'perception of time.' It is but an incident that judgments of time are often based on rhythms; and everything that Meumann has said of a 'mental prius,' or a 'synthesizing activity' in the case of rhythms, may just as well be said in the case of any coördinated act.
[9] Meumann, E.: Phil. Stud., 1894, X., S. 249 ff.
Meumann discussed in detail the characteristics of the rhythm of a simple series of sounds, of music, and of verse. He assumed that in the simple sound series we have rhythm in its barest form, and only the rhythmic synthetic activity is at work; while in music there is a content which to some extent prescribes unities, and the objective regularity of the rhythm is broken. In verse we have much more content, and the rhythmization is no longer regular in its temporal relations; it is entirely dominated at times by the 'logical unities' of the 'thought.'
One great difficulty with such a differentiation of the three types of rhythms presents itself when one inquires into the objective regularity of the types; the fact is that music is by far the most regular in its time values, though it has more content than the sound series; and that just as great irregularities are possible in the bare sound series as in the rhythm of verse with its rich and definite content.
Later statements of the facts and theories relating to rhythm have inclined more and more to an emphasis of the motor aspect, even on the part of Wundtians. Since Meumann there has been some detailed laboratory work published, but the amount of accurately measured rhythmic material is astonishingly small. Meumann established experimentally the well-known relation between the length of a rhythmic element and its accent, and corroborated the earlier work on subjective accentuation. The reports contain the measurements of but about eighty individual unit groups (iambs, trochees, etc.). Ebhardt[10] gave the measurements of from 150 to 300 taps from each of three subjects. But his work is vitiated, as far as any application to rhythm is concerned, because he based everything on the judgment of equality, which has nothing to do with rhythm.
[10] Ebhardt, K.: _Zeilschr. f. Psych, u. Physiol. d. Sinnesorgane,_1898, Bd. 18, S. 99.
Hurst, McKay and Pringle[11] published measurements of about 600 individual unit groups from three different subjects; in several cases, the material consists rather too much of records of the experimenters themselves, but in general their results agree very well with those of other authors. Scripture[12] published the measurements of a single stanza of poetry. It is but a single stanza and quite too little material on which to base any conclusions, but it is notable as a measurement of freely spoken rhythm. No experiments have been published which bear on the nature of the rhythmic phrase, of the period, or of the stanza.
[11] Hurst, A.S., McKay, J., and Pringle, G.C.F.: _Univ. of Toronto Studies,_ 1899, No. 3, p. 157.
[12] Scripture, E.W.: Studies from the Yale Psych. Lab., 1899, VII., p. 1.
Our problem is: What part do the recurrent qualitative factors, like rhyme, play in the grouping of rhythms? They function evidently, in the main, as factors determining the periods or larger phrases of the rhythm structure--the verses and stanzas of poetry and nonsense verse. As no work has been done on the nature of such larger rhythmic unities, a large share of the investigation was concerned with the nature of the verse unity.
Two methods of investigation were used: Subjects listened to rhythmic series, into which various modifications were introduced; and secondly, rhythms of a prescribed type, produced by the subject, were recorded and measured.
II. THE PERCEPTION OF A RHYTHMIC SERIES.
Apparatus: A disc (Fig. 1, Plate IX.) about 50 c. in diameter, rotating on a vertical pivot, was driven by a pulley-cone underneath mounted on the same spindle (not shown in the figure). On the face of the disc were four concentric rings of regularly spaced holes, which received pegs of uniform height and provided with a shoulder. Corresponding holes of each circle lay on the same radius. On a plate supported by a bracket were mounted four levers whose heads stood in line radially to the movable disc. When the disc rotated to the right under the levers, the pegs forced up the lever heads and made an electric contact. The dip of the levers was controlled by a screw adjustment. The apparatus was driven by a motor and reducing gear, which were isolated in a sound-proof box. The rate of speed was controllable.
The apparatus was built for use with sounders connected with the binding-posts, but in this investigation sounders were dispensed with, and the clicks from the apparatus itself were used, since but one qualitative difference was introduced. As a rule, the objective accent of the foot was not given; the subjective accentuation was nearly always sufficient. Subjects were quite unable to say whether the accent was objective or not. If necessary, an accentuation was produced by raising the pegs representing the accentuated part of the foot. The group elements were represented by single, simple clicks made by a brass screw on the lever arm striking an iron plate (the noise of the brass peg striking the lever head was eliminated by damping with cloth). The rhyme was represented by a compound noise consisting of a click higher in pitch than the verse element click, made by the peg striking the lever head, and an almost simultaneous click lower in pitch than the verse element click, made by the screw of the lever arm striking another iron plate. The rhyme noise was not louder than the verse element click, and as a whole gave the impression of being a lower tone because the first click was very brief. Subjects did not analyze the rhyme noise, and had no difficulty in making it represent rhyming syllables. The pauses throughout had no filling.
The subject was always given a normal series until the type was clearly established, and when the variations to be judged were introduced his attention was directed as far as possible to the factor to be introduced. This seemed the only way to obtain trustworthy judgments. If the subject waits blindly for some perceptual change in the whole complicated mass of sensations which the simplest rhythmic series constitutes, he is apt to fit his attention on some irrelevant detail, and the change may not be noted until greatly exaggerated, and he may not judge that particular factor at all.
The subject was always asked to choose a rate of delivery which would correspond to his natural rate of reading nonsense verse, and the clicks were always associated with syllables, though not with words. An effort was made to keep the series as colorless and devoid of content as possible, to eliminate uncertain association. Beyond suppressed articulation, the subject was not encouraged to mark the rhythm with any part of the body, but a number of involuntary movements of neck, body, hand, or foot were nearly always observed. Occasionally, when a subject's expression was doubtful, he was asked to say a nonsense series with the clicks.
The nomenclature to be used in this paper is that of meter, but it is always subject to the reservation that the material is only analogous to series of nonsense syllables.
Records were kept in terms of the intervals on the revolving disc; the time of revolution was also taken, so that the figures may be translated in time intervals if desired. Thus, 34, 34, 34, 34, 34 represents a series of iambs in which the unaccented click has the length of three, and the accented click the length of four spaces between pegs. A uniform verse represented by a digit giving the number of feet, followed by digits in parenthesis giving the character of the foot, e.g., 4 (34), is an iambic tetrameter.
For convenience, the verse pause is written independently of the last foot of the verse, e.g., 4 (34) p. 7 represents a tetrameter line having the intervals 34, 34, 34, 37. The interval of the last accented syllable is counted twice.
Occasionally this is disregarded and vs. p. equals o is written to indicate that the vs. p. is equal to the foot pause.
The results of the experiments may be grouped under three heads:
1. Why does a synthesizing factor such as rhyme occur at the end of the verse?
2. What is the relation between the verse pause and the rhyme?
3. What is the relation of rhyme to the cyclic movement of the unit group and of the verse?
1. Why the Synthesizing Factor Occurs at the Close of the Verse.
To determine a possible difference in the sense of rhythm at the beginning and the close of a verse, pauses ('lags') were introduced into the earlier and later parts of the verse. These pauses were made barely perceptible, i.e., barely perceptible in any part of the verse. Usually in iambic verse the barely perceptible lag shows the following proportions to the other pauses:
34 35 34 etc., or 47 48.5 47.
Most of the experiments were performed with iambic tetrameter. The subject was told to note the lags in the verse: these were introduced either in both parts of the verse or at its close only. At least three verses were given, and records were kept of the false judgments. When lags of identical duration were introduced between the first and second and between the third and fourth feet, it was found that nearly always the lag would not be detected in the earlier part of the verse but would be detected in the later part. Out of eighty-two cases, there were but six in which the same lag was recognized in the first as well as in the last position. In two of these cases the subject's attention had been called to the first part of the verse; and in the four other cases the lag was still found more marked at the close than at the beginning.
There were no cases in which a lag detected in the earlier part of the verse was not also detected in the later part. False judgments, when they occurred, were made as to a lag in the earlier part of the verse. One subject falsely located a lag in the first of the verse four times. Judgments as to the earlier part of the verse were uncertain and frequently changed.
The maximum lag possible without breaking the unity of the verse was determined for the earlier and later parts of the verse. The verse unity was tested by adding enough feet to make a full verse, after the break, and asking the subject to mark the close of the verse. In every case this irregularity was introduced into the second verse, and the first verse was normal, e.g. (pentameter),
I. 5 (34). II. 34 lag 34 34 34 34 34.
If the lag does not break the verse, the subject should hear the close of the verse at the end of the fifth foot in II. If the verse is broken he should ignore the first foot and make a new verse, ending with the sixth foot.
J. Iamb. tet. 1st pause of verse, max. pos. lag 9 3d 7 L. 1st 9 3d 7 R. 1st 11 3d 9 G. 1st 9 3d 7 Mi. 1st 10 3d 8 B. 1st 7 H. 1st 10 3d 6
Later, in the attempt to determine natural divisions, or nodes in the verse, the following were determined:
L. Max. pos. lags in f. p. of iamb. pent. in order 8 13 9 6 G. 10 11 9 8 Mi. 15 18 17 14 Me. 7.5 13 9.5 6 R. 9 9 11 7 B. 12 8 15 7 H. 7.5 8 10 7
B. Max pos. lags in dac. let., cat., in order 12 16 8 S. 10 11 7 Mc. 7 10 6 G. 11 11 7 L. 19 16 7 H. 7 6 4
This shows that an irregularity in the time intervals may be greater in the earlier than in the later part of the verse. This last table is further evidence of the increased exactness of the rhythmic perception at the close of the verse. As far as nodes are concerned, they show clearly two types: (1) A node after the second foot (L., G., Mi., Mc.) and (2) a node after the third foot (R., B., H.). For the tetrameter there is some indication in the cases of B., S. and Mc., but the other cases are negative and further evidence is needed.
With three of the subjects, Mi., J. and K., it was not always possible to get records of the maximum lag, since it was impossible to define the verse unity. When this was unbroken it was the unanimous testimony of the subjects, corroborated by their unconscious movements, that there was a feeling of tension during the lag. But the subjects just referred to got a type of unity, and there was no tension. The lags were indefinite and very long (35-90). This unity must be of the same kind as the unity of the stanza, which includes long expressional pauses, as well as rhythmic verse pauses.
If a subject is asked to fall in at the beginning of a rhythmic series his first attempts are decidedly incoördinated. His earliest reactions follow the clicks which they are intended to represent, but presently the series of motor impulses generated by the sounds and the voluntary movements which the subject makes fuse into a voluntary type of reaction in which the cycle has become automatic and definite, and the clicks take their proper places as coöperating and controlling factors along with the motor cues of the process itself. The accuracy of the judgments of time, if such judgments be made, or the estimation of the likeness of the groups, depends on the definiteness with which movement sensations follow each other in a regular series.
The following experiments (Table I.) concern the perception of a lag in different parts not of a verse but of a stanza. It was a question, namely, whether a lag in the first rhythmic series (first verse) which establishes the motor cycle in the subject would be detected in the later rhythmic series (later verses of the stanza) after the motor cycle in the subject has been inaugurated. This responsive motor cycle should itself, of course, contain the lag given with the first rhythmic series.
A stanza of the form of A (Table I.) was clicked out by the instrument, but the subject had no clue as to the regularity or irregularity of any verse. The stanza was repeated as often as the subject wished, but not without a pause of a few moments between each repetition.
TABLE I.
THE INFLUENCE OF A LAG IN THE FIRST VERSE ON THE JUDGMENT OF IDENTICAL LAGS IN LATER VERSES.
A. Stanza given: I. 34 34 35 34 p. 7-9 II. " " " " " III. " " " " "
In 14 cases the following was reported:
I. Lag noted. II. " not noted. III. " " "
In 9 cases the following was reported:
I. Lag noted. II. " " but shorter than first. III. " " " " " "
In 6 cases the following was reported:
I. Lag noted. II. " " and equal to first. III. " " " " " "
B. Stanza given: I. 35 34 34 34 p. 7-9 II. " " " " " III. " " " " "
Any pause large enough to be noted in I. was noted in II. and III. (This table contains the judgments made on all trials.)
Most of the judgments of the third set are due to the fact that the subject first attended to the series on the second or third verse. The large number of cases (83 per cent.) in which the lags in the second and third verses were concealed by the equal lag in the first verse, makes it very probable that the type of a verse is somehow altered by the impression left by the preceding verse.
The method of determining the maximal lags (as previously described) gave interesting evidence on the point at which the unity of the verse is actually felt. In the form
I. 5 (34) II. 34 lag 34 34 34 34-34
as the lag increases, a point is reached at which the unity may be made to include the first foot or to ignore it. Which of these is done depends on the subject's attitude, or on the point at which the verse is brought to a close. In either case the unity, the 'pentameter feeling,' is not experienced until the end of the series unified is reached. This is the case with all the subjects.
This development of the feeling of the particular verse form only at the end of the verse, and the fact that the subject may be uncertain which form he will hear until the series has actually ceased, shows that the verse-form movement is not of such a character that the close of it may not be considerably modified. A form which may fit the pentameter can be broken off early, and become a satisfactory tetrameter. The feeling seems to depend on some total effect of the verse at the close. This effect is probably a blending of the mass-effect of the impressions received thus far, which have a definite character and feeling significance, and which form the motor disposition for the next verse. The essential thing in the determination of verse unity seems to be the dying out of the automatism, the cessation of the coördination of the cyclic movement. The rhyme, it would seem, emphasizes the close of the automatic cycle. But it is probable that satisfactory phrasing has other characteristics, and a definite form as a movement whole.
2. The Relation of the Rhyme to the Verse Pause.
Determinations of the minimal satisfactory verse pause were made with a view to comparing the minimum in unrhymed with that in rhymed verses.
The stanza used was of the following form:
I. 34 34 34 p. II. " " " " III. " " " "
The minimal satisfactory verse pauses were:
Without Rhyme. With Rhyme. Subject. L. 6 4 " J. 5 4 " Mc. 6 4 " R. 7 4 " B. 6-7 3.5 " G. 6 3.5 " Mi. 6-7 3.25
It thus appears that the minimal pause which is satisfactory, is less when rhyme is present than when it is not present. Similar determinations were made for the maximal satisfactory verse pauses, as follows:
Without Rhyme. With Rhyme. Subject. L. 9-10 11 " J. 8 9 " Mc. 9 9 " R. 10-11 10-11 " B. 9 9 " G. 11-12 11 " Mi. 10 10
(A few experiments were tried with verse pauses of different length in the same stanza. A difference of one fourth the value of the pause is not detected, and unless attention is called to them, the pauses may vary widely from one another.)
This shows that the rhyme reduces the necessary pause in verse to the mere foot pause; while at the same time as great a pause is possible with rhyme as without it. Aside from the table above, a large number of the records made for other purposes support this statement: whenever rhyme was introduced, the verse pause was made equal to the foot pause, or even slightly less than it, and was always found satisfactory.
Numerous cases of introduction of lags into the verses of rhymed stanzas go to show that irregularities in such verses do not affect the length of the pauses.
Two hypotheses suggest themselves in explanation of the striking fact that the verse pause becomes unnecessary at the close of a rhymed verse.
The unity is now a new kind of verse unity; the rhyme is a regular recurrent factor like the accent of a foot, and the series of rhymes generates a new rhythm. In the rhymed stanza we are to see not a set of verses, like the verse of blank verse, but a new and enlarged verse unity.
There are several decided objections to this conception. First, the verse pause may be eliminated, but its elimination is not essential to the rhyme effect; the verse pause may still be as long, if not longer, with rhyme. Secondly, the larger unity into which the verses enter is not in many cases a unity made up exclusively of rhymed verses. Verses without rhyme alternate with rhymed verses, and have the usual verse pause. Thirdly, the rhyme is not merely a regularly recurring element: it is essentially a recurring element of which one may say what has been said falsely of the rhythm elements, that each rhyme is either a repetition of something gone before to which it refers, or the anticipation of something to which it looks forward. In most cases, rhymes function in pairs. Such peculiarities distinguish the rhyme from the accent of the foot. Lastly, the freedom of the whole stanza structure into which rhyme is introduced is much greater than that of the single verse; pauses much larger than the admissible lags of a single verse are possible between the verses, and there is no tension which persists throughout. There is no feeling of strain if the series halts at the verse ends.
A second hypothesis is that there is some definite process at the end of the verse which marks the close of the verse and which takes more time in the case of blank verse than in the case of rhymed verse. If we conceive the end of the verse as a point where a dying out of the tension occurs, we may imagine that the rhyme brings an emphasis, and becomes a qualitative signal for this release. The slight increase of intensity on the rhyme contributes to the breaking up of the coördination, and at the same time exhausts and satisfies the feeling of tension which the verse embodies. It is at the point for finishing and releasing the set of strains which constitute the motor image of the verse. A qualitative change may be supposed to produce the effect more rapidly than the simple dying out of the tensions, which occurs in blank verse without a differentiated end accent.
3. The Relation of the Rhyme to the Cyclic Movement of the Unit Group and of the Verse.
A series was arranged in which the accent of an ordinary foot and a rhyme occurred side by side; the distance between them was gradually lessened, and the effect on the rhyme and on the ordinary accented element was noted.
A preliminary set of experiments on the effect of two accents which approach each other gave some very interesting results. Thus Table II. shows the effect of gradually eliminating the verse pause from the couplet.
TABLE II.
Dactylic, catelectic couplet of the general form:
ÍII ÍII ÍII Í / ÍII ÍII ÍII Í Without rhyme.
Each dactyl (ÍII) is, in terms of spaces between the pegs, 3 2 4; or in seconds, .25, .17, .33.
The pause between the two verses was gradually lessened
B. At 5 (.42 sec.) The verses are normal. 4.5 The verses are normal, but first accent of II. is fading. 4 The accent is less and less on first element of II. 3.3 The accent is almost gone on first element of II. 3 (.25 sec.) First foot of II. has quite lost accent. There is now but one verse. 'Amalgamation.' Mc. 7 (.58 sec.) The verses are normal. 5.3 Either first element of II. has its normal accent, or it wavers to a secondary accent, and the verses become one. 5 (.416 sec.) First foot of II. has quite lost accent. Amalgamation. 3 (.25 sec.) 'Last verse completely spoiled.' Last verse ' ' ' ' becomes -- /- -, -- - -, -- - -, -- --. Unsatisfactory. 2 (.16 sec.) The II. has become mere 'medley.' H. 6 (.5 sec.) Normal. 5 First element of II. attaches to I., and its accent is lessened. 3 (.25 sec.) First element of II. has lost its accent; the verses ' ' ' ' ' ' ' become --- --- --- - / - --- --- ---. But one verse. Amalgamation. J. 5 (.42 sec.) Normal. 4.6 First element of II. is losing accent. 3 (.25 sec.) First two elements of II. 'tumble over each ' ' ' ' ' ' ' other.' --- --- --- - / ---- --- ---. Unsatisfactory. Amalgamation. L. 5 (.42 sec.) Normal. 4 Last element of I. losing accent. 3.3 Last element of I. and first of II. have completely lost accent. Amalgamation. G. 7 (.58 sec.) Normal. ' ' ' ' ' ' 3 (.25 sec.) --- --- --- - / - ----- --- -. Amalgamation.
Mi. 4.3(.35 sec.) Normal. 4 First two elements of II. equal in accent. ' ' ' ' ' ' ' ' 3 (.25 sec.) --- --- --- - / - -- --- --- -. Amalgamation.
As soon as the accents are within a certain distance they affect each other. As a rule the first retains its original intensity and the second is weakened; rarely the first yields to the second. The table shows that the distance at which this occurs is about .42 seconds. Under many conditions it is quite possible for two accents to occur at that distance, e.g., in rapid rhythms, without any 'fusing.' The subject has a type of rhythm very definitely in mind and the only hypothesis which will explain the difficulty in observing the type, in spite of the slight change in time values, is that somehow the cyclic automatic movement has been affected and can no longer produce the normal, limiting sensation at the accent. There is not time for the phase of relaxation before the next, objective, limiting sensation occurs. We may figure the movement as follows:
A is a curve in which B is the relaxation phase. At C the tensions are rapidly increasing in anticipation of the next limiting sensation at A. But if the objective factor appears too early, the tensions will be discharged prematurely, and the second accent will be weakened. Exactly the obverse of these phenomena is often noticed, when a slight retardation of the second accent produces a slight increase in its intensity. When, finally, the second accent has been moved so near the first accent that it occurs within the phase of the first, it disappears as an independent accent. At the same time the objective stimuli immediately following now appear at quite irregular intervals in the cycle, the coördination is broken up, and chaos without accentuation for some distance is the result. Occasionally the process does not right itself before the close of the verse. As this process eliminates the verse pause, the two verses become one, as the accents approach each other. In cases where the first accent is lost, one may suppose that the first accent functions as an anticipatory stimulus, while the second simply increases the effect (cf. Hofbauer and Cleghorn), and marks the culmination. The fact that the second accent is only lost at very close range favors this idea.
TABLE III.
Dactylic, catalectic couplet of the general form: ÍII ÍII ÍII Í / ÍII ÍII ÍII Í (with rhyme).
Each dactyl (ÍII) is, in terms of spaces between the pegs, 324; or, in seconds, .25, .17, .33.
The pause between the two verses was gradually lessened.
B.
At 4 (.33 sec.) Normal. 2 (.17 sec.) First accent of II. is weakening. 1.3(.21 sec.) Amalgamation. Rhyme retains the accent. Mc. 5 (.42 sec.) Normal. 4 II. has become anapæstic. 2 (.17 sec.) Rhyme is lost. Amalgamation. J. 3 (.25 sec.) Normal. 2 (.17 sec.) Accent of rhyme is lost. Amalgamation. L. 4 (.33 sec.) Normal. 1.6(.18 sec.) Rhyme retains accent, first accent of II. is lost. Amalgamation. G. 4 (.33 sec.) Normal. 2 (.17 sec.) Accent of rhyme retained. Amalgamation. Mi. 2 (.17 sec.) Normal. 1.6 First foot of II. amphibrachic. .4(.03 sec.) Accent of rhyme retained. Accent of first foot of II. lost. Amalgamation.
When the qualitatively different click representing the rhyme is introduced, its most striking effect is decidedly to shorten the possible distance between the two accents. This is in accord with the notion suggested of the function of rhyme at the verse end. The rhyme seems greatly to hasten the relaxation phase, as compared with the time required in the ordinary foot.
There is a variety of forms possible to the unrhymed verse, but that with the climax at the close is decidedly the most frequent. When the rhyme is introduced the climax goes with it, and the verse flows down as it were to the end. When the rhyme is put in the very first of the verse, however, a secondary or even a primary accent may be developed at the close of the verse. The natural place for the climax of the verse movement is apparently at the close, and the fact that not only is the earlier part of the verse more vague, but also that the end is the natural, climactic position, makes the synthesizing and delimiting factor, rhyme, preferable at the close.
The records of the next table were obtained by asking the subjects to repeat the series with prescribed accents, until they decided whether or not the rhyme could be felt under the conditions.
TABLE IV.
Rhymes under prescribed accentual conditions: iambic tetrameter. Heavy accent marked acute (´). Slight accent marked grave (`). Rhyme indicated by brace.
Ta ta ta ta ta ta ta dó) gò) dò dò Hu. Rhymes imperfectly. Mc. Rhymes imperfectly. G. Rhymes imperfectly. Ha. Rhymes imperfectly. Hy. Rhymes fairly well.
Ta ta ta ta ta ta ta dò) gó) dò dò Hu. Cannot get rhyme. Mc. Rhymes imperfectly. 'Produced by some sort of tension.' G. Rhymes imperfectly.
Ta ta ta ta ta ta ta dò) gò) dó dò Hu. Rhymes well. Mc. Rhymes well. G. Rhymes well.
Ta ta ta ta ta ta ta dò gò) dó) dò) Hu. Cannot get rhyme. Hy. Cannot get rhyme. 'Accent spoils it.' G. Cannot get rhyme. 'Accent breaks it all up.' Mc. Rhymes imperfectly.
The table shows that rhymes of syllables which have accents of strikingly different degrees are difficult to feel. In the last case, of the rhyming verses separated by a verse having a heavy end accent, it was practically impossible to hear the rhyme across the break made by the heavy accent. Somehow the particular condition of the organism which constitutes the expectation of a rhyme is broken up by a heavy accent.
The material for the records of Table V. was read to the subjects, the tones were in every case those of the speaking voice, and intervals having a definite speech character were chosen. The fifth is the interval of the rising inflection of the question, the fourth is the interval of the rising inflection of indifference or negation, and the single falling slide used is a descending interval of a third or fourth at the close of the sentence. The fifth appears in the table as 5/, the fourth as 4/, and the single descending interval of finality as the period (.). Each verse was read on approximately the first tone of the interval, the rhyming syllable only had the second tone of the interval.
TABLE V.
RHYMES UNDER GIVEN PITCH CONDITIONS.
Iambic tetrameters: two-verse stanzas.
The body of the verse is omitted; the closing intervals alone are indicated. '1' is read 'good rhyme;' '2' is 'poor rhyme'; and '0' is 'no rhyme.'
Couplets: --do 5/} 5/} .} .} 5/} --go .} 4/} 5/} .} 5/} G. 2 2 0 S. 0 0 2 1 R. 2 2 1 2 2 Mc. 0 0 0 1 1 Hu. 0 0 ? 1 Ha. 1 2 1 2
Iambic tetrameters; four-verse stanzas.
Rhymes are indicated by 'a' and 'a,' 'b' and 'b.' Capital* letters are read 'poor rhyme;' 'o' is read 'no rhyme.'
I. II. III. IV. I. II. III. IV. I. II. III. IV. I. II. III. IV. do, no, go, so. do, no, go, so. do, no, go, so. do, no, go, so. 5/ . 5/ . . 5/ . 5/ 5/ 5/ . . 5/ 5/ . 5/ G. a b a b a b a b a a b b a a a o R. a b a b a a b b Mc. a b a b a o a o Hu. a b a b a b a b a a b b a a o a Ha. a b a b o o o o a a B B a a o a
5/ 5/ 5/ . . . . 5/ . . . . . 5/ . . G. a a a a a a a o a a a a o o a a Hu. a a a o a a a o a a a a a o a a Ha. a a a o a a A o a a a a a o a a Mc. a a a o a a a o A A A A A o A A R. a a a o a a a o a a a a A o A A
5/ 5/ 4/ 5/ . . 5/ 5/ 5/ . 4/ . 5/ . . 5/ G. a a o o /a a b b /o a o a o o o o \a b a b \A A B B R. A A A A /o o a a\ a a b b \a a o o/ Hu. a a o a Mc. a a o a A A B B Ha. A A B B a a b b o a o a
4/ 4/ 4/ . 5/ 5/ 5/ 5/ 5/ 4/ 5/ 4/ G. a a a a o a o a Mc. a a a o R. a a a o a a b b Ha. A A A A
*Transcriber's Note: Original used italic lower case letters.
The table shows that there is a decided tendency to prefer rhymes in which the members of the rhyme have the same interval. The only exception is in the case of couplets, where two contrasting slides 5/ and . rhyme, whenever the finality interval occurs last. Perhaps the similarity of pitch of the rhyming syllables is a part of the 'Gestaltqualität' whose recognition brings about the release and satisfaction of the state which we know as the 'feeling of expecting a rhyme.' Definite pitch relations in music seem to make rhyme of little significance. We seldom notice the rhymes in a hymn or in a song of any musical worth. In comic operas and popular ditties rhyme does now and then figure. In such cases the pitch of the two or more rhyming syllables is identical; often the whole phrase is repeated for each rhyming verse. A few experiments in singing a rhyme to simple intervals show that when the identical interval is used the two syllables rhyme well, but if the interval be in the opposite direction, or in another chord, the rhyme is very uncertain. It seems that in music we usually have 'feelings of expectation' (i.e., tensions of some sort, central or peripheral), which are adequate to unite the phrases into larger unities. These tensions are so definite and vivid that they quite obscure and swallow up the related condition of rhyme expectation. These experiments on the modification of the rhyme by the various pitch and accent factors are not at all exhaustive or conclusive. An extended series of experiments is needed. The study of sound records for pitch is peculiarly tedious, but it should reveal some interesting relations between rhyme and speech melody.
III. THE SPEAKING OF A RHYTHMIC SERIES.
I. Methods of Making Speech Records.
The study of spoken rhythm is of primary importance. Observations on what the subject really does are always open to the objections that subjective factors play a large part, and that the observer's perception of a rhythm is after all his perception of the rhythm, not the subject's. The voice is an important indicator of the activities which generate the rhythms of verse and music, and some objective method of measuring the sounds made is essential to a study of the rhythm production.
Methods of recording and studying the tones of the voice are as numerous as they are unsatisfactory. In the main the work has been done for purposes of phonetics, and but few of the methods are applied in the psychological laboratory.
Marage[13] has an excellent summary of the methods with practical comments on their applicability. Rousselot[14] (Histoire des applications de phonétique expérimentale, 401-417: objets et appareils, 1-10 et 669-700) gives a careful history of the methods from the phonetic point of view. Scripture[15] gives a convenient English summary of the processes.
[13] Marage: l'Année psychologique, 1898, V., p. 226.
[14] Rousselot: La Parole, 1899.
[15] Scripture, E.W.: Studies from the Yale Psych. Lab., 1899, VII., p. I.
A few methods have been devised which avoid the difficulties incident to the use of a diaphragm, but they are not applicable to the measurement of rhythm material. The instruments which might be used for recording spoken rhythms are all modifications of two well-known forms of apparatus, the phonautograph and the phonograph. The phonograph record is incised in wax, and presents special difficulties for study. Boeke, however, has studied the wax record under a microscope, with special arrangements for illumination. The work is quite too tedious to permit of its use for material of any length, though it is fairly satisfactory when applied to single vowels. In order to enlarge the record, and at the same time to obtain the curves in the plane of the record surface, Hermann devised an attachment to the phonograph (cf. Marage, loc. citat.) by which the movements of the stylus of the phonograph are magnified by a beam of light and recorded on photographic paper. The measurements of entire words by this method would be as tedious as by Boeke's.
E.W. Scripture has chosen another type of talking machine from which to obtain transcribed records. The permanent record of the gramophone (which makes a record in the plane of the surface, like the phonautograph) is carefully centered, and a lever attached to a stylus which follows the furrow of the record transcribes the curve on the kymographic drum as the plate is slowly revolved. The method has the advantage of using a record which may be reproduced (i.e. the original gramophone record may be reproduced), and of giving fairly large and well defined curves for study. It is too laborious to be applied to extended research on speech rhythms, and has besides several objections. The investigator is dependent on the manufacturer for his material, which is necessarily limited, and cannot meet the needs of various stages of an investigation. He knows nothing of the conditions under which the record was produced, as to rate, on which time relations depend, as to tone of voice, or as to muscular accompaniments. There are also opportunities for error in the long lever used in the transcription; small errors are necessarily magnified in the final curve, and the reading for intensity (amplitude of the curve) is especially open to such error.
The stylus of such a recording apparatus as is used by the gramophone manufacturers, is subject to certain variations, which may modify the linear measurements (which determine time relations). The recording point is necessarily flexible; when such a flexible point is pressed against the recording surface it is dragged back slightly from its original position by friction with this surface. When the point is writing a curve the conditions are changed, and it sways forward to nearly its original position. This elongates the initial part of the sound curve. This fact is of little importance in the study of a single vowel, for the earlier part of the curve may be disregarded, but if the entire record is to be measured it is a source of error. Hensen[16] first turned the phonautograph to account for the study of speech. He used a diaphragm of goldbeater's skin, of conical shape, with a stylus acting over a fulcrum and writing on a thinly smoked glass plate. The apparatus was later improved by Pipping, who used a diamond in place of the steel point. The diamond scratched the record directly on the glass. The Hensen-Pipping apparatus has the advantage of taking records directly in the plane of the surface, but it does not make a record which can be reproduced; in case of doubt as to the exact thing represented by the curve, there is no means of referring to the original sounds; and it involves working with a microscope.
[16] Hensen: Hermann's Handbuch d. Physiol., 1879, Bd. I., Th. II., S. 187.
The apparatus which was used in the following experiments consisted essentially of two recording devices--an ordinary phonograph, and a recorder of the Hensen type writing on a rotary glass disc (see Fig. 5, Plate X.). Of the phonograph nothing need be said. The Hensen recorder, seen in cross section in Fig. 3, was of the simplest type. A diaphragm box of the sort formerly used in the phonograph was modified for the purpose. The diaphragm was of glass, thin rubber, or goldbeater's skin. The stylus was attached perpendicularly to the surface of the diaphragm at its center. The stylus consisted of a piece of light brass wire bent into a right angle; the longer arm was perpendicular to the diaphragm; the shorter arm was tipped with a very fine steel point, which pointed downward and wrote on the disc; the point was inclined a trifle to the disc, in order that it might 'trail,' and write smoothly on the moving disc. The stylus had no fulcrum or joint, but recorded directly the vibrations of the diaphragm. In early experiments, the diaphragm and stylus were used without any other attachment.
But a flexible point writing on smoked glass is a source of error. When the disc revolves under the stylus, the flexibility of the diaphragm and of the stylus permit it to be dragged forward slightly by the friction of the moving surface. When the diaphragm is set vibrating the conditions are altered, and the stylus springs back to nearly its original position. The apparent effect is an elongation of the earlier part of the curve written, and a corresponding compression of the last verse written. This error is easily tested by starting the disc, and without vibrating the diaphragm stopping the disc; the stylus is now in its forward position; speak into the apparatus and vibrate the diaphragm, and the stylus will run backward to its original position, giving an effect in the line like a (Fig. 4). If the error is eliminated, the stylus will remain in position throughout, and the trial record will give a sharp line across the track of the stylus as in b.
This source of error was avoided by fixing a polished steel rod or 'guide' at right angles to the vertical part of the stylus, just in front of the stylus; the stylus trailed against this rod, and could not spring out of position. The friction of the rod did not modify the record, and the rod gave much greater certainty to the details of the sound curve, by fixing the position of the vibrating point. This rod or guide is shown in Fig. 3 (g).
The disc was driven directly from the phonograph by a very simple method. A fine chain was fixed to the shaft carrying the disc, and wrapped around a pulley on the shaft. The chain was unwound by the forward movement of the recording apparatus of the phonograph against the constant tension of a spring. When the phonograph apparatus was brought back to the beginning of a record which had been made, the spring wound up the chain, and the disc revolved back to its original position.
A T from the speaking-tube near the diaphragm box was connected by a rubber tube with the phonograph recorder, so that the voice of the speaker was recorded both on the smoked glass plate and on the phonograph cylinder. The advantages of such a double record are that the possible error of a transcription process is eliminated, and yet there is an original record to which it is possible to refer, and by which the record measured may be checked.
An important feature in the method was the rate at which the disc revolved. The disc turned so slowly that the vibrations, instead of being spread out as a harmonic curve, were closely crowded together. This had two great advantages; the measurements were not so laborious, and the intensity changes were much more definitely seen than in the elongated form of record. Each syllable had an intensity form, as a 'box,' 'spindle,' 'double spindle,' 'truncated cone,' 'cone,' etc. (cf. p. 446).
The disc was run, as a rule, at a rate of about one revolution in two minutes. The rate could be varied to suit the purposes of the experimenter, and it was perfectly possible to procure the usual form of record when desired. As a result of the low rate, the records were exceedingly condensed. The records of the 300 stanzas measured are on two glass discs of about 25 cm. diameter, and as much more could still be recorded on them.
The diaphragm and the speaking tube were the great sources of error. For measurements of time values the particular component of the tone to which the diaphragm happens to vibrate is not important, but the record of intensities depends on the fidelity with which the diaphragm responds to a given component, preferably the fundamental, of the tone. The speaking tube has a resonance of its own which can be but partly eliminated. For the records here recorded either glass or goldbeater's skin was used as a diaphragm. Goldbeater's skin has the advantage of being very sensitive, and it must be used if the subject has not a resonant voice. It has the great disadvantage of being extremely variable. It is very sensitive to moisture, even when kept as loose as possible, and cannot be depended on to give the same results from day to day. The records marked Hu., Ha. and G. were usually taken with a glass diaphragm, which has the advantage of being invariable. As the phonograph records show, glass does not modify the lower tones of the male voice to any extent.
The speaking-tube used was of woven material, not of rubber, and a pad of felt was kept in the tube near the diaphragm box. As far as possible more damping was used at the other end of the tube, but this had to depend on the voices of the subjects.
The best check on the performances of a diaphragm is the number per second and character of the vibrations. The pitch may be calculated from the rotation rate of the disc, which is very constant, as it is driven at a low rate by the well-regulated high-speed motor of the phonograph. But it is better to place a fork in position to write on the disc and take a parallel record. All the records were taken with the vowel 'a' (sound as in father). This vowel has a very characteristic signature, which is easily seen, even in a very closely packed curve, and the correctness of this is one of the best guarantees that the fundamental of the tone is actuating the diaphragm (though that does not mean that the diaphragm is actually giving the vibration frequency of that fundamental).
Every record was repeated at least twice, and both records were measured. In many of the experiments the intensities were fixed by the conditions of the experiment. There was always the corroborative testimony of the phonograph diaphragm; for the two were not apt to err together. It was easy to determine if the actual intensity relations were preserved in the phonograph (but it could not be taken for granted). Each record was reproduced on the phonograph immediately after it had been taken, and both subject and operator listened for anomalies. In practice it was not hard to get records of the single vowel used (at a small range of pitch which was never more than a third or fourth and was nearly always much less) which represented fairly well the relative intensities. Beside the checks spoken of above, every record was repeated by a number of subjects, and the comparison of the results of different voices shows uniformity.
The recording of spoken verse is another matter. It is not difficult to test a diaphragm carefully through a small range, but to be certain of its action at all the pitches and qualities of the speaking voice is impossible. A stable diaphragm, glass or mica, would have to be used, and careful corrections made for the different vowels.
At best, when the records are satisfactory, nothing can be said for the measurements of intensity but that they represent relations of more or less; the diaphragm has a minimum intensity, below which it does not vibrate, and a maximum intensity, above which the amplitude of its vibrations does not materially increase without breaking into partials and 'blasting.'
The disc recorder, which had for a mount a modified microscope stand, was placed on the shoe of the disc stand and clamped. The wax and disc records were adjusted at known starting-points and the stylus carefully lowered, by the rack and pinion adjustment, to the surface of the disc. After a preliminary trial of the diaphragm the apparatus was started, and when at full speed at least two satisfactory records of the material were taken. When the disc had made a single revolution--a record of some ten or fifteen stanzas--the recorder was fed inward to a new circle on the disc. After the records were taken, a microscope with either 2 or 4 Leitz objective and a micrometer ocular was substituted for the recorder. The phonograph recorder was raised and drawn back to its starting point, and the disc came back to its original position. The microscope was focussed, and adjusted by the screw of the shoe until it had the record line in its field; the micrometer furnished an object of reference in the field. The phonograph, now carrying the reproducer--if possible without a horn, as the tones are truer--was started. At the first syllable of the record the apparatus was stopped by the device furnished on the 'Commercial' phonograph, and the plate was turned by adjusting the screw at the phonograph carriage, which changed the length of the chain connecting the two records, until the record of the first syllable was at some chosen point in the field. In cases of records of poetry it was found better to have a set of syllables, say 'one, two, three' prefixed to the record, for this adjustment. The phonograph was again started, and the curve-forms representing the spoken syllables filed past the point as the phonograph repeated each syllable. The rate was slow enough, with the objective 2, so that there was no difficulty in observing the passing syllables. After the conformity of the phonograph record had been noted by the operator, and the subject had passed judgment on the phonograph as saying satisfactorily what he had said, the curve-forms were measured with the micrometer. The record was fed slowly through the field by means of the chain screw on the phonograph carriage; and measurements of the lengths of syllables gave their time values. The micrometer was passed back and forth across the form by the shoe screw, for the measurements of amplitude (intensity). The micrometer measurements in this case could be made at least as rapidly as measurements of kymograph curves. The measurements, with the powers used, are accurate to.01 sec.
The smoked disc records are to be preferred to those scratched with a diamond, because of the superior legibility of the line, an important item if thousands of measurements are to be made. The records are fixed with shellac and preserved, or they may be printed out by a photographic process and the prints preserved. The parallel set of wax records is preserved with them. There are several ways in which the wax records lend themselves to the study of rhythmic questions. It is easy to change the rate, and thereby get new material for judgment, in a puzzling case. Consonant qualities are never strong, and it is easy so to damp the reproducer that only the vowel intensities are heard. The application in the study of rhyme is obvious.
All the series consisted of regular nonsense syllables. The accented and unaccented elements were represented by the single syllable 'ta' ('a' as in father). Rhymes were of the form 'da,' 'na,' 'ga' and 'ka.' In other parts of the work (cf. Table IV.) the vowel o had been used in rhymes for contrast; but the same vowel, a, was used in these records, to make the intensity measurements comparable.
The records of the measurements were as complete as possible. The sonant and the interval of each element were measured, and all the pauses except the stanza pause were recorded. The intensity of each syllable was recorded beneath the length of the syllable, and notes were made both from the appearance of the curve and from the phonograph record.
2. The Normal Form of Unrhymed Verse.
To determine the influence of a subordinate factor in rhythm such as rhyme, it is necessary to know the normal form of verse without this factor. It is natural to assume that the simplest possible form of material would be individual feet recorded seriatim. But on trial, such material turned out to be very complex; the forms changed gradually, iambs becoming trochees and trochees changing into spondees. It is very probable that the normal foot occurs only in a larger whole, the verse.
To corroborate the conclusions from perceived rhythms as to the existence of variations in earlier and later parts of the verse, a table of mean variations was prepared from the material recorded and measured for other purposes.
TABLE VI.
MEAN VARIATIONS.
Iambic tetrameters; variations of each element from the average foot of the entire stanza.
[Label 1: Unaccented Element of Foot.] [Label 2: Accented Element of Foot.] [Label 3: Percentage M.V. of Unac. El.] [Label 4: Percentage M.V. of Ac. El.]
Hu. 8 stanzas [1] [2] [3] [4] M.V. 1st foot 0.9688 1.3125 11.1 7.8 2d " 0.8125 0.6563 9.3 3.9 3d " 0.8438 1.1875 9.7 7.1 4th " 0.9688 11. Av. foot of all stanzas 8.69 16.88
Geo. 10 stanzas, no accents or rhymes within the verse: M.V. 1st foot 2.725 2.775 24.6 13.3 2d " 1.300 1.325 11.8 6.4 3d " 1.400 2.050 12.7 9.8 4th " 2.750 24.9 Av. foot of all stanzas 11.05 20.85
Geo. 8 stanzas, accents and rhymes within the verse: M.V. 1st foot 1.4843 2.4687 13.1 11.5 2d " 1.4219 2.6875 12.6 12.6 3d " 1.7031 2.5312 15.1 11.8 4th " 1.8594 16.4 Av. foot of all stanzas 11.31 21.38
The last element has the 'finality-form' and is not comparable to the other accented elements and therefore is not given.
Dactylic tetrameters (catalectic); variations of each element from the average foot of the entire stanza:
[Label 1: Accented elements of Foot] [Label 2: 1st Unaccented element of Foot] [Label 3: 2d Unaccented element of Foot] [Label 4: Percentage M.V. of Ac. El.] [Label 5: Percentage M.V. of 1st Unac. El.] [Label 6: Percentage M.V. of 2d Unac. El.]
[1] [2] [3] [4] [5] [6] Me., Ha., 8 stanzas, normal: M.V. 1st foot 1.6875 1.2813 1.8125 9.70 9.76 10.5 " 2d " 1.0613 1.0613 1.4061 6.1 8.0 8.1 " 3d " 1.6875 1.3125 1.3750 9.7 9.9 7.9 Av. foot 17.38 13.18 17.31
Geo. 4, stanzas, abnormal type of dactylic foot: M.V. 1st foot 1.5000 1.1250 1.2813 11.5 11.0 8.7 " 2d " 1.5625 1.1250 1.1250 12.0 11.0 7.6 " 3d " 1.3437 1.1873 0.8737 10.3 11.5 5.9 Av. foot 13.00 10.25 14.75
Me., Ha., G., Hu., Am., accent on 2d foot, 8 stanzas: M.V. 1st foot 2.4688 1.3125 2.2813 12.7 12.7 11.5 " 2d " 2.3750 1.1250 3.8438 12.2 8.7 19.3 " 3d " 2.9688 1.3750 2.2500 15.5 10.7 11.3 Av. foot 19.44 12.88 19.88
Me., Ha., G., Hu., 19 stanzas, normal: M.V. 1st foot 1.9474 1.2500 2.2763 10.8 8.6 11.4 " 2d " 1.3816 1.2369 1.7766 7.7 8.5 9.3 " 3d " 1.3158 1.2105 1.6382 7.3 8.4 8.6 Av. foot 18.00 14.24 19.05
Me., Ha., G., 6 stanzas, normal: M.V. 1st foot 2.0000 1.2083 1.8750 10.5 10.4 10.7 " 2d " 2.6250 1.0416 2.1666 13.8 9.1 12.3 " 3d " 2.1250 1.3333 1.3333 11.3 11.4 7.6 Av. foot 18.92 11.58 17.50 The last foot (catalectic) is not comparable in these dactylic stanzas.
The mean variations of the table (Table VI.) were calculated as follows: The average for all the elements of the stanza was obtained and an average foot constructed (excluding the last sonant and the pause of the verse). From this average foot the variations of all the first feet were computed, then the variations of all the second feet, etc. Then the variations of the first feet of the stanza were averaged and percentages taken, etc.; it is this last value which goes to the making up of the tables. In inspecting the averages the corresponding elements of the feet should be compared. Any increased length due to a prescribed accent within the verse, etc., appears in the averages as a corresponding increase in the mean variation at that point, and only the first and last feet can be compared as to the variations in the verse as a whole. In making up the tables the material was grouped, not by combining the records of each subject, but by combining all the stanzas of a single type, in order to eliminate individual peculiarities.
TABLE VII.
Verse pauses in unrhymed stanzas, together with the foot pause within the verse. Length of last foot, together with the average foot within the verse:
Average first Last foot Average of first Verse Pause. 3 feet of verse. of verse. 3 foot pauses of verse. Iambs: 36 56.5 24 45.5 57 122 35 100 68.5 125 45 102 63.5 111.5 42 93 63.5 117.5 39 93.5 66 135 42 110 53.5 59 40 45 60 76 45 61 56.5 68 41 54 55.5 56 39 41 53 53.5 37 41.5 56 73 34 45 85 98 56 54 39 50 26.5 36 37 43 17 30 42.5 45 28 30 38.5 49 26 36 40 79 26 55 31 72.5 21 55 33 66 23 54 33 76 22 64 Dactyls, catalectic: 56 63 (The pauses cannot be 60 62 compared because of the 55 66 omission of elements in 51.5 76 the final foot.) 37 40 55 58.5 53 59.5 40 73 38 65 37.5 56 37 73
Throughout the series of measurements made the accented element was nearly always longer, and in no case did the accent fail to increase the length of the sonant. Ebhardt's suggestion that there are two significant parts in each foot-element, viz., sonant and pause, does not seem good. Although the sonant is much longer when accented, the ratio between the sonant and the following interval is not definite.
An examination of thirty-two stanzas of unrhymed iambic and dactylic (catalectic) tetrameters (cf. Table VII.) shows that the verse pause is always at least one fourth larger than the foot pause. In the unrhymed stanzas the verse pause varies widely, and may be as large as three times the foot pause. A pause longer than the foot pause is absolutely essential to the unity of the verse. All sorts of ratios are presented; evidently the verse pause is not a function of the foot pause.
The next table (Table VIII.) shows a variety of different dynamic shadings in the verse. It is noteworthy that in these nonsense verses the type is uniform throughout the stanza. Representing the intensities by curves similar to those used by the subjects in listening to rhythms, we have the forms shown in Fig. 6 (a).
The general curve is like that in Fig. 6(b).
When a special emphasis is prescribed on some particular accent in the verse, the type becomes invariable, not only in each stanza, but for all stanzas of all subjects.
The records show that the accent is produced in a variety of ways. One, for example, gets the accent by a slight increase in intensity, but especially by a pause following the sonant.
TABLE VIII.
THE INTENSITY RELATIONS WITHIN THE TOTAL, UNRHYMED VERSE.
UNRHYMED IAMBIC TETRAMETERS. Average Intensities. length Length ' ' ' ' of first of last _ - _ - _ - _ - 3 sonants. sonant.
Ha. 2 5 4 5 2 4 3 6 31 31s 4 4 2 4 2 5 3 7 33 36s 2 5 3 4 1 5 3 9 32 29s 2 4 2 5 2 5 3 7 31 22s 3 5 1 5 3 4 3 5 37 35s 2 5 2 4 2 4 3 6 35 27s 2 4 2 4 2 4 2 6 38 22s 1 4 3 4 1 5 3 6 34 23s Hu. 6 6 6 6 6 6 6 5 25 33 5 5 5 5 5 5 5 6 26 32 5 5 5 4 5 5 5 5 19 33 5 5 5 6 8 9 8 9 28 50 9 9 8 9 9 9 9 8 43 51 9 7 8 7 7 8 9 10 48 45s 6 7 7 7 6 7 6 7 43 43s 6 6 5 6 4 7 7 8 36 50 G. 9 14 7 14 4 12 6 10 20 25 7 12 7 14 7 10 6 10 16 26 7 12 6 11 4 12 5 10 17 26 6 13 6 11 1 9 7 12 16 26 10 8 7 30 6 15 7 16 18 25 7 14 8 12 6 15 10 13 15 28 7 16 9 15 4 14 7 12 16 25 7 15 7 13 5 13 6 12 17 25
In verses marked 's' the last sonant is shorter than the average of the preceding sonants.
UNRHYMED IAMBIC TETRAMETERS: PRESCRIBED ACCENT ON THE THIRD FOOT.
' \/ -- \/ -- \/ -- \/ -- Mc. Couplets. 4 6 6 7 4 6 4 4 5 8 5 6 2 12 8 5 4 6 5 10 4 11 5 3 4 6 5 10 4 10 4 4 7 11 5 9 9 15 5 5 5 19 20 22 21 24 6 6 12 22 16 22 20 22 8 7 12 22 14 31 10 26 6 7 Ha. Couplets. 4 7 4 8 8 9 5 7 5 7 4 6 6 8 2 7 2 6 2 6 5 6 3 6 2 7 3 6 2 10 3 4 3 7 3 7 4 6 4 6 4 5 3 6 4 7 2 6 5 7 1 6 4 8 2 5 2 7 3 5 3 7 2 6
UNRHYMED IAMBIC TETRAMETERS: PRESCRIBED ACCENT ON THE SECOND FOOT.
' \/ -- \/ -- \/ -- \/ -- Mc. Couplets. 13 22 22 30 22 18 15 18 11 20 22 26 15 19 15 10 10 25 20 26 20 24 12 23 10 19 17 26 19 11 9 10 12 23 18 26 22 17 10 15 8 23 20 27 16 22 15 16 12 23 26 30 22 21 10 17 14 28 26 34 11 28 11 21
Ha. Couplets. 6 9 4 12 4 5 3 4 5 4 12 1 5 2 5 3 5 3 12 2 5 2 6 1 6 4 15 1 6 2 7 - 15 3 12 - 8 - 5 - 6 4 12 - 7 - 5 - 7 - 7 4 13 - 4 - 6 3 13 - 5 - 4
G. Couplets. 9 19 11 20 4 12 3 10 5 13 6 16 5 10 6 11 8 16 10 18 5 10 6 11 6 12 6 16 6 10 6 10 8 16 13 19 5 13 8 12 9 17 11 19 3 10 6 12 9 16 9 18 6 10 7 9 7 15 7 15 5 10 5 10
Frequently the special accent seems to be made by a contrast between the accented foot and the feet which follow. In most cases the influence of the special accent is to be seen, not merely within the accented foot itself, but both before and after the accented foot. Often the appearance under the microscope is very striking; the sonants of the feet, both accented and unaccented, increase to the special accent and then decrease in a regular crescendo--diminuendo form. Much of this is not shown by the mere measurements.
In general the special accent may he said to be the climax of the verse movement. It is the crest of the wave, and, as noted above, the dynamic shading is not always made by an increase up to the accent, nor by a stress on a special accent, but by a sharp diminuendo immediately following the accent. A study of the phonograph record brings out these forms of shading, especially when the record is repeated slowly, exaggerating the dynamic variations and giving an opportunity for more careful observation.
Within the verse the general form of the syllable as it appears in the mass of closely written vibrations, often varies, but nearly always shows a square end. Several very common shapes are noticed and appear in the record as (1) 'truncated cones,' (2) 'boxes,' and (3) 'truncated spindles.' (See Fig. 7.)
With the particular syllable used, 'ta,' the beginning of curve form was usually square and abrupt (4), and not gradual (5), although a few of the latter type are found ('spindle').
One syllable form has an especial interest, because of its bearing on the problem of 'finality' feeling at the close of the verse. At the close of each verse, whether with or without rhyme, the syllable form is always a 'cone' (6) (cf. Fig. 8). Of about 600 verses measured not more than 15 are exceptions to this rule. Of these 15 exceptions 10 are under special conditions and confirm the hypothesis that this form is related to the finality process. The form very rarely occurs within the verse, and when it does it is usually before some cæsura, or under unusual conditions.
This 'cone' form of the closing syllable of the verse indicates a falling of the intensity of the voice. It is often, though not always, associated with a fall in the pitch, showing relaxation of the vocal cords. It seems to be an indication of the dying out of the intensity factor, a sinking of the tension, at the close of the verse. In the case of unrhymed verses, with long verse pause, the cone is often very much elongated, and it is quite impossible to say where the sound ceases.
Special accentuation of the long syllable of the foot increases the length of the sonant, of the accented element, and of the entire foot. There is probably a slight increase of the total length of an accented verse as compared with the similar unaccented, but no calculations were made to show that point. This is quite in accord with other results (Meumann, Ebhardt). This special accentuation is connected with an increased mean variation of the time values, as noted above. It is in that sense a 'disturbing factor.'
TABLE IX.
VERSE PAUSES (INCLUDING FINAL SONANT) TOGETHER WITH THE AVERAGE OF THE CORRESPONDING ELEMENT WITHIN THE VERSE.
Average long Verse pause Verse pause Verse pause element of of 1st verse of 2d verse of 3d verse first 3 feet. of stanza. of stanza. of stanza. End Rhymes. Mc. 26 34 104a 35 45 _45_a 80b 80a 31 33 64a 36 41 52a 51b 75a Ha. 41 _44_a 44 45a 43 47a _43_b 46a 39 _41_a 49b 46a 43 46a _45_b _45_a 36 44 41a 53 35 44a 58a 38b 33 40 73a ×30 Hu. 28 ×25a 50 28a
Feminine Rhymes. Hu. 18 21a 37a 19b 19 _20_a 22a 16b 19 _21_a _21_a 16b Mc. 36 72a 64 51a 36 ×32 41a 40 22 _22_a ×18 29a Ha. 27 31a 44b _28_a 36 79 ×30 40 30 36 79a _30_b 31 38 50a 36 32 39a 42 40a Am. 34 70 95a 85 35 73a 94 89a 30 45 47a 86 28 54 53a 70 G. 19 64a 64 79a 19 73a 83b 76a 21 81 67a -- 19 61 83a 79
The rhymes are marked 'a' and 'b'; e.g., couplets a, a, b, b, etc. Verse pauses in italics are equal to the foot pause; those marked 'x' are less than the foot pause.
3. Modification of the Normal Form of Verse due to Rhyme.
Verse Pause in Rhymed Material.
There are as wide, isolated variations as in the case of unrhymed material. As compared with unrhymed verse, the pause is in general decidedly shorter. The verse pauses of the feminine rhymes are generally much like those of the end rhymed material. But there are very few cases of the verse pause being as short as the foot pause--only four cases in sixty (6.6 per cent.). See Table IX.
This wide variation of the verse pause and its occasional equivalence to the foot pause in rhymed verses is in accord with the notion that the rhyme in some way brings the verse to a close by a process more rapid than that in unrhymed material.
The introduction of rhyme seems to be favorable to the division of a stanza into two parts by producing an unusually long verse pause after the second verse. Of 43 unrhymed stanzas there are 19 which show a decidedly long pause at the close of some one of the verses. But of these 19 cases, only 8 (18 per cent.) have the break at the close of the second verse. Of 64 rhymed stanzas, 29 show the division, and of this 29, 22 (34 per cent.) have the break at the close of the second verse.
Influence of the Rhymes on Intensities.
The intensities at the close of the verse, without rhyme, may be slightly greater than within the verse. The dynamic shading of the verse is elastic, and a variety of forms is possible, a decrescendo at the close of the verse is not unusual (cf. Table VIII.). But when the rhyme is introduced the general dynamic form of the verse is fixed, and in the material measured this is true not only of the verses in a stanza which contain the rhyme but of other verses in the same stanza.
Of the 32 verses containing rhymes in Table X., but four verses are exceptions to the rule of an increase of intensity on the rhyme. There are two cases of double, alternating rhymes where it is doubtful if the subject actually felt one of the alternating rhymes. This increase of intensity on the rhyme is not confined to that particular syllable or foot; often, as indicated by the italics, the influence of the accent makes itself felt earlier in the verse.
TABLE X.
INTENSITIES OF IAMBIC TETRAMETER WITH END RHYME (SHOWING INCREASED INTENSITY OF THE RHYMING SYLLABLE). ALSO AVERAGE LENGTH OF THE FIRST THREE SONANTS, TOGETHER WITH THE LENGTH OF THE LAST SONANT.
Intensities. Average length of first 3 Length of last sonants. sonant. \/ - \/ - \/ - \/ - Mc. -- 5 -- 5 -- 4 -- 5 19 27 -- 4 -- 4 -- 4 -- _11_a 34 -- 4 -- 4 -- 4 -- 7 21 -- 4 -- 5 -- 3 -- _8_a 23
-- 6 -- 6 -- 5 -- 6 19 22 -- 8 -- 7 -- 6 -- _10_a 34 -- 4 -- 3 -- 4 -- 5 26 -- 3 -- 5 -- 4 -- _5_a 30
2 3 5 4 4 5 6 _7_a 29 34 2 3 3 4 2 4 2 _7_b 48 1 2 3 2 2 2 1 _4_a 35 2 3 3 3 2 3 4 _5_b 20
-- -- -- -- -- -- -- --a 25 40 3 4 4 14 3 4 5 _5_b 39 2 3 1 2 2 3 1 _3_a 25 1 3 2 2 1 3 3 _5_b 43
Ha. 6 15 9 12 3 10 4 16 No increase in length. 3 5 3 7 3 5 5 15a 1 15 1 5 4 6 2 9 4 5 2 5 1 5 2 _14_a
2 6 4 8 1 6 5 _11_a No increase in length. 1 7 5 7 3 6 7 _11_b 2 5 2 6 2 6 4 _12_a 1 5 1 5 2 6 3 _15_b 33 38
4 9 5 9 1 3 6 _9_a 25 33 2 8 5 6 4 5 5 _10_b No increase in length. 2 5 2 5 2 5 5 _11_a 1 5 2 5 5 10 2 _12_b 32 34
The evidence of an increased intensity on the rhyme is not so positive in the case of rhymes in the third foot. Among the rhymes in the second foot there is but one exception. The rhymes in the second and third feet were never given very satisfactorily by several of the subjects. The rhymes within the verse determine a climax in the foot in which they occur, and all the verses follow this well-defined type. It is interesting to note, in studying the phonographic record, that in verses in which the accentuation of the rhythm is not very definite, the accentuation is perceived when the record is repeated at the normal speed. If the record is repeated more slowly, and especially at such a distance that the rhyming consonants cannot be distinguished, then the accentuation seems to disappear. It is probable that after a verse or stanza type has been established the voice may deviate from the type, and the accentuation will be supplied by the hearer.
TABLE XI.
INTENSITIES OF IAMBIC TETRAMETERS WITH RHYMES IN THE THIRD FOOT (SHOWING INCREASE IN INTENSITY OF THE RHYME SYLLABLE).
' ' ' ' \/ -- \/ -- \/ -- \/ -- Ha. 13 18 10 16 7 _9_a 6 12 9 10 4 11 7 _14_a 4 7 -- 12 5 10 7 9b 6 9 2 12 5 12 3 _14_b 4 6
2 12 4 13 7 8a 4 9 6 8 4 14 4 _15_a 2 9 2 13 -- 12 8 8b -- -- 5 9 6 10 -- 3b 4 6
Am. 10 10 4 12 6 _14_a 5 5 4 12 6 9 7 8a 4 4 5 12 8 9 7 _10_b 3 4 3 7 5 8 5 7b 2 4
10 13 5 10 4 _10_a 4 6 1 9 4 9 3 5a 3 5 2 8 3 5 -- _8_b 1 5 1 7 2 7 5 _8_b 2 3
G. 6 13 6 13 7 _12_a 1 10 6 10 6 6 7 _7_a 1 8 4 9 7 7 6 9b 1 7 7 12 4 10 2 7b 1 7
10 12 4 11 6 _10_a -- 8 5 12 5 11 6 _10_a -- 8 3 9 6 9 7 _9_b 3 8 2 8 5 9 5 5b 1 6
D. 10 12 10 10 7 9a 7 11 5 8 6 9 7 7? 6 6 5 12 7 9 6 _10_b -- 8 6 9 7 10 7 7b 5 5
10 15 5 11 6 9a -- 9 5 9 4 8 6 6a? 6 7 7 11 7 11 11 _13_b 8 10 8 11 8 10 7 9b 6 8
INTENSITIES OF IAMBIC TETRAMETERS WITH RHYMES IN THE SECOND FOOT.
' ' ' ' _ - _ - _ - _ - Hu. 5 6 6 6a 5 7 5 6 5 6 5 4a 5 4 5 6? 5 6 6 7b 5 6 4 7 5 6 4 4b 5 7 4 7 5 7 7 7a 6 7 6 6 5 7 5 5a 5 6 5 6? 5 7 6 8b 6 7 6 7 6 7 6 5b 6 7 6 7 Mc. 5 7 6 10a 5 4 3 5 1 6 6 8a - 6 1 4 1 6 6 10b 1 4 - 4 - 7 6 5b 3 3 - 3 Ha. 16 14 8 10a 6 10 5 9 5 10 7 8a 5 9 5 7 2 8 4 11b 4 7 2 8 2 8 4 6b 1 9 4 8 7 12 7 10a - 10 6 10 3 10 5 8a 5 8 6 10 2 8 3 11b 3 7 3 10 - 7 5 9b 4 8 6 12 Am. 4 9 9 10a 4 7 4 5 4 8 9 7a 5 7 4 6 1 8 5 10b 4 6 3 6 - 10 10 7b_ 3 5 2 7 15 15 10 13a_ 9 11 - 11 5 12 7 9a 4 10 4 9 5 8 8 9b 4 7 - 6 7 8 5 9b 2 4 - 3 G. 2 6 6 8a 1 7 2 3 - 10 7 12a 1 9 4 8 4 9 6 9b 8 8 2 7 - - - -b - - - - 4 9 5 _11_a - 7 4 6 - 8 6 7a 2 7 4 5 - 9 7 _6_b - 7 3 6 - 7 3 5 - 5 - 3 D. - - - - - - - - 7 11 11 _9_a 7 11 6 10 11 15 11 11a 8 11 9 14 6 10 10 8b 7 8 7 11 12 13 10 10a 7 1? 8 11 6 10 9 8a 5 8 5 9 9 12 12 13b 8 10 7 9 7 11 10 7b 4 8 4 8
The values surrounded by '_'s (Transcriber's Note: Original italics) show the increase in intensity. Rhymes are indicated by 'a' and 'b.'
IV. SUGGESTIONS FOR A MOTOR THEORY OF RHYTHM.
If the basis of rhythm is to be found in muscular sensations, rather than in the supposed activity of some special 'mental' function, the nature of the movement cycle involved is of the greatest interest.
In every case where a rhythm comes to peripheral expression, there are two opposing sets of muscles involved. If a rhythmic movement be attempted with but a single set of muscles at work, it is very unsatisfactory and soon ends in the tonic contraction of the muscle set. One may assume that in all cases of rhythm perception there is a cycle of movement sensations involved, and that the simplest possible case of a peripheral rhythmic movement is the type of any rhythm. In tapping a rhythm with the finger, the flexors which bring the finger down become the positive muscle set, and the opposing extensor muscles which raise the finger for the next blow become the negative muscle set.
In Fig. 9 the upper curve represents the actual movement of the finger tip, and the heavy lines a, a', a'' represent the pressure-tension-sound sensation which we call the 'beat,' and which is the limiting sensation of the rhythm, and the regulating factor in the movement cycle of the rhythm. The movement is divided into two phases; B, the phase of relaxation, during which the finger is raised, and A, the phase of contraction, during which the finger delivers the blow which produces the beat.
The curves below represent the changes in the two opposing sets of muscles whose interaction brings about the movement cycle. The contraction of the flexors, the positive muscle set, is represented by the curve above the base line. It is obvious that during the contraction phase, the contraction in the positive muscle set is at its height; it continues at a maximum during the limiting sensation and then dies away during the relaxation phase. The sensations from this positive muscle set have the principal place in consciousness during the rhythm experience. The curve below the base line represents the contraction of the extensors, the negative muscle set. The contraction of the negative muscles reaches its climax very soon after the maximum contraction of the positive muscles, in the contraction phase. The sharp tension between the two opposing sets of muscles at the limiting sensation may be made very apparent if the finger beats the rhythm entirely in the air; in that case the limiting sensation consists entirely of the feeling of a sudden increase of tension between the positive and negative muscle sets. During the relaxation phase the contraction of the negative muscles continues, but the tension between the two sets grows less and less, for the positive muscles are rapidly relaxing. At the highest point in the movement either muscle set is exerting but very little strain; the condition is represented in the figure by the approach of either curve to the base-line; the amount of tension between the two sets is figured by the distance of the two curves from each other.
Assuming such a movement cycle, in which the tension between the two opposing sets never comes to zero until the close of the series, it is not difficult to arrange many of the facts of rhythmic perception under the motor theory.
1. The feeling of rhythm is more definite as we proceed in a verse, or a series of simple sound sensations. At first the cycle is not perfectly adjusted and complete automatism established.
2. If an observer is listening to a series, and an unusually long pause is introduced between two beats, there is always a feeling of suspense or tension during the 'lag.' As long as the tensions are maintained there is a rhythmic continuity; the feeling of tension is the strain of opposition between the opposing muscle sets.
3. The continuity of the rhythmic series, whereby all the beats of a period seem to belong to a single whole, is due to the continuity of the muscle sensations involved and the continuous feeling of slight tension between the positive and negative muscle sets; nowhere within the period does the feeling of strain die out.
4. But at the close of the period we have a pause which is demonstrably not a function of any of the intervals of the period. During this pause the tension between the two sets 'dies out,' and we have a feeling of finality. This gradual dying out of the tension is clearly seen in the constant appearance of the cone-shaped final syllable at the end of each nonsense verse.
5. The period composed of a number of unit groups (the verse, in nonsense syllables) has a general form which suggests strongly that it has the unity of a single coördinated movement. There is no more reason for assuming a transcendental mental activity in the case of a rhythmic period than in the case of a single act which appears in consciousness as a unity. Undoubtedly the breathing is correlated with the rhythmic movements and may be a factor in determining the verse period. Meumann's principal accent, about which a number of subordinate accents are grouped, is characteristic not only of poetry but of the simplest rhythms. At some point in the period there is a definite climax, a chief accent; the movement 'rises' to that point and then falls off. This is strikingly seen in nonsense verses spoken with a heavy accent within the verse. The accent does not stand out from a dead level, but the verse culminates at that point.
Unfortunately very little is known of the mechanism of so simple a coördinated muscular activity as that necessary for a simple rhythm. Sherrington[17] and Hering[18]have pointed out the primary character of the grouping of the muscles in opposing sets and the reciprocal nature of almost all muscular activity, but in a review of the work of coördinated movements Hering denies any simultaneous stimulation of the two sets and considers the question of the innervation mechanism of opposing muscle-sets entirely unsettled.
[17] Sherrington, C.S.: Proceedings Royal Soc., 1897, p. 415.
[18] Hering, H.E.: Archiv f. d. ges. Physiol. (Pflüger's), 1897, Bd. 68, S. 222; ibid., 1898, Bd. 70, S. 559.
That the connection between the positive and negative set of muscles in a rhythmic movement is very close, and that the reaction is of the circular type, is evident from the automatic character of all rhythmic movements, and it is evident that the limiting sensation is the primary cue in the reaction. Anything further is mere hypothesis. Robert Müller's[19] thorough criticism of the Mosso ergograph throws great doubt on the present methods of investigation and invalidates conclusions from the various curves of voluntary movements which have been obtained.
[19] Müller, R.: Phil. Stud., 1901, Bd. 17, S. 1.
The curve of contraction and relaxation of a simple muscle is well known and is not affected by Müller's criticism. Its chief characteristic, with or without opposing tension, is the inequality of the intervals of the contraction and relaxation phases. As one might expect, since a single set of muscles dominates in a rhythmic movement, the typical rhythmic curve has the general character of the curve of the simple muscle. The average values of the phases of curves of simple rhythmic movement obtained by A. Cleghorn[20] from a large number of observations with at least three subjects, are as follows: phase of contraction, .44 second; phase of relaxation, .54 second. It is very significant for a motor theory of rhythm that this general form of the curve of rhythmic movement may easily be altered in all sorts of fashions by unusual stimuli to the two muscle sets.
[20] Cleghorn, A.: Am. Journal of Physiol., 1898, I., p. 336.
While it is well recognized that a rhythm does not consist necessarily of sound sensations, the 'rhythmization' of a series of sound sensations in the ordinary perceived rhythms is a matter of great interest. Ewald found strong reasons for believing that the ear is peculiarly connected with the motor apparatus. The experiments of Hofbauer[21] and Cleghorn[22]show that any strong stimulus to either eye or ear modifies decidedly the reactions of coördinated muscles. How shall we assume that the automatic movement cycle necessary to rhythmic perception is set up when one listens to a series of sounds?
[21] Hofbauer: Archiv f. d. ges. Physiol. (Pflüger's), 1897, Bd. 68, S. 553.
[22] Cleghorn, A.: op. cit.
It must be assumed that any chance sound sets up a contraction in a set of muscles, however large or small. If but a single sound occurs, the phase of contraction in that muscle set is followed by a longer phase of relaxation, and the musculature is passive as before; it may be that the stretching of the antagonistic set of muscles weakly stimulates them, and they then contract during the relaxation phase and assist in restoring the original condition.
But if a second sound occurs toward the end of the relaxation phase, before the tension is quite exhausted, the movement will be repeated; the negative set of muscles will be more definitely stimulated, for the activity will not have been exhausted when the second sound occurs. If the sound continues to recur at regular intervals, the movement cycle thus established will rapidly become coördinated. The positive set in its vigorous contraction furnishes a limiting sensation which becomes a cue for its own relaxation and for the reciprocal contraction of the negative muscle set. The contraction of the negative muscle set and the resulting changes in tension may become in turn a cue for the positive set. The reaction is now of the circular type and the process has become self-regulative, though constantly reinforced by the recurring sound (which has become a part of the limiting sensation of the rhythmic movement cycle).
But it is very probable that the second sound may not be timed so as to come at the close of the relaxation phase in the set of muscles roused; moreover, in almost all rhythms there are secondary sounds occurring between the main beats. What happens when a sound occurs out of place, early in the phase of relaxation, or just before or just after the climax in the contraction phase? Does it make it impossible to establish the coördination, or destroy it if already established?
Hofbauer demonstrated that a stimulus which appears in close proximity to the limiting sensation, either before or after, always increases the force of the reaction, so that such a slight displacement could not affect the rhythm, which would quickly readjust itself. The possibility of a stimulus occurring in the relaxation phase is of much more importance for a motor theory of the initiation of a rhythmic movement. Cleghorn made the stimulus occur at the beginning of the relaxation phase. Instead of prolonging or reinstating the contraction phase, he found that the stimulus intensified the relaxation process and shortened its period. "The stimulated relaxation is not only quicker than the normal, but also more complete; the end of the normal relaxation is slow; ... relaxation under the influence of the stimulus, on the contrary, shows nothing of this, but is a sudden sharp drop directly to the base line and sometimes below it." A comparison of the normal phases with the same phases, when the stimulus occurs within the relaxation phase, follows:
Normal: Contraction-phase, .44 sec.; relaxation-phase, .54 sec.; total, .98 sec. With stim.: Contraction-phase, .47 sec.: relaxation-phase, .30 sec.; total, .77 sec.
It will be noticed that the total time of the movement cycle is reduced. One may then assume that a sound which occurs too early to become a factor in the limiting sensation, functions as a stimulus to the relaxation process and shortens the interval between the limiting sensations. Thus the movement cycle would be modified, but not destroyed. It is impossible to say just how the relaxation process is affected, and Cleghorn's own conclusions are open to criticism in the light of Müller's comments on the method. The simplest assumption would be that the stimulus acted on the negative set of muscles.
E.W. Scripture[23] objects to such a 'tonus theory,' because some subjects regularly react before the signal. But in no case in the published records to which he refers is the error more than.05 sec. either before or after the signal. The investigation of Hofbauer shows conclusively that in such cases the effect of the external stimulus simply fuses with the limiting sensation. Scripture overlooks the automatic character of the rhythmic movement.
[23] Scripture, E.W.: 'The New Psychology,' London, 1897, p. 182.
There is a striking difference between rhythmic movement from unit group to unit group within a period, and movement from period to period (i.e., from verse to verse of nonsense syllables). Each foot is simply the repetition of the movement cycle; all the tensions are maintained, and each foot is an integral part of a larger act. At the close of the period (verse) the active tensions die out, either because of the introduction of some unusual stimulus which causes the positive muscle set to strike a heavy blow, and abruptly upset the balanced tensions, or because a pause of indefinite length ensues in which the tensions die out. This is the process which we call 'finality.'
In the stanza there is evidently a different type of unity from that in the single verse. When we hear the first verse of the stanza, we do not know what the verse whole is, until the finality factor or the verse pause is reached, at its close. Then the verse has a certain definite cumulative effect, a synthetic effect which results from the echoes of the various movements and the total effect on the organism. One may call it the tetrameter feeling. The verse pause may vary within large limits, but after a few verses there is a definite scheme, or 'Gestaltqualität,' which represents the verse unity. It is some sort of a memory image, which functions as a cue to the motor process. This motor image, set of strains, or whatever it be, is more than a mere standard by which we judge the present verse. The memory image fuses in some way with the living motor process. The preceding verse affects the character of the following verse. An irregularity, easily noted in the first verse, is obscure in the second, and not detected in the third verse, when the verses are identical.
The experiments of Hofbauer and Cleghorn, and many facts about the unit groups themselves, make it evident that the function of stimuli, during the movement cycle, varies with the position of the stimulus in that cycle. This offers a possible explanation of the striking peculiarities of the unit groups. The iamb [\/ '] and the trochee [' \/] should be quite alike for a general synthesizing process; but not only is the experiential character of the two quite unlike, but the ratio between their intervals is entirely different.
A number of measurements by different observers show that in the iambic foot the unaccented syllable is proportionately much shorter than the unaccented syllable in the trochaic foot. It is very easy to beat a simple up-and-down accompaniment to a series of simple feet of nonsense syllables; in the accompaniment the bottom of the down stroke, the limiting sensation of the movement cycle, coincides with the accented syllable of the foot. It is not an unwarranted assumption that such a fundamental accompaniment represents the fundamental movement cycle of that rhythm.
During the present investigation several observers were asked to determine at just what point in the fundamental movement the unaccented syllable occurred, when the subject gave a series of nonsense syllables. In the fundamental accompaniment the excursion of the hand and arm was at least.4 meter. Four subjects were thus tested, and the results were uniform in the case of all the simple types of unit groups.
In the case of the iamb the unaccented syllable occurs at the top of the movement, at the very beginning of the contraction phase (A, in Fig. 5).
In the case of the trochee the unaccented syllable occurs in the first third of the relaxation phase (B).
It is interesting to note that the unaccented element of the trochee comes at the earlier part of the relaxation phase, where it must intensify the relaxation process, and tend to shorten the total length of the cycle. This may be the reason for its peculiar buoyant, vigorous and non-final character. On the other hand the unaccented element of the iamb occurs at a point where it may initiate and intensify the contraction, which gives the limiting sensation; it is, therefore, more closely bound to the limiting sensation, and has the character of intensifying the beat. There is a similar contrast in the cases of the dactyl and anapæst. The accented syllable of the dactyl is longest, and the second unaccented syllable, the last in the group, is shortest. The accented syllable of the anapæst is much longer in proportion than that of the dactyl, and the unaccented syllables are very short, and hence, very close to the accented syllable, as compared with the dactyl.
In the case of the dactyl the first unaccented syllable in the movement cycle occurs at the beginning of the relaxation phase (B), in the same zone as the unaccented of the trochee. The second unaccented syllable of the dactyl appears at the beginning of the next contraction phase (A), in the zone of the unaccented syllable of the iamb. The group seems a sort of combination of the iamb and trochee, and has an element in every possible zone of the movement cycle. Like the trochee the dactyl is a non-final foot.
The unaccented syllables of the anapæst both occur at the beginning of the contraction phase (A). They are both within the zone of the unaccented syllable of the iamb. The group seems an iamb with a duplicated unaccented syllable. It is possible to form a unit group in nonsense syllables where the unaccented syllable of the iamb shall be represented not by two syllables, as in the anapæst, but by even three.
The anapæst and dactyl, if they correspond to this construction, should show a decided difference as to the possibility of prolonging the foot pause. The prolongation of the foot pause would make the dactyl but a modified trochee.
It is significant that in poetry no other types of unit groups are often recognized. The amphibrach, laid out on this scheme, would coincide with the dactyl, as there are but three possible zones for foot elements: the zone of the limiting sensation (always occupied by the accented syllable), the zone of the contraction phase (occupied by the unaccented syllables of the iamb and anapæst), and the zone of the relaxation phase (occupied by the unaccented syllable of the trochee and the middle syllable of the dactyl).
The simple sound series is fairly regular, because of its cyclic and automatic character. It is not a matter of time estimation, and the 'Taktgleichheit' is not observed with accuracy. The primary requisite for the unit groups is that they shall be alike, not that they shall be equal. The normal cycle with a heavy accent is longer than the normal cycle with a lighter accent, for the simple reason that it takes muscles longer to relax from the tenser condition. Time is not mysteriously 'lost'; the objective difference is not noticed, simply because there are no striking differences in the cycles to lead one to a time judgment. Ebhardt's notion that the motor reaction interferes with the time judgment, and that a small amount of time is needed in the rhythmic series in which to make time judgments, is a mere myth.
An unusual irregularity, like a 'lag,' is noted because of the sense of strain and because other events supervene in the interval. But such lags may be large without destroying the rhythm; indeed cæsural and verse pauses are essential to a rhythm, and in no sense rhythm-destroying. An unbroken series of unit groups is an abstraction to which most forms of apparatus have helped us. Between the extreme views of Bolton[24] and Sidney Lanier,[25]who make regularity an essential of the rhythm of verse, and Meumann, on the other hand, who makes the meaning predominate over the rhythm, the choice would fall with Meumann, if one must choose. Bolton comes to the matter after an investigation in which regularity was a characteristic of all the series. Lanier's constructions are in musical terms, and for that very reason open to question. He points out many subtle and interesting relationships, but that verse can be formulated in terms of music is a theory which stands or falls by experimental tests.
[24] Bolton, T.L.: loc. cit.
[25] Lanier, S.: 'The Science of English Verse.'
TABLE XII.
I saw a ship a sailing 50 16 20 13 9 18 32 23- 132 A sailing on the sea 10 16 45 22 8 15 49 -68 And it was full of pretty things 8 6 20 6 6 27 37 12 8 7 20 12 41 -34 For baby and for me 14 9 27 37 18 20 14 8 46 --
Totals of the feet: --/66/60/187 26/45/45/117 14/59/49/47/75 23/64/60/46--
Who killed Cock Robin 19 34 23 24 17-77 I said the sparrow 45 21 19 3 47 29 -- With my bow and arrow 22 36 25 49 11 38 12 23 33-42 I killed Cock Robin 33 12 33 21 22 5 21 16-95
(The first stanza was measured in the Harvard Laboratory. The last is modified from Scripture's measurements of the gramophone record (1899). As the scansion of the last is in doubt with Scripture, no totals of feet are given.)
In the cases given in the above table there is an irregularity quite impossible to music.
In the movement cycle of the simple sounds there is a perfect uniformity of the movements of the positive and negative sets of muscles from unit group to unit group. But in verse, the movements of the motor apparatus are very complicated. Certain combinations require more time for execution; but if this variation in the details of the movement does not break the series of motor cues, or so delay the movements as to produce a feeling of strain, the unit groups are felt to be alike. We have no means of judging their temporal equality, even if we cared to judge of it. It is a mistake, however, to say that time relations ('quantity') play no part in modern verse, for the phases of the movement cycle have certain duration relations which can be varied only within limits.
Extreme caution is necessary in drawing conclusions as to the nature of verse from work with scanned nonsense syllables or with mechanical clicks. It is safe to say that verse is rhythmic, and, if rhythm depends on a certain regularity of movements, that verse will show such movements. It will of course use the widest variation possible in the matter of accents, lags, dynamic forms, and lengths of sonant and element depending on emphasis. The character of the verse as it appears on the page may not be the character of the verse as it is actually read. The verses may be arbitrarily united or divided. But in any simple, rhythmic series, like verse, it seems inevitable that there shall be a pause at the end of the real verse, unless some such device as rhyme is used for the larger phrasing.
There is a variety of repetitions in poetry. There may be a vague, haunting recurrence of a word or phrase, without a definite or symmetrical place in the structure.
Repetition at once attracts attention and tends to become a structural element because of its vividness in the total effect. There are two ways in which it may enter into the rhythmic structure. It may become a well-defined refrain, usually of more than one word, repeated at intervals and giving a sense of recognition and possibly of completeness, or it may be so correlated that the verses are bound together and occur in groups or pairs. Rhyme is a highly specialized form of such recurrence.
The introduction of rhyme into verse must affect the verse in two directions.
It makes one element in the time values, viz., the verse pause, much more flexible and favors 'run on' form of verses; it is an important factor in building larger unities; it correlates verses, and contributes definite 'Gestaltqualitäten' which make possible the recognition of structure and the control of the larger movements which determine this structure. Thus it gives plasticity and variety to the verse.
On the other hand, it limits the verse form in several directions. The general dynamic relations and the individual accents must conform to the types possible with rhyme. The expressional changes of pitch, which constitute the 'melody,' or the 'inflections' of the sentences, play an important part. The dynamic and melodic phases of spoken verse which have important relations to the rhyme are not determined by the mere words. The verses may scan faultlessly, the lines may read smoothly and be without harsh and difficult combinations, and yet the total rhythmic effect may be indifferent or unpleasant. When a critic dilates on his infallible detection of an indefinable somewhat, independent of material aspects of the verse and traceable to a mystic charm of 'thought,' it may very well be that the unanalyzed thing lies in just such dynamic and melodic conditions of rhythm and rhyme.
The most primitive characteristic of music is the ensemble. Savage music is often little else than time-keeping. When the social consciousness would express itself in speech or movement in unison, some sort of automatic regulation is necessary. This is the beginning of music. The free reading of verse easily passes over into singing or chanting. When this happens, the thing most noticeable in the new form is its regulated, automatic and somewhat rigid character. It is stereotyped throughout. Not only are the intervals and accents fixed, but the pitch and quality changes are now definite, sustained and recurrent. The whole sum of the motor processes of utterance has become coördinated and regulated. Along with this precision of all the movements comes a tendency to beat a new rhythm. This accompanying rhythm is simpler and broader in character; it is a kind of long swell on which the speech movements ripple. This second rhythm may express itself in a new movement of hand, head, foot or body; when it has become more conscious, as in patting time to a dance or chant, it develops complicated forms, and a third rhythm may appear beside it, to mark the main stresses of the two processes. The negro patting time for a dance beats the third fundamental rhythm with his foot, while his hands pat an elaborate second rhythm to the primary rhythm of the dancers.
The essential character of musical rhythm, as contrasted with the rhythm of both simple sounds and of verse, is just this coördination of a number of rhythms which move side by side. This is the reason for the immense complexity and variety of musical rhythms. The processes check each other and furnish a basis for a precision and elaborateness of rhythmical movement in the individual parts which is quite impossible in a simple rhythm.
Even when the concomitant rhythms are not expressed, as in an unaccompanied solo, an accompaniment of some sort is present in the motor apparatus, and contributes its effect to the consciousness. This regulation of the movement by the coincidence of several rhythms is the cause of the striking regularity of the temporal relations. At some points in the musical series the several movement cycles may appear in the same phase, and at these points the same irregularities as in verse are possible, as in the case of pauses at the ends of periods and the irregularities of phrasing. It is evident in cases of expressional variations of tempo that a single broad rhythm is dominating and serving as a cue for the other more elaborate rhythmic processes, instead of being regulated by them.
* * * * *
STUDIES IN SYMMETRY.[1]
BY ETHEL D. PUFFER.
[1] SOURCES OF ILLUSTRATIONS.
Fig. 1 was copied from Reiss u. Stübel, 'Todtenfeld v. Ancou,' Berlin, 1880-1887.
Figs. 2, 3, 4, 5, 6, 7, 8 and 11 were copied from the publications of the American Bureau of Ethnology by the kind permission of the Direction.
Fig. 9. was copied from A.C. Haddon, 'The Decorative Art of British New Guinea,' Cunningham Memoir, N., Royal Irish Academy, 1894.
Fig. 10 was copied from Franz Boas, 'The Decorative Art of the Indians of the North Pacific Coast,' Bulletin of the Am. Mus. of Nat. Hist., Vol. IX.
I. THE PROBLEMS OF SYMMETRY.
The problem of æsthetic satisfaction in symmetrical forms is easily linked with the well-known theory of 'sympathetic reproduction.' If there exists an instinctive tendency to imitate visual forms by motor impulses, the impulses suggested by the symmetrical form would seem to be especially in harmony with the system of energies in our bilateral organism, and this harmony may be the basis of our pleasure. But we should then expect that all space arrangements which deviate from complete symmetry, and thus suggest motor impulses which do not correspond to the natural bilateral type would fail to give æsthetic pleasure. Such, however, is not the case. Non-symmetrical arrangements of space are often extremely pleasing.
This contradiction disappears if we are able to show that the apparently non-symmetrical arrangement contains a hidden symmetry, and that all the elements of that arrangement contribute to bring about just that bilateral type of motor impulses which is characteristic of geometrical symmetry. The question whether or not this is the fact makes the leading problem of this paper, and the answer to it must throw light on the value of the theory itself.
An exhaustive treatment of our question would thus divide itself into two parts; the first dealing with real (or geometrical) symmetry, the second with apparent asymmetry; the first seeking to show that there is a real æsthetic pleasure in geometrical symmetry, and that this pleasure is indeed based on the harmony of the motor impulses suggested by symmetry, with the natural motor impulses of the human organism; the second seeking to show in what manner æsthetically pleasing but asymmetrical arrangements conform to the same principles. Within these two groups of problems two general types of investigation are seen to be required; experiment, and the analysis of æsthetic objects.
The main question, as stated above, is of course whether the theory can explain our pleasure in arrangements which are completely or partly symmetrical. It is, however, an indispensible preliminary to this question, to decide whether the pleasure in symmetrical arrangements of space is indeed immediate and original. If it were shown to be a satisfaction of expectation, bred partly from the observation of symmetrical forms in nature, partly from the greater convenience of symmetrical objects in daily use, the whole question of a psychophysical explanation would have no point. If no original æsthetic pleasure is felt, the problem would be transformed to a demand for the explanation of the various ways in which practical satisfaction is given by symmetrical objects and arrangements. The logical order, then, for our investigation would be: First, the appearance of symmetry in the productions of primitive life, as a (debatable) æsthetic phenomenon emerging from pre-æsthetic conditions; secondly, the experimental study of real symmetry; thirdly, the analysis of geometrical symmetry in art, especially in painting and architecture, by means of which the results of the preceding studies could be checked and confirmed. Having once established a theory of the æsthetic significance of real symmetry, we should next have to examine asymmetrical, beautiful objects with reference to the relation of their parts to a middle line; to isolate the elements which suggest motor impulses; to find out how far it is possible to establish a system of substitution of these psychological factors and how far such substitution takes place in works of art--i.e., to what extent a substitutional symmetry or balance is found in pleasing arrangements. These investigations, again, would fall into the two groups of experiment and analysis. The products of civilized art are too complicated to admit of the complete analysis and isolation of elements necessary to establish such a system of substitution of psychological factors as we seek. From suggestions, however, obtained from pleasing asymmetrical arrangements, first, isolated elements may be treated experimentally, and secondly, the results checked and confirmed by works of art.
With regard to the study of objects without a natural or suggested middle line, as for instance sculpture, many types of architecture, landscapes, gardens, room-arrangements, etc., we may fitly consider it as a corollary to the study of asymmetrical objects with artificial limits which do suggest a middle. If we find, by the study of them, that a system of substitution of psychological factors does obtain, the whole field can be covered by the theory already propounded, and its application extended to the minutest details. The hypothesis, having been so far confirmed, may be then easily applied to the field of asymmetrical objects without a natural middle line.
The set of problems here suggested to the student of symmetry will not be fully followed out in this paper. The experimental treatment of geometrical symmetry, the analysis of the completely symmetrical products of civilized art, and the analysis of all forms of asymmetry except asymmetry in pictures will be omitted. If, however, the fact of an original æsthetic feeling for symmetry is established by the study of primitive art, and the theory of the balance of motor impulses through the substitution of factors is established by the experimental treatment of isolated elements, and further confirmed by the analysis of pictures, the general argument may be taken as sufficiently supported. This paper, then, will contain three sections: an introductory one on symmetry in primitive art, and two main sections, one on experiments in substitutional symmetry, and one on substitutional symmetry or balance in pictures.
II. SYMMETRY IN PRIMITIVE ART.
The question which this section will attempt to answer is this: Is there in primitive art an original and immediate æsthetic feeling for symmetry? This question depends on two others which must precede it: To what extent does symmetry actually appear in primitive art? and, How far must its presence be accounted for by other than æsthetic demands?
For the purpose of this inquiry the word primitive may be taken broadly as applying to the products of savage and half-savage peoples of to-day, as well as to those of prehistoric races. The expression primitive art, also, requires a word of explanation. The primitive man seldom makes purely ornamental objects, but, on the other hand, most of his articles of daily use have an ornamental character. We have to consider primitive art, therefore, as represented in the form and ornamentation of all these objects, constituting practically an household inventory, with the addition of certain drawings and paintings which do not appear to serve a definite practical end. These last, however, constitute only a small proportion of the material.
The method of the following outline treatment will be to deduct from the object under consideration those symmetrical elements which seem to be directly traceable to non-æsthetic influences; such elements as are not thus to be accounted for must be taken as evidence of a direct pleasure in, and desire for symmetry on the part of primitive man. These possible non-æsthetic influences may be provisionally suggested to be the technical conditions of construction, the greater convenience and hence desirability of symmetrical objects for practical use, and the symmetrical character of natural forms which were imitated.
The first great group of objects is given in primitive architecture. Here is found almost complete unanimity of design, the conical, hemispherical or beehive form being well-nigh universal. The hut of the Hottentots, a cattle-herding, half-nomadic people, is a good type of this. A circle of flexible staves is stuck into the ground, bent together and fastened at the top, and covered with skins. But this is the form of shelter constructed with the greatest ease, suitable to the demands of elastic materials, boughs, twigs, reeds, etc., and giving the greatest amount of space with the least material. There are, indeed, a few examples of the rectangular form of dwelling among various primitive races, but these seem to be more or less open to explanation by the theory advanced by Mr. V. Mendeleff, of the U.S. Bureau of Ethnology. "In his opinion the rectangular form of architecture which succeeds the type under discussion, must have resulted from the circular form by the bringing together within a limited area of many houses.... This partition would naturally be built straight as a two-fold measure of economy."[2] This opinion is confirmed by Mr. Cushing's observations among the Zuñi villages, where the pueblos have circular forms on the outskirts. Thus the shape of the typical primitive dwelling is seen to be fully accounted for as the product of practical considerations alone. It may therefore be dismissed as offering no especial points of interest for this inquiry.
[2] Cushing, F.H.: 'Pueblo Pottery and Zuñi Culture-growth,' Rep. of Bur. of Ethnol., 1882-3, p. 473.
Next in the order of primitive development are the arts of binding and weaving. The stone axe or arrow-head, for example, was bound to a wooden staff, and had to be lashed with perfect evenness,[3] and when in time the material and method of fastening changed, the geometrical forms of this careful binding continued to be engraved at the juncture of blade and handle of various implements. It should be noted, however, that these binding-patterns, in spite of their superfluous character, remained symmetrical.
[3] Haddon, A.C.: 'Evolution in Art,' London, 1895, pp. 84 ff.
On the great topic of symmetry in weaving, monographs could be written. Here it is sufficient to recall[4] that the absolutely necessary technique of weaving in all its various forms of interlacing, plaiting, netting, embroidering, etc., implies order, uniformity, and symmetry. The chance introduction of a thread or withe of a different color, brings out at once an ordered pattern in the result; the crowding together or pressing apart of elements, a different alternation of the woof, a change in the order of intersection, all introduce changes by the natural necessities of construction which have the effect of purpose. So far, then, as the simple weaving is concerned, the æsthetic demand for symmetry may be discounted. While it may be operative, the forms can be explained by the necessities of construction, and we have no right to assume an æsthetic motive.
[4] Holmes, W.H.: 'Textile Art in its Relation to the Development of Form and Ornament,' Rep. of Bur. of Ethnol., 1884-5, p. 195.
The treatment of human and animal forms in weaving is, however, indicative of a direct pleasure in symmetry. The human form appears almost exclusively (much schematized) en face. When in profile, as for instance in Mexican and South American work, it is doubled--that is, two figures are seen face to face. Animal figures, on the other hand, are much used as row-ornaments in profile.[5] It would seem that only the linear conception of the row or band with its suggestions of movement in one direction, justified the use of profile (e.g., in Peruvian woven stuffs), since it is almost always seen under those conditions, indicating that a limited rectangular space is felt as satisfactorily filled only by a symmetrical figure.[6] Moreover, and still more confirmatory of this theory, even these row-pattern profiles are immensely distorted toward symmetry, and every 'degradation' of form, to use Professor Haddon's term, is in the direction of symmetry. (See Fig. 1.)
[5] Reiss, W., und Stubel, A.: 'Todtenfeld von Ancon,' Berlin, 1880-7, Bd. II.
[6] Hein, W.: 'Die Verwendung der Menschen-Gestalt in Flechtwerken,' Mitteil. d. Anthrop. Gesellsch. in Wien, Bd. XXI.
The shape of primitive pottery is conditioned by the following influences: The shapes of utensils preceding clay, such as skins, gourds, shells, etc., which have been imitated, the forms of basket models, and the conditions of construction (formation by the hands). For all these reasons, most of these shapes are circular. The only (in the strict sense) symmetrical shapes found are of unmistakably animal origin, and it is interesting to notice the gradual return of these to the eurhythmic form; puma, bird, frog, etc., gradually changing into head, tail and leg excrescences, and then handles and nodes (rectangular panels), upon a round bowl or jar L, as shown in the figures. In fact, in ancient American pottery,[7] at least, all the symmetrical ornamentations can be traced to the opposition of head and tail, and the sides between them, of these animal forms. But beyond this there is no degradation of the broad outline of the design. The head and tail, and sides, become respectively handles and nodes--but the symmetry becomes only more and more emphasized. And as in the case of textiles, the ornaments of the rectangular spaces given by the nodes are strikingly symmetrical. Many of these are from animal motives, and nearly always heads are turned back over the body, tails exaggerated, or either or both doubled, to get a symmetrical effect. Although much of the symmetrical ornament, again, is manifestly from textile models, its symmetrical character is so carefully preserved against the suggestions of the circular form that a direct pleasure in its symmetry may be inferred. (See Figs. 2-7.)
[7] Cushing, F.H.: op. cit.; Holmes, W.H.: three articles on pottery, Rep. of Bur. of Ethnol., 1882-83, p. 265, p. 367, and p. 443.
The subject of drawing can be here only touched upon, but the results of study go to show, in general, two main directions of primitive expression: pictorial representation, aiming at truth of life, and symbolic ornament. The drawings of Australians, Hottentots and Bushmen, and the carvings of the Esquimaux and of the prehistoric men of the reindeer period show remarkable vigor and naturalness; while the ornamentation of such tribes as the South Sea Islanders has a richness and formal beauty that compare favorably with the decoration of civilized contemporaries. But these two types of art do not always keep pace with each other. The petroglyphs of the North American Indians[8] exhibit the greatest irregularity, while their tattooing is extremely regular and symmetrical. The Brazilian savage [9] draws freehand in a very lively and grotesque manner, but his patterns are regular and carefully developed. Again, not all have artistic talents in the same direction. Dr. Schurtz, in his 'Ornamentik der Aino,'[10] says: "There are people who show a decided impulse for the direct imitation of nature, and especially for the representation of events of daily life, as dancing, hunting, fishing, etc. It is, however, remarkable that a real system of ornamentation is scarcely ever developed from pictorial representations of this kind; that, in fact, the people who carry out these copies of everyday scenes with especial preference, are in general less given to covering their utensils with a rich ornamentive decoration."[11] Drawing and ornament, as the products of different tendencies, may therefore be considered separately.
[8] Mallery, Garrick: 'Pictographs of the North American Indians,' Rep. of Bur. of Ethnol., 1882-3, p. 13.
[9] Von den Steinen, Karl: 'Unter den Naturvôlkern Zentral-Brasiliens,' Berlin, 1894.
[10] Internal. Archiv s. Ethnog., Bd. IX.
[11] Cf. Andrée, Richard: 'Ethnographische Parallelen,' Neue Folge, Leipzig, 1889, S. 59.
The reason for the divergence of drawing and ornament is doubtless the original motive of ornamentation, which is found in the clan or totem ideas. Either to invoke protection or to mark ownership, the totem symbol appears on all instruments and utensils; it has been shown, indeed, that practically all primitive ornament is based on totemic motives.[12] Now, since a very slight suggestion of the totem given by its recognized symbol is sufficient for the initiated, the extreme of conventionalization and degradation of patterns is allowable, and is observed to take place. The important point to be noted in this connection is, however, that all these changes are toward symmetry. The most striking examples might be indefinitely multiplied, and are to be found in the appended references (see Figs. 8 and 9).
[12] Haddon, op. cit.; Frazer, J.G.: 'Totemism,' 1887; Grosse, Ernst: Anfänge der Kunst,' Freiburg i. B. u. Leipzig, 1894.
We may distinguish here, also, between the gradual disintegration and degradation of pattern toward symmetry, as seen in the examples just given, and the deliberate distortion of figures for a special purpose. This is strikingly shown in the decorative art of the Indians of the North Pacific coast. They systematically represent their totem animals--their only decorative motives--as split in symmetrical sections, and opened out flat on the surface which is to be covered[13] (see Fig. 11). Dr. Boas argues that their purpose is to get in all the received symbols, or to show the whole animal, but, however this may be, every variation introduces symmetry even where it is difficult to do so, as in the case, for instance, of bracelets, hat-brims, etc. (Fig. 10). This may in some cases be due to the symmetrical suggestions of the human body in tattooing,[14] but it must be so in comparatively few.
[13] Boas, Franz: 'Decorative Art of the Indians of the North Pacific Coast,' Bulletin of Am. Mus. of Nat. Hist., Vol. IX.
[14] Mallery, G.: op. cit.; Haddon, A.C.: op. cit., p. 257; 'Decorative Art of British New Guinea,' Cunningham Memoir X., Royal Irish Acad., 1894, p. 26.
The primitive picture has for its object not only to impart information, but to excite the very definite pleasure of recognition of a known object. All explorers agree in their accounts of the savage's delight in his own naïve efforts at picture making. All such drawings show in varying degrees the same characteristics; first of all, an entire lack of symmetry. In a really great number of examples, including drawings and picture-writing from all over the world, I have not found one which showed an attempt at symmetrical arrangement. Secondly, great life and movement, particularly in the drawings of animals. Thirdly, an emphasis of the typical characteristics, the logical marks, amounting sometimes to caricature. The primitive man draws to tell a story, as children do. He gives with real power what interests him, and puts in what he knows ought to be there, even if it is not seen, but he is so engrossed by his interest in the imitated object as to neglect entirely its relation to a background.
Now, this very antithesis of ornament and picture is enlightening as to the dawn of æsthetic feeling, and the strongest confirmation of our hypothesis of an original impulse to symmetry in art. In the ornamentation of objects the content or meaning of the design is already supplied by the merest hint of the symbol which is the practical motive of all ornamentation. The savage artist need, therefore, concern himself no more about it, and the form of his design is free to take whatever shape is demanded either by the conditions of technique and the surface to be ornamented, or by the natural æsthetic impulse. We have found that technical conditions account for only a small part of the observed symmetry in pattern, and the inference to a natural tendency to symmetry is clear. Pictorial representation, on the other hand, is enjoyed by the primitive man merely as an imitation, of which he can say, 'This is that animal'--to paraphrase Aristotle's Poetics. He is thus constrained to reproduce the form as it shows meaning, and to ignore it as form, or as his natural motor impulses would make it.
To sum up the conclusions reached by this short survey of the field of primitive art, it is clear that much of the symmetry appearing in primitive art is due (1) to the conditions of construction, as in the form of dwellings, binding-patterns, weaving and textile patterns generally; (2) to convenience in use, as in the shapes of spears, arrows, knives, two-handled baskets and jars; (3) to the imitation of animal forms, as in the shapes of pottery, etc. On the other hand (1) a very great deal of symmetrical ornament maintains itself against the suggestions of the shape to which it is applied, as the ornaments of baskets, pottery, and all rounded objects; and (2) all distortion, disintegration, degradation of pattern-motives, often so marked as all but to destroy their meaning, is in the direction of geometrical symmetry. In short it is impossible to account for more than a small part of the marked symmetry of primitive art by non-æsthetic influences, and we are therefore forced to conclude an original tendency to create symmetry, and to take pleasure in it. A strong negative confirmation of this is given, as noted above, by the utter lack of symmetry of the only branch of art in which the primitive man is fully preoccupied with meaning to the neglect of shape; and by the contrast of this with those branches of art in which attention to meaning is at its minimum.
The question put at the beginning of this section must thus be answered affirmatively. There is evidence of an original æsthetic pleasure in symmetry.
III. EXPERIMENTS IN SUBSTITUTIONAL SYMMETRY.
A. Method of Experiment.
A certain degree of original æsthetic pleasure in symmetry may be considered to have been established by the preceding section, and, without considering further the problems of real or geometrical symmetry, it may now be asked whether the pleasure aroused by the form of asymmetrical objects is not at bottom also pleasure in symmetry; whether, in other words, a kind of substitution of factors does not obtain in such objects, which brings about a psychological state similar to that produced by real symmetry.
The question what these substituted factors may be can perhaps be approached by a glance at a few pictures which are accepted as beautiful in form, although not geometrically symmetrical. Let us take, for instance, several simple pictures from among the well-known altar-pieces, all representing the same subject, the Madonna Enthroned with Infant Christ, and all of generally symmetrical outline. It seems, then, reasonable to assume that if the variations from symmetry show constantly recurring tendencies, they represent the chief factors in such a substitutional symmetry or balance, supposing it to exist. The following pictures are thus treated in detail, M. denoting Madonna; C., Child; and Cn., Central Line. The numbers refer to the collection of reproductions used exclusively in this investigation, and further described in section IV.
1. 56, Martin Schöngauer: Madonna in Rose-arbor. M. is seated exactly in Cn., C. on Right, turning to Right. M. turns to Left, and her long hair and draperies form one long unbroken line down to Left lower corner. All other details symmetrical.
2. 867, Titian: Madonna. The picture is wider than it is high. M. stands slightly to Right of Cn.; C. on Right. Both turn slightly to Left, and the drapery of M. makes a long sweep to Left. Also a deep perspective occupies the whole Left field.
3. 248, Raphael: Madonna (The Bridgewater Madonna). M. sits in Cn., turning to Left; C. lies across her lap, head to Left, but his face turned up to Right, and all the lines of his body tending sharply down to Right.
In 1, all the elements of the picture are symmetrical except the position of C. on the Right, and the long flowing line to Left. In 2, there is a slightly greater variation. The mass of the figures is to Right, and the C. entirely over against the deep perspective and the flowing line on the Left, and the direction of both faces toward that side. In 3, the greater part of C.'s figure on Left is opposed by the direction of his lines and movement to Right. Thus these three pictures, whether or not they are considered as presenting a balance, at least show several well-defined factors which detach themselves from the general symmetrical scheme. (1) Interest in C. is opposed by outward-pointing line; (2) greater mass, by outward-pointing line, deep vista, and direction of attention; and (3) again interest by direction of line and suggestion of movement.
This analysis of several æsthetically pleasing but asymmetrical arrangements of space strongly suggests that the elements of large size, deep perspective, suggested movement, and intrinsic interest are in some way equivalent in their power to arouse those motor impulses which we believe to constitute the basis of æsthetic response. It is the purpose of these experiments to follow up the lines of these suggestions, reducing them to their simplest forms and studying them under exact conditions.
But before describing the instruments and methods of this experimental treatment, I wish to speak of the articles on the 'Æsthetics of Simple Form,' published as Studies from the Harvard Psychological Laboratory, by Dr. Edgar Pierce.[15] These articles, sub-entitled 'Symmetry' and 'The Functions of the Elements' seem at first sight to anticipate the discussions of this paper; but a short analysis shows that while they point in the same direction, they nevertheless deal with quite different questions and in a different manner. In the statement of his problem, indeed, Dr. Pierce is apparently treading the same path.
[15] Pierce E.: PSYCH. REV., 1894, I., p. 483; 1896, III., p. 270.
He says: "Can a feeling of symmetry, that is, of æsthetical equality of the two halves, remain where the two sides are not geometrically identical; and if so, what are the conditions under which this can result--what variations of one side seem æsthetically equal to the variations of the other side?" Some preliminary experiments resulted in the conclusion that an unsymmetrical and yet pleasing arrangement of a varied content rests on the pleasure in unity, thus shutting out the Golden Section choice, which depends on the pleasure in variety. That is, the choices made will not in general follow the golden section, but 'when the figure consists of two halves, the pleasure must be a feeling of æsthetical symmetry.'
The final experiments were arrangements of lines and simple figures on a square, black background in which the center was marked by a white vertical line with a blue or a red line on each side. On one side of these central lines a line was fixed; and the subject had to place on the other side lines and simple figures of different sizes and different colors, so as to balance the fixed line. The results showed that lines of greater length, or figures of greater area must be put nearer the center than shorter or smaller ones--'A short line must be farther than a long one, a narrow farther than a wide, a line farther than a square; an empty interval must be larger than one filled, and so on.' And for colors, "blue, maroon and green, the dark colors, are the farthest out; white, red and orange, the bright colors, are nearest the center. This means that a dark color must be farther out than a bright one to compensate for a form on the other side. The brightness of an object is then a constant substitute for its distance in satisfying our feeling of symmetry."
Now from these conclusions two things are clear. By his extremely emphasized central line, and his explicit question to the subjects, 'Does this balance?' the author has excluded any other point of view than that of mechanical balance. His central fulcrum is quite overpowering. Secondly, his inquiry has dealt only with size and color, leaving the questions of interest, movement, and perspective untouched. But just the purpose of this experimental study is to seek for the different and possibly conflicting tendencies in composition, and to approximate to the conditions given in pictorial art. It is evident, I think, that the two studies on symmetry will not trespass on each other's territory. The second paper of Dr. Pierce, on 'The Functions of the Elements,' deals entirely with the relation of horizontal and vertical positions of the æsthetic object and of the subject to æsthetic judgments, and has therefore no bearing on this paper.
For his apparatus Dr. Pierce used a surface of black cloth stretched over black rubber, 1 m. square. Now an investigation which is to deal with complicated and varied relations, resembling those of pictures, demands an instrument resembling them also in the shape of the background. A rectangle 600 mm. broad by 400 mm. high seemed to meet this requirement better than the square of Dr. Pierce. Other parts, also, of his instrument seemed unfitted for our purpose. The tin, 5 cm. broad and confined to the slits across the center of the square, gave not enough opportunity for movement in a vertical direction, while the scale at the back was very inconvenient for reading. To supply these lacks, a scale graduated in millimeters was attached on the lower edge of the board, between a double track in which ran slides, the positions of which could be read on the scale. To the slides were attached long strips of tin covered with black cloth. On these strips figures glued to small clamps or clasps could be slipped up or down; this arrangement of coördinates made it possible to place a figure in any spot of the whole surface without bringing the hands into the field of view. The experiments were made in a dark room, in which the apparatus was lighted by an electric globe veiled by white paper and hung above and behind the head of the subject, so as not to be seen by him and to cast no shadow: in this soft light of course the black movable strips disappeared against the black background. A gray paper frame an inch and a half wide was fitted to the black rectangle to throw it up against the black depths of the dark room--thus giving in all details the background of a picture to be composed.
The differences in method between the two sets of experiments were fundamental. In Dr. Pierce's experiments the figures were pulled from one side to the other of the half-square in question, and the subject was asked to stop them where he liked; in those of the writer the subject himself moved the slides back and forth until a position was found æsthetically satisfactory. The subject was never asked, Does this balance? He was indeed requested to abstract from the idea of balance, but to choose that position which was the most immediately pleasing for its own sake, and so far as possible detached from associations.
I have said that Dr. Pierce intentionally accentuated the center. The conditions of pictorial composition suggest in general the center only by the rectangular frame. Most of my experiments were, therefore, made without any middle line; some were repeated with a middle line of fine white silk thread, for the purpose of ascertaining the effect of the enhanced suggestion of the middle line.
But the chief difference came in the different treatment of results. Dr. Pierce took averages, whereas the present writer has interpreted individual results. Now, suppose that one tendency led the subject to place the slide at 50 and another to place it at 130 mm. from the center. The average of a large number of such choices would be 90--a position very probably disagreeable in every way. For such an investigation it was evident that interpretation of individual results was the only method possible, except where it could be conclusively shown that the subjects took one and only one point of view. They were always encouraged to make a second choice if they wished to do so, as it often happened that one would say: 'I like both of these ways very much.' Of course, individual testimony would be of the highest importance, and a general grouping into classes and indication of the majority tendency would be the only way to treat the results statistically. And indeed in carrying out the experiments this caution was found absolutely necessary. In all but one or two of the sections, the taking of averages would have made the numerical results absolutely unintelligible. Only the careful study of the individual case, comparison of various experiments on the same person to find personal tendencies, and comparison of the different tendencies, could give valuable results for the theory of symmetry.
The first question to be taken up was the influence of right and left positions on choice. A long series of experiments was undertaken with a line 80×10 mm. on one side and a line 160×10 mm. on the other, in which the positions of these were reversed, and each in turn taken as fixed and variable, with a view to determining the effect of right and left positions. No definite conclusions emerged; and in the following experiments, most of which have been made for both right and left positions, the results will be treated as if made for one side alone, and, where averages are taken, will be considered as indifferently left or right.
The experiments of Dr. Pierce were made for only one position of the fixed line--at 12 cm. distance from the center. The characteristic of the following experiments is their reference to all positions of the fixed line. For instance a fixed line, 10 cm. in length at 12 cm. distance from the center, might be balanced by a line 5 cm. in length at 20 cm. distance. But would the distance be in the same proportion for a given distance of the fixed line of say 20 or 25 cm.? It is clear that only a progressive series of positions of the fixed line would suggest the changes in points of view or tendencies of choice of the subject. Accordingly, for all the experiments the fixed line or other object was placed successively at distances of 20, 40, 60 mm., etc., from the center; or at 40, 80 mm., etc., according to the character of the object, and for each of these fixed points the subject made one or two choices. Only an understanding of the direction in which the variable series moved gave in many cases an explanation for the choice.
Each choice, it should be added, was itself the outcome of a long series of trials to find the most pleasing position. Thus, each subject made only about ten choices in an hour, each of which, as it appears in the tables, represents a large number of approximations.
B. Experiments on Size.
I have said that different tendencies or types of choice in arrangement appeared. It will be convenient in the course of explaining in detail the method of experiment, to discuss at the same time the meaning of these types of choice.
From analysis of the pictures, the simplest suggestion of balance appeared in the setting off against each other of objects of different sizes;--an apparent equivalence of a large object near the center with a small object far from the center; thus inevitably suggesting the relations of the mechanical balance, or lever, in which the heavy short arm balances the light long arm. This was also the result of Dr. Pierce's experiments for one position of his fixed line. The experiments which follow, however, differ in some significant points from this result. The instrument used was the one described in the preceding section. On one side, in the middle of the vertical strip, was placed the 'fixed' line, denoted by F., and the subject moved the 'variable' line, denoted by V., until he found the arrangement æsthetically pleasing. The experimenter alone placed F. at the given reading, and read off the position of V. After the choice F. was placed at the next interval, V. was again tried in different positions, and so on. In the following tables the successive positions of F. are given in the left column, reading downward, and the corresponding positions of V. in the right column. The different choices are placed together, but in case of any preference the second choice is indicated. The measurements are always in millimeters. Thus, F. 40, V. 60, means that F. is 40 mm. to one side of the center, and V. 60 mm. to the opposite side. F. 80×10, V. 160×10, means that the white cardboard strips 80 mm.×10 mm., etc., are used. The minus sign prefixed to a reading means that the variable was placed on the side of the fixed line. An X indicates æsthetic dislike--refusal to choose. An asterisk (*) indicates a second choice.
The following tables are specimen sets made by the subjects C, O, and D.
I. (a) F. 80×10, V. 160×10.
F. V. C. O. D.
40 62, 120 166, 130 28, 24 80 70, 110 104, 102 80, 126 120 46, X 70, 46 68,--44, 128* 160 26, 96 50, 25 85, 196,--88* 200 20, X 55, X --46, 230,* 220,--110*
I. (b) F. 160×10, V. 80×10.
F. V. C. O. D.
40 74, 64 60, 96 27, 34 80 76, 65 72, 87 55, 138 120 60, 56 48, 82 70, 174 160 29, 74 16, 77 --114, 140, 138, 200 200 96, 36 25, 36 177,--146,--148, 230
Now, on Dr. Pierce's theory, the variable in the first set should be nearer the center, since it is twice the size of the fixed line;--but the choices V. 120, 166, 130 for F. 40; V. 110, 104, 102, 126 for F. 80; V. 128 for F. 120; V. 196 for F. 160; V. 230, 220 for F. 200, show that other forces are at work. If these variations from the expected were slight, or if the presence of second choices did not show a certain opposition or contrast between the two positions, they might disappear in an average. But the position of F. 40, over against V. 120, 166, 130, is evidently not a chance variation. Still more striking are the variations for I. (b). Here we should expect the variable, being smaller, to be farther from the center. But for F. 40, we have V. 27, 34; for F. 80, all nearer but two; for F. 120, V. 60, 56, 48, 82, 70; for F. 160, V. 29, 74, 16, 77, 138, and for F. 200, V. 96, 36, 25, 36, 177--while several positions on the same side of the center as the constant show a point of view quite irreconcilable with mechanical balance.
II. (a) F. 2 LINES 80×10. V. SINGLE LINK 80×10.
F. V. C. O. P.
40- 60 58, 114* 138, 20 96, 84 166 60- 80 48 40, 138* 100, 56 150 80-100 64 70, 162* 47, 87 128 100-120 70 to 80 60 53, 53 X 120-140 58 82 50, 48 35 140-160 74 95 to 100 22, 32 37 160-180 72 102 X, X 42 180-200 90 X X, X 50
Here the variable should supposedly be the farther out; but we have V. 58, 20 for F. 40-60; V. 48, 40, 56 for F. 60; V. 64, 70, 87 for F. 80; no larger choice for F. 100-120; indeed, from this point on everything nearer, and very much nearer. We can trace in these cases, more clearly perhaps than in the preceding, the presence of definite tendencies. O and P, from positions in accord with the mechanical theory, approach the center rapidly; while C is seldom 'mechanical,' but very slowly recedes from the center. The large number of refusals to choose assures us that the subjects demand a definitely pleasant arrangement--in other words, that every choice is the expression of a deliberate judgment.
Taking again the experiments 1. (a) and 1. (b), and grouping the results for nine subjects, C, O, A, S, H, G, D, and P, we obtain the following general types of choice. The experiments were repeated by each subject, so that we have eighteen records for each position. I should note here that preliminary experiments showed that near the frame the threshold of difference of position was 10 mm., or more, while near the center it was 4 or 5 mm.; that is, arrangements were often judged symmetrically equal which really differed by from 4 to 10 mm., according as they were near to or far from the center. In grouping types of choice, therefore, choices lying within these limits will be taken as belonging to the same type.
EXP. 1. (a) F.(80 X 10). V.(160 X 10).
1. F. 40. V. 40.¹
Types of Choice for V. (1) 24 24 25 28 (2) 40 42 45 45 40 40 40 (3) 62 65 (4) 100 105 1O9 120 130 136 120 (5) 166 180 200 200 200 200 160 160
¹This table is obtained by taking from the full list, not given here, of 1. (b) F. (l60 X 10), V. (80 X 10), those positions of 160 X 10 where the variable 80 X 10 has been placed at or near 40, thus giving the same arrangement as for 1. (a).
It might be objected that a group 40-65 (2-3) would not be larger than one of 100-136 (4), but the break between 45 and 62 shows the zones not continuous. Moreover, as said above, the positions far from the center have a very large difference threshold.
I. (a) 2. F. 80:--(1) 24, (2) 50, (3) 68 70, (4) 80 85 94 95 85, (5) 102 104 110 120 124 126 125* 132, (6) 187; also V. 80:--(2) 40 40, (4) 80, (5) 120 120, (6) 160 160.
I. (a) 3. F. 120:--(1) 44 46, (2) 64 48 70 70, (3) 85 95 97 91, (4) 113 113 118, (5) 168 169 178;--44, X; also V. 120:--(1) 40 40, (3) 80 80 80, (4) 120 120, (5) 160 160.
I. (a) 4. F. 160:--(1) 25 26, (2) 40 50 57, (3) 82 85 95 100*, (4) 114 115 130, (5) 145 145 156 162, (6) 196, (7)--88*--150*--105.
I. (a) 5. F. 200:--(1) 20 23 28 36, (2) 55, (3) 108 124 130*, (4) 171 189 199 195, (5) 220 230*, (6)--46--90--110*.
On comparing the different groups, we find that in 1 and 2 there is a decided preference for a position somewhat less than half way between center and frame--more sharply marked for 1 than for 2. From 3 onward there is a decided preference for the mechanical arrangement, which would bring the larger strip nearer. Besides this, however, there are groups of variations, some very near the center, others approaching to symmetry. The maintenance of geometrical symmetry at a pretty constant ratio is to be noted; as also the presence of positions on the same side of the center as the fixed line. Before discussing the significance of these groups we may consider the results of Experiment II. (F. double line 80×10, V. single line 80×10) without giving complete lists.
We notice therein, first of all, the practical disappearance of the symmetrical choice; for F. 40-60, 60-80, 80-100, a tendency, decreasing, however, with distance from the center, to the mechanical arrangement; for F. 100-120, and all the rest, not one mechanical choice, and the positions confined almost entirely to the region 35-75. In some cases, however, the mechanical choice for (1) 40-80, (2) 60-80, was one of two, e.g., we have for (1) 20 and 138, for (3) 70 and 162; in the last two cases the mechanical being the second choice.
Now the reversals of the mechanical choice occur for Exp. I. in 1 and 2 (F. 40 and F. 80); that is, when the small fixed line is near the center, the larger variable is distant. For Exp. II. the reversals, which are much more marked, occur in all cases beyond F. 40, F. 60 and F. 80; that is, when the double constant line is far from the center, the single variable approaches. If the mechanical theory prevailed, we should have in Exp. I. the lines together in the center, and in Exp. II. both near the fringe.
From the individual testimony, based both on I. (a) and I. (b), it appears that subject M is perfectly uniform in mechanical choice when the fixed line is the small line--i.e. when it moves out, the larger is placed near the center; but when the conditions of mechanical choice would demand that, as the larger fixed line moves out, the small variable one should move out farther, he regularly chooses the reverse. Nevertheless, he insists that in just these cases he has a feeling of equilibrium.
A also takes the mechanical choice as the small fixed line goes farther from the center; but when the fixed line is large and leaves the center, he reverses the mechanical choice--evidently because it would take the small line too far out. As he says, 'he is always disturbed by too large a black space in the center.'
G almost always takes the mechanical choice;--in one whole set of experiments, in which the fixed line is the large line, he reverses regularly.
H takes for F. (80×10) the mechanical choice only for the positions F. 160 and F. 200--i.e., only when F. is very far from the center and he wishes V. (160×10) nearer. For F. (160×10) he makes six such choices out of ten, but for positions F. 160 and F. 200 he has V. 44, 65 and 20.
S takes for F. (160×10) at F. 120, V. 185 and-70; says of V. 185, which is also his choice for F. (160×10) at F. 80, 'I cannot go out further, because it is so hard to take in the whole field.' For F. (160×10) at F. 200, he has V. 130 and 60; says of V. 60, 'Very agreeable elements in connection with the relation of the two lines.'
C takes for F. (80×10) only one mechanical choice until it is at F. 120. Then always mechanical, i.e., nearer center; for F. (160×10) makes after the position F. 40 no mechanical choice, i.e., V. is nearer center.
It is evident from the above tables and individual cases that the reversals from the mechanical choice occur only when the mechanical choice would bring both lines in the center, or both near the edges, and the subjective testimony shows from what point of view this appears desirable. The subjects wish 'to take in the whole field,' they wish 'not to be disturbed by too large a black space in the center'; and when, in order to cover in some way the whole space, the small line is drawn in or the large one pushed out, they have, nevertheless, a feeling of equilibrium in spite of the reversal of mechanical balance.
Accepting for the present, without seeking a further psychological explanation, the type of 'mechanical balance,' in which amount of space is a substitute for weight, as the one most often observed, we have to seek some point of view from which this entire reversal is intelligible. For even the feeling that 'the whole field must be covered' would hardly account for an exact interchanging of positions. If size gives 'weight,' why does it not always do so? A simple answer would seem to be given by the consideration that we tend to give most attention to the center of a circumscribed space, and that any object in that center will get proportionately more attention than on the outskirts. The small line near the center, therefore, would attract attention by virtue of its centrality, and thus balance the large line, intrinsically more noticeable but farther away. Moreover, all the other moments of æsthetic pleasure, derived from the even filling of the space, would work in favor of this arrangement and against the mechanical arrangement, which would leave a large black space in the middle.
The hypothesis, then, that the demand for the filling of the whole space without large gaps anywhere enters into competition with the tendency to mechanical balance, and that this tendency is, nevertheless, reconciled with that demand through the power of a central position to confer importance, would seem to fit the facts. It is, of course, clear that neither 'mechanical balance' nor the balance of 'central' with 'intrinsic' importance have been yet accounted for on psychological grounds; it is sufficient at this point to have established the fact of some kind of balance between elements of different qualities, and to have demonstrated that this balance is at least not always to be translated into the 'mechanical' metaphor.
C. Experiments on Movement.
In the preceding experiments the element of size was isolated, and it was sought to discover, in pleasing combinations of objects of different sizes, the presence of some kind of balance and the meaning of different tendencies of arrangement. The relative value of the two objects was taken as determined on the assumption, supported by common sense, that under like conditions a large object is given more attention than a small one. If the unequal objects seem to balance each other, then the only other condition in which they differ, their distance from the center, must be the cause of their balancing. Thus the influence of relative position, being the only unknown quantity in this balance-equation, is easily made out.
The following experiments will deal with the as yet quite undetermined elements of suggested movement, perspective and intrinsic interest. By combining objects expressing them, each with another simple object of the same size, another equation will be obtained in which there is only one unknown quantity, the sizes of the objects being equal and the influence of relative position being at least clearly indicated.
1. Movement.
The experiments on suggestion of movement were made by C, O and P. Suggestions of movement in pictures are of two kinds--given by lines pointing in a direction which the eye of the spectator tends to follow, and by movement represented as about to take place and therefore interpreted as the product of internal energy. Thus, the tapering of a pyramid would give the first kind of suggestion, the picture of a runner the second kind. Translated into terms of experiment, this distinction would give two classes dealing with (A) the direction of a straight line as a whole, and (B) the expression of internal energy by a curve or part of a line. In order to be able to change the direction of a straight line at a given point, a strip of tin two inches long was fastened by a pivot to the usual clasp which slipped up and down on the vertical black strip. The tin strip could be moved about the pivot by black threads fastened to its perforated ends. A strip of cardboard glued upon it would then take its direction. The first experiments, made with the usual 80×10 strip, proved very disagreeable. The subject was much disturbed by the blunt ends of the strip. The variable (pivoted) line was then slightly pointed at the upper end, and in the final experiments, in which both are oblique, both strips were pointed at each end. In Exp. III. a line pointing at an angle from the perpendicular was set over against a line of the same dimensions in the ordinary position.
Exp. III. (a) F. (80×10) pointed up toward center at 145°, V. (80×10).
F. 40:--(1) 39 48 48, (2) 60 66 68, (3) 97 97, (4) 156* 168*.
F. 60:--(1) 45, (2) 60 62 65 68 90, (3) 90 94, (4) 117 128 152 155.
F. 80:--(1) 50 44*, (2) 74 76 77, (3) 94 100 106 113 115 116, (4) 123 124* 140 165* 169*.
F. 100:--(1) 36 58 60 65* 65 74 77 80 87, (2) 98 108 118, (3) 114* 168 186* 170 136*.
F. 120:--(1) 40 46 54 60 63 76 96 97 111, (2) 115 120 126* 137*, (3) 170 170*.
F. 140:--(1) 45 52 65 65 76 76 86 90, (2) 109 111, (3) 125 140*, (4) 168*.
F. 160:--(1) 38 50 50 60, (2) 80 90 96 98 98, (3) 176*.
F. 180:--(1) 21 23, (2) 54 70 84 90, (3) 100 100 108 114 120, (4) 130 145*.
F. 200:--(1) -2, (2) 33 37 50, (3) 106 110 to 120 115 120 130 132 138 142.
The most striking point about these groups is the frequency of positions far from the center when F. also is far out. At F. 120, a position at which the mechanical choice usually prevails if F. is smaller, a very marked preference indeed appears for positions of V. nearer the center--in fact, there is only one opposing (first) choice. Now, if it is not the wide space otherwise left which pulls the variable in,--and we see from a note that the subjects have no feeling of a large empty space in the center,--it must be that F. has the same effect as if it were really smaller than V., that is, mechanically 'light.' We see, in fact, that the moment F. has passed the point, between 80 and 100, at which both lines close together in the center would be disagreeable, the preference is marked for inner positions of V., and I repeat that this cannot be for space-filling reasons, from the testimony of F. 200 (3).
And this 'lightness' of the line pointed in at 45° is indeed what we should have expected a priori since we found that objective heaviness is balanced by a movement out from the center on the mechanical principle. If movement out and objective heaviness are in general alike in effect, then movement in and objective lightness should be alike in effect, as we have found to be the case from the preceding experiments. The inward-pointed line does not actually move in, it is true, but it strongly suggests the completion of the movement. It enters into the 'mechanical' equation--it appears to balance--as if it had moved.
The point, however, in which this 'lightness' of the inward-pointed line differs from that of the small or short line is its space-filling quality. It suggests movement in a certain direction, and, while giving the mechanical effect of that movement as completed, seems also in a sense to cover that space. We see from F. 180 (3), (4), and 200 (3), that the subject does not shrink from large spaces between the lines, and does not, as in Exp. I. (a), 4 and 5, bring the variable, which in both cases is evidently 'heavier,' to the center. This must be from the fact that the empty space does not in this experiment feel empty--it is filled with energy of the suggested movement. This view is confirmed by the dislike which the subjects show to the position F. 40; F., being 'lighter,' but the object of attention as close to the center, might well balance V. far out. But as if the whole variable field would be in that case 'overfilled,' the records show 50 per cent. of refusals to choose for this position.
In brief, then, a straight line suggesting movements in a certain direction has the effect, in the general scheme of mechanical balance, of a static position in which this movement has been carried out, with the added suggestion of the filling of the space over which such movement is suggested.
A few additional experiments were made with a point on the upper end of V. The groups of III. (a) are maintained almost exactly: F. 120 is again strikingly 'mechanical'; after F. 120 there are only two mechanical choices out of nineteen; while for F. 40, as in Exp. III. (a), out of six choices, four are either refusals or question-marked.
Exp. IV. Both lines took oblique directions, and, to get a pleasing effect, were pointed at both ends. They were of the usual size, 80×10 mm., but 1 mm. broader to allow for the effect of length given by the points. F. was fixed at 45°, as in III. (a), on the points 40, 80, 120 and 160; V. moved also on fixed points, 60, 100, 140, 180, for each position of F., but on each point was adjusted at a pleasing angle. Thus, there were four positions of V. to each of F., each with one or two angular positions; V. was always in the first quadrant.
The numbers of the table give the angular degrees of V.
F. 40, V. 60:--(1) 10 12 38 44, (2) 50 57* 60, (3) 70. V. 100:--(1) 15 15 30 30, (2) 50 55 50, (3) 69 70*. V. 140:--(1) 12* 14 18 18, (2) 60 60 49, (3) 72. V. 180:--(1) 12 10 38, (2) 60 50, (3) 75. [Many refusals at 140 and 180.]
F. 80, V. 60:--(1) 11, (2) 25 35 36*, (3) 45 48 55 58 60, (4) 69. V. 100:--(1) 16 15, (2) 24 27 35 40, (3) 52, (4) 62 74*. V. 140:--(1) 10 15 16, (2) 22 28, (3) 40 40 59 59, (4) 70. V. 180:--(1) 14 8, (2) 28, (3) 41 46, (4) 68 79.
F. 120, V. 60: (1) 28, (2) 42 44 35, (3) 52 58 62 65 65. V. 100:--(1) 9, (2) 23 25, (3) 38 40 40 42 58, (4) 68 70. V. 140:--(1) 10, (2) 20 26 21* 24 29, (3) 34 42 42 44 55*, (4) 75. V. 180:--(1) 17 26, (2) 40 42 46, (3) 62 64 70 70*.
F. 160, V. 60:--(1) 20 39, (2) 18, (3) 58 60 64 68 70. V. 100:--(1) 23 25 30 38, (2) 44 44 49, (3) 55 58 65. V. 140:--(1) 5, (2) 31 35 40 40 32, (3) 54 55 68. V. 180:--(1) 50 50 58 60, (2) 75.
The tendency to mechanical balance would, according to our previous analysis, lead the variable to take a direction which, in its suggestion of motion inward, should be more or less strong according as it were farther from or nearer to the center than the fixed line. Such motion inward would, of course, be more strongly suggested by an angle less than 45° than by an angle greater than 45°, and it seems that the angles chosen are in general in harmony with this expectation. For the positions where F. is nearer the center than V. there is a preponderance of the angles less than 45° (cf. F. 40 and F. 80, V. 100 and 140; F. 120, V. 140, 180). When V. passes over to a position farther from the center than F. (e.g., from F. 80, V. 60, to F. 80, V. 100 and from F. 120, V. 60, to F. 120, V. 140) the change is marked. In every case where F. is farther from the center than V. (i.e., F. 80, V. 60; F. 120, V. 60 and V. 100; F. 160, V. 60, V. 100 and V. 140), there are to be noticed a lack of the very small angles and a preponderance of the middle and larger angles. F. 160, V. 140 and 180 seem to be the only exceptions, which are easily explainable by a dislike of the extremely small angle near the edge; for it appears from the remarks of the subjects that there is always a subconsciousness of the direction suggested by the lower pointed end of the line. For the outer positions of both lines, a large angle would leave the center empty, and a small one would be disagreeable for the reason just given; and so we find, indeed, for F. 160, V. 100, 140, 160, the middle position the favorite one.
The representation of action may be translated into experimental terms by expressing it as a line which changes its direction, thus seeming to be animated by some internal energy. The forms chosen were three curves 'bulging' from a straight line in differing degrees, and two straight lines with projections. C and O were the subjects. The results are given in outline.
Exp. V. Curve I. See Fig. 12, I
(1) Curve out (turned away from center).
(a) F. (80×10), V. Curve.
About half the positions of V. are farther from the center than F. O at first refuses to choose, then up to F. 120 puts V. farther from the center than F. C has a set of positions of V. nearer the center and several second choices farther than F.
(b) F. Curve, V. (80×10).
No position of V. nearer center than F. O puts line farther out up to F. 160, then nearer than F. C has a set of nearly symmetrical choices and another where V. is much farther out than F.
(2) Curve in (turned toward center).
(a) F. (80×10), V. Curve.
C is absolutely constant in putting V. farther from center than F. O, after F. 100, brings it slightly nearer.
(b) F. Curve, V. (80×10).
C, except for F. 40, invariably puts V. nearer center than F. O moves between 90 and 135, putting V. farther to F. 100, nearly symmetrical at F. 100 and 120, and after F. 120, from 100 to 135.
Exp. V. Curve II. See Fig. 12, II.
(1) Curve out.
(a) F. (80×10), V. Curve.
In every case but one V. is nearer center than F.
(b) F. Curve, V. (80×10).
C puts V. farther from center than F. O puts V. farther or symmetrical up to F. 120, then nearer than F.
(2) Curve in.
(a) F. 80×10, V. Curve.
C has V. always farther from center than F., but a second parallel set, omitting F. 40 (all second choices), of symmetrical positions. O begins with V. farther from center, but from F. 120 has V. always nearer, though gradually receding from the center.
(b) F. Curve. V. (80×10).
C, refusing for F. 40, continues his parallel sets, one with V. always nearer than F., another with symmetrical positions. O begins with V. nearer, changes at F. 120, and continues with V. farther.
Recapitulating these results, grouping together the outward and inward positions of the curves, and indicating the distance of the line from the center by C.-L., and of the curve from the center by C.-Cv., we have:
Out.
Cv. I. (a) Indeterminate. (b) C.-Cv. < C.-L. (except where large gap would be left).
Cv. II. (a) C.-Cv. < C.-L. (all cases but one). (b) C.-Cv. < C.-L. (except where large gap would be left).
In.
Cv. I. (a) C.-Cv. > C.-L. (except a few cases to avoid gap). (b) C.-Cv. > C.-L. (more than half of cases).
Cv. II. (a) C.-Cv. > C.-L. (except a few cases to avoid gap). (b) C.-Cv. > C.-L. (except a few cases to avoid gap).
It is evident that in the great majority of cases when the curve turns out it is placed nearer the center, when it turns in, farther from the center, than the straight line. The numerical differences for choices of the same type for the two curves are slight, but regular, and the general tendencies are more sharply marked for the line of greater curvature. When Curve II. is 'out,' it is usually nearer the center than Curve I. for the corresponding positions of the straight line; when 'in' it is always farther from the center than Curve I. The greater curvature of II. has clearly produced this difference, and the effect of the curvature in general is evidently to make its side 'lighter' when turned toward the center, and 'heavier' when turned away. Thus, all but the exceptions already noted seem to belong to the mechanically balanced arrangement, in which the suggestion of force working in the direction of the curve has the same effect as, in Exp. IV., the direction of the line. The exceptions noted, especially numerous choices of O, seem governed by some fixed law. The evidence would seem to be overwhelming that the reversals of the mechanical balance occur only where the lines would be crowded together in the center or would leave an empty gap there. The remaining exceptions--the symmetrical choices mentioned, made by C--are explained by him as follows. He says there are two ways of regarding the curve, (1) as a striving in the direction of the 'bulge,' and (2) as the expression of a power that presses together; and that the usual choices are the result of the first point of view, the symmetrical choices of the second. Naturally, a pressure bending down the line would be conceived as working in a vertical direction, and the line would be treated as another (80×10)--giving, as is the case, symmetrical positions. Thus, we may consider the principle of the suggestion of movement by a curve, as giving the same effect as if the movement suggested had actually taken place, to have been established, the positive evidence being strong, and the exceptions accounted for. It is worth noting that the curve-out series are always more irregular--the subject repeating that it is always harder to choose for that position. Probably the demands of space-filling come into sharper conflict with the tendency to mechanical balance, which for the outward curve would always widely separate the two lines.
Exp. V. Curve III. See Fig. 12, III.
A series with the upper end turned out from the center was unanimously pronounced as ugly. The inward position only appears in the results, which are given in full.
(a) F. (80×10), V. CURVE.
F. V. O. C.
40 106 126 68 73 80 106 128 109 102 120 140 88 156 110* 154 72* 160 104 66 182 80 136* 130* 200 X 52 178 220* 162
(b) F. CURVE, V. (80×10)
F. V. O. C.
40 126 122 73 80 80 122 128 66 112* 40 120 90 116 97 156* 55 105 160 65 43 120 182* 87 134 200 70 50 148 66
This curve exemplifies the same principles as the preceding. O takes the natural mechanical choice from (a) F. 40 to F. 120, and from (b) F. 120 to F. 200. A mechanical choice, however, for (a) F. 120 ff., and for (b) F. 40 to F. 120, would have brought the lines too far apart in (a), and too near together in (b), hence the reversal. C inclines always to the mechanical choice, but recognizes the other point of view in his second choices.
Exp. V. Curve IV. See Fig. 12, IV.
Curve in.
(a) F. (80×10), V. Curve.
C puts V. always further than F. and, even for F. 200, has V. 230, X. O puts V. farther up to F. 120, then puts it nearer than F., and always refuses to choose for F. 200.
(b) F. Curve, V. (80×10).
C always puts V. nearer than F. O puts V. farther for F. 40 and F. 80, beyond that, nearer than F.; but refuses to choose once each for F. 40, and F. 200.
The same principles of choice appear. C maintains the mechanical choice, and O reverses it only beyond (a) F. 120, and up to (b) F. 120, to fill space well, showing his preference for the mechanical choice by changing into it at an unusually early point.
Exp. V. Curve V. See Fig. 12, V.
Curve in.
(a) F. (80×10), V. Curve.
C puts V. farther than F., except for F. 200, V. 125 and X. O also, changing as usual at F. 120 to V. nearer than F.
(b) F. Curve, V. (80×10).
O puts V. always farther than F. O has V. farther for F. 40 and F. 80, then nearer than F. Refuses to choose for F. 200. Results exactly parallel with those of Curve IV.
Comparing all the results of this whole series of experiments on the suggestion of movement, we may conclude that movement, whether suggested by a whole line or part of a line, produces in terms of mechanical balance the same effect that the balanced object would produce after the completion of the suggested motion. This tendency to balance, it appears, lies at the basis of our preference; it often gives way, however, before considerations of space-filling, when the figure which on the scheme of mechanical balance is weaker, gains interest and so 'heaviness' by being brought nearer the center.
D. Experiments on Interest.
By intrinsic interest is meant the interest which would attach to an object quite apart from its place in the space composition. In a picture it would be represented by the interest in an important person, in an unusual object, or in an especially beautiful object, if that beauty were independent of the other forms in the picture--as, for instance, a lovely face, or a jeweled goblet, etc. When the question of the influence of interest on composition came to be discussed, it was found very difficult to abstract the form of the object from the content presented; still more difficult to obtain an effect of interest at all without the entrance of an element of form into the space arrangement. Disembodied intellectual interest was the problem, and the device finally adopted seemed to present, in as indifferent a form as possible, a content whose low degree of absolute interest was compensated for by constant change. Stamps of various countries in black and white reproductions and very small outline pictures on squares of the same size as the stamps were taken as material. The figures were so small in relation to the board that any influence on composition of the lines composing them was impossible; the outline pictures, indeed, gave to the eye which abstracted from their content an impression scarcely stronger than the neighboring blank square.
The first set of experiments (VI.) had a small outline picture on the side, and on the other a white paper square of the same size. The necessary interest was given in the form of novelty by changing the picture for every choice. The subjects were M, G and D. The results were of the same type for each subject and could therefore be averaged.
Exp. VI. (1).
(a) F. Picture, V. Blank. Eight choices for each. M, Average: V. 17 mm. farther from center. G, Average: V. 10 mm. farther from center. (Symmetrical position beyond F. 120.) D, Average: V. 25.8 mm. farther from center.
(b) F. Blank, V. Picture. M, Average: V. 33 mm. nearer center. G, Average: V. 4 mm. nearer center. (Symmetrical beyond F. 120.) D, Average: V. 30 mm. nearer center. (But V. farther at F. 40.)
These results are practically unanimous. They show that an object which possesses intrinsic interest acts like a mechanically heavy object, being placed nearer the center than a blank. Two marked deviations from the mechanical choice occur--although they have not affected the average sufficiently to destroy the general harmony of results. G, in both (a) and (b), chooses symmetrical positions from F. 120 on. His notes ['(a) F. 140, V. 136, picture unimportant'; '(b) F. 120 and ff., loses relation as they separate'; '(b) F. 160, picture makes no impression'] show clearly that for positions wide apart the picture, already a faint outline, becomes only a white square like the other and is put into geometrical symmetry.
Exp. VI. (2), by G and D. A stamp on one side unchanged, took the place of the blank; on the other side the stamp was changed for each choice.
(a) F. unchanged stamp; V. changed stamp.
D. Two series, (1) V. always nearer center. (2) Same, except F. 20, V. 52; F. 80, V. 94; F. 140, V. 152; F. 160, V. 175.
G. Two series. (1) V. much farther from center up to F. 140, then nearer. (2) V. farther throughout, except F. 160, V. 121.
(b) F. changed stamp; V. unchanged stamp.
D. Two series. (1) V. farther up to F. 100, then symmetrical. (2) V. farther up to F. 100, then symmetrical or nearer center.
G. Two series. (1) V. farther up to F. 120, then symmetrical, and beyond F. 140, nearer center. F. 140, V. 63. (2) V. much farther up to F. 120, then nearer center, but more nearly symmetrical than (1). A complete series of second choices beginning at F. 40, V. slightly nearer center than F.
Analyzing results, we find the changed stamp, which has the interest of novelty, nearly always nearer the center than the unchanged. This would indicate a balance of the mechanical type, in which the interest makes an object 'heavier.' The exceptions are in (a) four choices of D, G to F. 140, and in (b), D's choice beyond F. 200, and G's beyond F. 120. The deviations are thus seen to be all of the same type: for positions of F. near the center, when a mechanical choice would have brought V. still nearer [(a)], it is instead put farther away; for positions of F. far from the center, when a mechanical choice would have put V. still farther away [(b)], it is instead brought near. The exceptions are thus fully accounted for by the demand for space-filling.
E. Experiments on Depth.
The experiments on suggestion of depth in the third dimension were as follows. It was desired to contrast two objects differing only with respect to the degree to which they expressed the third dimension. Those objects that do express the third dimension are, in general, views down streets, colonnades, corridors, gates, etc., or, in landscape, deep valleys, vistas between trees, distant mountains, etc. It is evident that representations of products of human handiwork would be less unnatural when isolated for experiment, and two pairs of pictures were accordingly prepared as follows: There was drawn on a square of 80 mm. the picture of the mouth of a railway tunnel, closed tightly by an apparently massive door; and another picture of identical form and surroundings, but showing the rails entering at a slight curve, the deep blackness within, and the small circle of light at the farther end. The second pair consisted of the gateway of a baronial castle, with heraldic bearings and closed iron-wrought doors; and the same gateway open, showing a flagged pavement and an open court with fountain beyond. The perspective effect was heightened by all possible means for both pictures, and care was taken to have the contrast of black and white the same for each pair, so that to the half-shut eye, opened and closed forms seemed to have the same tone.
The subjects were directed to try to feel the third dimension as vividly as possible--to project themselves down the vistas, as it were--and then to arrange the squares in the most pleasing manner. The experiments were made by A, M, S, H and D. Not all made the same number of repetitions, but as their notes were unusually suggestive, I have made use of all the results, and shall quote the notes for the most part verbatim:
Exp. VIII. F. Closed Tunnel. V. Open Tunnel.
F. V. Subject H. 40 90 60 57 80 13 100 12 120 39 140 - 1 160 -32 180 -71, +50
Notes.--H finds that he neglects the closed tunnel almost entirely, eye is constantly attracted to open tunnel, F. 180, choice of evils. Position of closed tunnel makes the pictures disagreeable. F. 80, V. 13, closed tunnel grows more uninteresting as it goes out, while the open tunnel seems heavier than ever. F. 140, V.-1, closed tunnel loses force and doesn't gain weight. Open tunnel hangs together with the black field beyond it.
F. V. Subject S. 40 85 95 60 170 195 80 160 180 100 185 200 120 185 - 35, 200 140 85 20 160 115 115 180 100
Notes.--F. 120, V. 185. After this there is too large a black space between squares, and so a more central position is taken, but there is the necessity of avoiding symmetry, which is displeasing. F. 160, V. 115 is not symmetrical and so is more pleasing. F. 60, V. 195:--the open tunnel holds the eyes, while the other allows them to wander, and so it needs a bigger field on each side. F. 80, V. 180:--a position close together is possible, but it is hard to take them so except as one picture, and that is also difficult. F. 100, V. 200:--there is the same objection to any position which seems to be an acknowledgment of similarity; that is, symmetrical position seems to imply that they are alike, and so is disagreeable. F. 120, V.-35, 200:--now they can be close together because the black tunnel harmonizes with the black to the right, and seems to correspond in distance and depth, while the tunnel 'hangs together' with the black to the left. (Cf. H, F. 160, V.--32.) F. 140, V. 20:--when they are together it is difficult to apperceive the frame as a whole; but this position is not far apart, and not disagreeable because the larger stretch of black to the right again hangs together with the tunnel. F. 160, V. 115:--when the open tunnel was in the middle, the closed one seemed to have no business at all, therefore the open tunnel had to be moved over. The only position which was not disagreeable.
SUBJECT G.
F. V. (1) (2) (3) (4)¹ (5)¹ 40 48 31 36 30 23 60 105 31 40 51 39 80 111 71 60 64 54 100 104 63 78 60 86 120 123 75 91 62 115 140 136 82 111 56 137 160 162 93 148 72 156 180 107 115 181 83 176
¹Second pair (Court).
Notes.--(1) All quite unsatisfactory. The arrangement difficult to apperceive as a whole. Each picture taken by itself. (2) The tunnel closed doesn't amount to much. (3) The significance of the tunnel gives it weight. For F. 160, V. 148, and F. 180, V. 180, relation difficult. (4) Court closed gets weaker as gets farther from center. (5) At F. 100, begins to lose relation between pictures, as if one were in one room, one in another.
SUBJECT A.
F. V. (1) (2) (3) (4)² (5)² 40 70 66 140 59 130 60 80 73 159 62 138 80 103 71 120 77 134 100 113 94 108 93 100 120 119 88 96 96 63 140 108 92 60,164 82 43 160 92 118 70 109 50 180 130 154 78 101 50
²Second pair (Court).
Notes.--(1) Difficult to apperceive together. From F. 140, V. 108, depth is more strongly imagined. (3) Tunnel closed has not much value. (5) F. 80, V. 134, taken with reference both to frame and to the other picture--must not be symmetrical nor too far out.
SUBJECT D.
F. V. (1) (2) (3) 40 100 47 38 60 75 60 68 80 104 78 80 100 148, -12 104 120 120 159 166 160 140 182 152, 84, 78 168 160 193 184, -75 180 180 200 - 95, 190 190
Note.--F. 100, V.-12; F. 140, V.-52; F. 160, V. -75: they must be close together when on the same side.
F. V. (1) (2)¹ Subject M. 40 55 50 60 56 74 80 64 84 100 86 102 120 93 111 140 124 130 160 134 146 180 144 178
¹Second pair (Court).
Note.--(1) Quite impossible to take both together; necessary to keep turning from one to the other to get perception of depth together with both.
The subjects agree in remarking on the lack of interest of the closed tunnel, and the attractive power of the open tunnel, and notes which emphasize this accompany choices where the open tunnel is put uniformly nearer. (Cf. H, F. 180, V. 50; F. 80, V. 13; G, (2), (3), (4), (5); A, (3), and F. 140.) As a glance at the results shows that the open tunnel is placed on the whole nearer the center, we may conclude that these choices represent a mechanical balance, in which the open tunnel, or depth in the third dimension, is 'heavier.'
But another point of view asserts itself constantly in the results of S, and scatteringly in those of the others. Analyzing at first only the results of S, we find that up to F. 140, with one exception, he places the open tunnel much farther out than the other; and from F. 140 on, nearer. He says, F. 120, V. 185, 'After this there is too large a black space'; that is, in bringing the open tunnel in, he is evidently filling space. But why does he put the open tunnel so far out? It seems that he is governed by the desire for ease in the apperception of the two objects. In his note for F. 80, V. 180, this point of view comes out clearly. He thinks of the objects as being apperceived side by side with the space about each (which apparently takes on the character of its object), and then he seems to balance these two fields. Cf. F. 60, V. 195: 'The closed tunnel allows the eyes to wander, and so it needs a bigger field on each side.' Evidently there is an implication here of the idea of balance. Cf. also F. 120: 'The black tunnel harmonizes with the black to the right, and seems to correspond in distance and depth,' while the closed tunnel 'hangs together with the black on the left.' In brief, the view of F. seems to be that the closed tunnel is less interesting, and partly because it 'allows the eyes to wander,' partly as compensation for the greater heaviness of the open tunnel, it takes with it a larger space than the open tunnel. It is on the whole better to put them apart, because it is more difficult to apperceive them when close together, and so the open tunnel in the earlier choices must, of course, go farther from the center. When these points conflict with the necessity of filling space, the open tunnel comes nearer the center. In general, the notes which emphasize the difficulty of apperceiving the two pictures as flat and deep together accompany choices where the tunnel is put uniformly farther out, or symmetrically. Cf. G, (1), (5); A, (1); M, F. 40, etc.
Thus we may continue to separate the two points of view, that of mechanical balance and that of another kind of balance, which we have known heretofore as 'space-filling,' made possible by the power of the center to give 'weight,' but which seems to be now more explicitly recognized as a balancing of 'fields.' At this point we need repeat only, however, that the suggestion of depth in the third dimension seems to confer 'weight,' 'heaviness,' 'balancing power' on its object.
Before making a general survey of the results of this chapter, it is necessary to consider a type of choice which has been up to this point consistently neglected--that in which the variable has been placed on the same side of the center as the fixed object. On the theory of balance, either in its simple mechanical form or in its various disguises, this choice would at first seem to be inexplicable. And yet the subjects usually took special pleasure in this choice, when they made it at all. These minus choices are confined to three or four subjects and to two or three experiments. Exp. I. (a) and (b) show the largest number. We have:
EXP. I. (a) F. (80×10); V. (160×10). F. V. 120 - 44, 160 -150, -105, -88 200 -94, -46, -110
(b) F. (160×10); V. (80×10). F. V. 120 -70, -80 160 -114 200 -155, -146, -148
It will be noticed that, with two exceptions, none of the positions chosen are nearer than 70 mm. to the center, and that most of them are much farther away. The two lines seem to be more pleasing when they are pretty close together on the same side. S, in I. (b) F. 120, V.-70, notes: 'If V. is nearer O, there is a tendency to imagine a figure by the connection of the ends of the two lines, which is disagreeable. 'The only other minus choices were in Exp. VII., by S,, H, and D. S, F. 120, V.-35, says: 'Now they can be close together,' and H, F. 140, 160 and 180, V. -1, -32, -71, notes the same. So also D, F. 100, V. -12; F. 140, V. -52; F. 160, V. -75; F. 180, V. -95. It is evident from this insistence on the closeness together of the objects, and this desire to form no figure, that the two are taken as one, and set off against the blackness on the other side. It seems as if this were not taken as empty space, but acquired a meaning of its own. The association with pictures in which the empty space is occupied by a deep vista or an expanse of sky is almost irresistible. The case of Exp. VII. seems a little different. S, at least, separates the two fields as usual, but for him also the black space is living, 'corresponds in distance and depth.' It is at least certain that there is no subjective feeling of emptiness or of unoccupied energies on the empty side. And it would seem that some influence from the objects sweeps across the central field and vitalizes it. The most natural view would seem to be that the ease of apperception of the two objects together, and the tendency of the eye movement to begin on the occupied side, and to sweep across to the unoccupied, which we think of as deep, combine to give a feeling of pleasure and of balance.
* * * * *
We have now reached a point from which a backward glance can be cast upon the territory traversed. Experiment with the isolated elements in pictorial composition has shown that pleasing arrangements of these elements can be interpreted by the formula of mechanical balance. This principle was obtained by opposing two lines whose relative value (corresponding to 'weight' in balance) was known; and it was found that their relative positions corresponded to the relation of the arms of a balance. Further opposition of lines, of which one was already determined in 'weight,' showed the same variations and suggested certain valuations of the undetermined lines on the basis of this common term of weight. Thus, the line suggesting movement out from the center fitted the formula if taken as 'heavy' and vice versa, the line suggesting movement in, if taken as 'light.' Similarly, objects of interest and objects suggesting movement in the third dimension were 'heavy' in the same interpretation. But this interpretation, in its baldest form, fitted only a majority of the pleasing arrangements; the minority, in which the consistent carrying out of the lever principle would have left a large unoccupied space in the center, exactly reversed it, bringing the 'light' element to the center and the 'heavy' to the outer edge. Later experiments showed that this choice implied a power in the 'lighter' objects, owing to their central position, to cover or infuse with vitality the empty space about them, so that the principle of balance seemed to maintain itself in one form or another.
All this does not go beyond the proof that all pleasing space arrangements can be described in terms of mechanical balance. But what is this mechanical balance? A metaphor, no matter how consistently carried out, explains nothing. The fact that a small object far from the center is usually opposed by a large object near the center tells us nothing of the real forces involved. Physical balance can be explained by principles of mechanics, but no one will maintain that the visual representation of a long line weighs more than that of a short one. Moreover, the elements in the balance seem utterly heterogeneous. The movement suggested by an idea--the picture of a man running--has been treated as if equivalent to the movement actually made by the eye in following a long line; the intrinsic interest--that is, the ideal interest--of an object insignificant in form has been equated to the attractive power of a perspective which has, presumably, a merely physiological effect on the visual mechanism. What justification can be given either of this heterogeneous collection of elements or of the more or less arbitrary and external metaphor by which they have been interpreted?
I believe that the required justification of both points of view is given in the reduction of all elements to their lowest term--as objects for the expenditure of attention. A large object and an interesting object are 'heavy' for the same reason, because they call out the attention; a deep perspective, because the eye rests in it;--why, is another question. And expenditure of effort is expenditure of attention; thus, if an object on the outskirts of the field of vision requires a wide sweep of the eye to take it in, it demands the expenditure of attention, and so is felt as 'heavy.' It may be said that involuntary attention is given to the object of intrinsic interest, while the uninteresting object far on the outskirts needs a voluntary effort to perceive it, and that the two attitudes cannot be treated as identical. To this it may be answered that an object on the outskirts of a field of view so definitely limited calls out of itself a reflex movement of the eye toward it, as truly spontaneous as the impulse toward the object of intrinsic interest. But what is 'the expenditure of attention' in physiological terms? It is nothing more than the measure of the motor impulses directed to the object of attention. And whether the motor impulse appears as the tendency to fixate an object or as the tendency to follow out the suggestions of motion in the object, they reduce to the same physiological basis. It may here be objected that our motor impulses are, nevertheless, still heterogeneous, inasmuch as some are toward the object of interest, and some along the line of movement. But it must be said, first, that these are not felt in the body, but transferred as values of weight to points in the picture--it is the amount and not the direction of excitement that is counted; and secondly, that even if it were not so, the suggested movement along a line is felt as 'weight' at a particular point.
From this point of view the justification of the metaphor of mechanical balance is quite clear. Given two lines, the most pleasing arrangement makes the larger near the center, and the smaller far from it. This is balanced because the spontaneous impulse of attention to the near, large line, equals in amount the involuntary expenditure of attention to apprehend the small farther one. And this expenditure of motor impulses is pleasing, because it is the type of motor impulses most in harmony with our own physical organism.
We may thus think of a space to be composed as a kind of target, in which certain spots or territories count more or less, both according to their distance from the center and according to what fills them. Every element of a picture, in whatever way it gains power to excite motor impulses, is felt as expressing that power in the flat pattern. A noble vista is understood and enjoyed as a vista, but it is counted in the motor equation, our 'balance,' as a spot of so much intrinsic value at such and such a distance from the center. The skilful artist will fill his target in the way to give the maximum of motor impulses with the perfection of balance between them.
IV. SYMMETRY IN PICTURES.
A. The Balancing Factors.
The experimental treatment of suggestions as to the elements in pictorial composition has furnished an hypothesis for the basis of our pleasure in a well-composed picture, and for the particular function of each of the several elements. This hypothesis may be expressed as follows: (1) The basis of æsthetic pleasure in composition is a balance of motor impulses on the part of the spectator; (2) this balance of motor impulses is brought about by means of the elements, through the power which they possess of drawing the attention with more or less strength towards a certain field. But to the experimental working out of an hypothesis must succeed a verification, in its application to the masterpieces of civilized art. We have, then, to ask whether there is in all great pictures a balance, i.e., an equal distribution of attention on the two sides of the central line suggested by the frame of the picture. It might be, for instance, that a picture of pleasing composition would show, when analyzed, all the attractions for attention on one side; which would go far to impugn either our hypothesis of balance as the basis of pleasure, or our attribution of particular functions to the elements. But as this second matter may be considered to have been sufficiently determined by the results of the preceding section, the first question only remains: Is there a balance of attention in a good picture--or rather, in the particular good pictures known to the student of art?
This question could only be answered by the examination of a large number of pictures of accepted merit, and it was also desirable that they should be studied in a form which lent itself to the easy comparison of one picture with another. These conditions seemed to be best fulfilled by the collection of reproductions in black and white known as the Classischer Bilderschatz, published by F. Bruckmann, at Munich, which contains over a thousand pictures arranged in schools. Of these a thousand were taken--substantially the first thousand issued, after the frescoes, triptych doors, panels, etc., which are evidently parts of a larger whole, had been laid aside. In the following discussion the pictures will be designated, when they are not further described, by the numbers which they bear in this collection.
The equations in the following discussion are based on a system of exact measurement, corresponding to that followed in the experimental section. This numerical treatment is pre-supposed in all the general attributions of balance in the analysis of single pictures. The method of measurement was given by the conditions of viewing pictures, which are framed and thus isolated from surrounding influences, and referred, as compositions, to the middle line suggested by this emphasized frame. An adjustable frame of millimeter paper, divided in half vertically by a white silk thread, was fitted over the picture to be measured, and measurements were made to left and to right of this thread-line and, as required, vertically, by reference to the millimeter frame divisions.
The main question, of course, to be answered by a statistical examination of these thousand pictures refers to the existence of balance, but many other problems of symmetry are also seen to be closely involved; the relative frequency of the elements in pictures of different types, and the result of their employment in producing certain emotional effects, also the general types of space arrangement as a whole, the feeling-tone belonging to them, and the relation between content and shape. The first question will not be treated in this paper in the statistical fulness which was necessary to establish my conclusions in the investigation itself, inasmuch as the tables were very extensive. But examples of the tables, together with the full results, will be given, and a sufficient amount of detailed discussion to show my methods. The two other subjects, the use of the elements and the types of composition, will be briefly treated. I expect in other publications to go more closely into statistical detail on these matters than is possible in a merely experimental thesis.
In the beginning of the proposed statistical analysis a natural objection must first be forestalled: it will be said, and truly, that color also has its effect in bringing about balance, and that a set of black and white reproductions, therefore, ignores an important element. To this it may be answered, first, that as a matter of fact the color scheme is, as it were, superimposed upon the space-shape, and with a balance of its own, all the elements being interdependent; and secondly, that the black and white does render the intensity contrasts of the colors very well, giving as light and dark, and thus as interesting (= attractive) and the reverse, those factors in the scheme which are most closely related to the complex of motor impulses. After having compared, in European galleries, the originals of very many of these reproductions with the equation of balance worked out from the black and white, the writer has seldom found an essential correction needed.
The pictures were first classified by subjects. This may seem less logical than a division by types of arrangement. But it really, for a majority, amounted to the same thing, as the historical masterpieces of art mostly follow conventional arrangements; thus the altarpieces, portraits, genre pictures, etc., were mostly after two or three models, and this classification was of great convenience from every other point of view. The preliminary classification was as follows: (1) Religious, Allegorical and Mythical Pictures; (2) Portraits; (3) Genre; (4) Landscape. The historical pictures were so extremely few that they were included in the religious, as were also all the allegorical pictures containing Biblical persons. Some pictures, of which Watteau's are representative, which hovered between genre and landscape, were finally classified according as they seemed to owe their interest to the figures or to the scenery. A preliminary classification of space arrangements, still with reference to content, showed three large general types: (1) A single subject or group in the middle; (2) the same somewhat on one side, with subordinate elements occupying the rest of the space; (3) two objects or groups each occupying a well-defined center. These were designated as Single Center, Single and Subordinate Center, and Double Center pictures, or S.C., S. & S., and D.C. They are in proportions of S.C. 79 per cent., S. & S. 5 percent., D.C. 16 per cent. The D.C. type is evidently already explicitly balanced as regards shape and intrinsic interest, and is hence of comparative unimportance to our problem. The S.C. will show a balance, if at all, in more or less accessory factors; S. & S., broadly, between interest and other factors. As logically more important, this last group will be treated more fully. The full classification of the thousand pictures by subjects is as follows:
S.C. D.C. S.S. Altarpieces 78 70 7 1 Madonna & Child 47 47 0 0 Holy Family 67 40 14 13 Adorations 19 19 0 0 Crucifixions 23 21 0 2 Descents f. Cross 27 26 0 1 Annunciations 21 0 21 0 Misc. Religious 162 93 55 14 Allegorical 46 36 6 4 Genre 93 63 19 11 Landscape 88 65 22 1 Portrait Groups 64 42 17 5 Relig. Single Fig. 28 28 0 0 Alleg. Single Fig. 12 12 0 0 Portrait Single Fig. 207 207 0 0 Genre Single Fig. 18 18 0 0
Altarpieces.
The pictures of the first group, consisting of the Madonna and Infant Christ surrounded by worshippers, and briefly designated as Altarpieces, are good for detailed study because they present a simple type, and it will be easy to show whether the variations from symmetry are in the direction of balance or not. A few examples will make this clear. The Madonna in the S.C. pictures is invariably seated holding the Christ.
In the following descriptions M. will denote Madonna, C. Child, Cn. central line. The elements, Size or Mass, Direction of Motion or Attention, Direction of Line, Vista, and Interest, will be set down as Ms., D., L., V., and I. A couple of examples will show the method of describing and of drawing a conclusion as to balance.
1. 969. Lorenzo Lotto, Madonna with St. Bernard and St. Onofrius. C. is on one side turning to the same; M. leans far to the other; hence interest in C., and direction of C.'s attention are over against Mass of M. and direction of M.'s attention; i.e., I. + D. = Ms. + D., and so far, balance. The surrounding saints are insignificant, and we may make the equation I. = Ms.
2. 368. Raffaelino di Francesco, Madonna Enthroned. The C. is on Right facing front, M. turns away Left, hence interest in C. is over against direction of M.'s attention. Moreover, all the saints but one turn Left, and of two small vistas behind the throne, the one on the Left is deeper. The superior interest we feel in C. is thus balanced by the tendency of attention to the opposite side, and we have I. = D. + V.
It is clear that the broad characteristics of the composition can be symmetrically expressed, so that a classification of the 70 S.C. altarpieces can be made on a basis of these constant elements, in the order of decreasing balance. Thus: Class 1, below, in which the C. is one side of the central line, turned away from the center, the M. turned to the other, balances in these broad lines, or I. + D. = D.; while in (9), I. + D. + D. = (x), the constant elements work all on one side.
CLASSIFICATION OF ALTARPIECES.
1 C. one side turned to same, M. to other 11 2 " " " other, " " 8 3 " " " front, " " 2 4 " " " other, M. front. 9 5 " " " facing M. 6 6 " " " front, M. front. 7 7 " " " " M. turned to same. 6 8 " " " to same M. turned front. 7 9 " " " " M. " to same, 14 10 " in middle, turned front. 0
Thus the constant elements, understanding always that C. has more interest than M., are as follows: For (1) I. + D. = D.; (2) I. = D. + D.; (3) I. = D.; (4) I. = D.; (5) I. + D. = D.; etc. These are in order of complete balance, but it will be seen that from (7) on, while the factors are constant, the framework is not balanced; e.g. in (9) both I. and D. work on the same side. For these groups, therefore, the variations, if there is balance, will be more striking. Eliminating the balancing elements in the framework, the tables for the ten groups are:
(1) I. + D. = D. (2) I. = D. + D(M). (3) I. = D. 969. I. = Ms. 680. I. = D. 1094. Ms. + I. = I. + D. 601. I. = Ms. 735. I. = D. 33. I. = I. + D 49. I. = Ms. + I. 1121. I. = D. 634. I. = Ms. + I. 1035. I. = D. (4) I. = D. 584. I. = I. 333. I. = I. + D. 775. I. = D. 686. I. = I. 80. I. = I. + D. 746. I. = D. 794. I. = D. 753. I. = I. + D. 1106. I. = Ms. + D. 164. I. = D. 1114. I. = D. + L. 781. I. = Ms. + D. 368. I. = D. + V. 1131. I. = I. + D. 927. I. = V. 517. I. = I. + D. 273. I. = V. 327. I. + Ms. = D. + V. 951. I. + L. = D. + V. 715. Unbalanced.
(5) I. + D. = D. (6) I. = (7) I. + D. = 43. I. = I. 854. I. = Ms. 725. I. + D. = I. + L. 711. I. = I. 1148. I. = I. 206. I. + D. = I. + L. 447. I. = Ms. 709. I. = D. 155. I. + D. = D. + L. 643. I. = Ms. 907. I. = D. 739. I. + D. = L. 777. I. = Ms. + I. 586. I. = Ms. + I. 331. I. + D. = V. 637. I. = Ms. + I. 137. I. = Ms. + I. 980. Unbalanced. 187. Unbalanced.
(8) I. + D. = (9) I. + (D. + D.) = (10) 0. 57. I. + D. = Ms. 835. I. + D. = Ms + I. 979. I. + D. = I. + L. 724. I. + D. = Ms + L. 134. I. + D. = D. 495. I. + D. = Ms + L. 106. I. + D. = D. + V. 182. I. + D. = Ms + V. 220. I. + D. = L. 817. I. + D. = I. 118. I. + D. = V. + L. 662. I. + D. = I. 157. Unbalanced. 806. I. + D. = I. 1136. I. + D. = I. + L. 865. I. + D. = I. + V. 1023. I. + D. = V. 531. I. + D. = L. 553. I. + D. = L.
The most used element is I., in 100 per cent. of cases; the least used, V., 13 per cent. D., in 91 per cent. of cases; Ms., 26 per cent.; L., 19 per cent. 175, 433, unbalanced.
As seen in the table, a balance of elements is kept, except in four cases which will be hereafter considered. In all cases the balance is between the interest in C., sometimes plus D., (in the attention of the figures to C.), on the one side, and other elements on the other. Very seldom are other salient points found on the C. side. When the C. side is especially 'heavy,' the number of opposing elements increases, and especially takes the form of V. and L. [cf. (7), (8), (9)], which were observed in the experimental chapter to be powerful in attracting attention. For the fairly well-balancing framework--(i), (2), (3) and (4)--Ms., I., and D. are much more often the opposing elements.
The pictures listed as unbalanced are, with one exception, among the oldest examples given; conceived in the most slavish geometrical symmetry in which, indeed, the geometrical outline almost hides the fact that the slight variations are all toward a lack of balance.
There is but one S. & S. case (1054), Titian, The Madonna of the House of Pesaro. In this, M. and C. are on a high throne on the Right, other figures lower down on the Left bearing a flag that leans back to the Left. All the lines of the figures and of the massive architecture and the general direction of attention bear down so strongly to Left that the importance of the Right figures is balanced. We should have, then, I. = I. + L. + D. The D.C. cases, seven in number, are remarkably alike. Six have a vista separating the two groups, in five remarkably deep and beautiful, as if to fix the oscillating attention there. In all, M. and C., either in position or by the direction of their lines, are nearer the Cn. than the opposing figures, which are naturally less interesting, thus giving an instance of the mechanical balance. Their general equation, then, would be I. = M. or M. + L. Having shown that the small variations from the general symmetrical type of altar-pieces are invariably, except in primitive examples, in the direction of substitutional symmetry, or balance, we may next study the Madonna pictures, using the same classifications for purposes of comparison.
MADONNA WITH INFANT CHRIST.
(1) I. + D. = D. (2) I. = D. + D. (4) I. = D. 56. I. = L. 271. I. = D. + L. 668. I. = D. + Ms. 332. I. = L. 867. I. = D. + V. + D. 14. I. = D. + I. 633. I. = D. 91. I. = D. + V. (3) I. = D. 1111. I. = D. + V. 144. I. = D. 1011. I. = D. = L. 521. I. = D. 915. I. = D. = L. 356. I. = L. + D. + D. 296. I. + Ms. = V. + L.
(5) I. + D. = D. (6) I. = 51. I. = D. 596. I. = Ms. 581. I. = D. 892. I. = Ms. 829. I. = D. + I. 224. I. = I. + D. 159. I. = I. + D. 908. I. = D. + L. 683. I. = D. + L. 1045. I. = I. + L. (7) I. + D. = 745. I. = I. + L. 344. I. + D. = Ms. 734. I. = D. + L. 949. I. + D. = Ms. + V. + L. 404. I. = D. + L. 608. I. + D. = L. 248. I. = L. 524. I. + D. = L. 37. I. = L. 97. I. = L. (8) 0. 363. I. = V. + L. 674. I. = V. + L. (9) I. + D. + D. = 62. I. = V. + L. 361. I. + D. = L. 1142. I. = V. + L. 1018. I. = V. + L. (10) 110. I. + V. = Ms. + L. 538. I. = D. 411. I. + V. = Ms. + L. 614. I. + Ms. = V. 771. I. + Ms. = V. + L. 34. D. = Ms. + L.
Most used element, I., 100 per cent.; least used, Ms., 21 per cent. D., 96 per cent.; L., 64 per cent.; V., 27 per cent.
The first thing to be noted, on comparing this table with the preceding, is the remarkable frequency of the use of the vista and the line. Among the altarpieces, the direction of attention was the element most often opposed to the interesting object; and next to that, another object of interest. These two elements, however, here sink into comparative insignificance. In general, balance is brought about through the disposition of form rather than of interests. This appears in comparing the numbers; against the use of L. in 19 per cent. of the cases among the altarpieces, we have 64 per cent. among the Madonna pictures; V. is used in the former cases 13 per cent. of the times, in the latter 27 per cent. The reason for this would appear to be that the lack of accessories in the person of saints, worshippers, etc., and the consequent increase in the size of M. and C. in the picture heightens the effect of any given outline, and so makes the variations from symmetry greater. This being the case, the compensations would be stronger--and as we have learned that V. and L. are of this character, we see why they are needed. None of the M. and C., S.C. pictures fails to give a complete balance of elements according to hypothesis. There are no well-defined cases of S. & S. or D.C.
Portraits.
A study of the Madonna pictures of all types, then, results in an overwhelming confirmation of the hypothesis of substitutional symmetry. It may be objected that the generally symmetrical framework of these pictures suggests a complete balance, and the next step in our analysis would, therefore, be a type of picture which is less bound by tradition to the same form. The portrait would seem to combine this desideratum with generally large and simple outlines, so that the whole surface can be statistically reported with comparative ease. A detailed analysis of a couple of portraits may justify the classification adopted.
900. Anton Raphael Mengs, Self-Portrait. The head of the painter is exactly in Cn., but is turned sharply to Right, while his shoulders turn Left. His arm and hand are stretched out down to Right, while his other hand, holding pencil, rests on his portfolio to Left. Hence, the D. of attention plus that of L. on Right, balances I. in implements, plus D. of body on Left, or D. + L. = D. + I.
438. B. van der Helst, Portrait of Paul Potter. The head of the subject is entirely to Left of Cn., his easel on Right. His body is turned sharply to Right, and both hands, one holding palette and brushes, are stretched down to Right. His full face and frontward glance are on Left. Hence, Ms. + I. in person balances I. in implements + D. of L., or Ms. + I. = I. + L.
It is seen that the larger elements in these pictures are the directions of the head and body, and the position of the head, with reference to Cn. The following classification is based on this framework.
CLASSIFICATION OF PORTRAITS.
A. Head in Cn. I. Body front, head front, 6 II. Body turned, head turned other way, 7 D. = D. III. Body turned, head front, 31 D. = IV. Body front, head turned, 1 D. = V. Body turned, head turned same way, 106 D. + D. =
B. Head not in Cn. I. Body turned to empty side, head to same, 18 Ms.=D. II. Body turned to empty side, head front, 23 Ms. = D. III. Body turned to empty side, head to other, 3 Ms. + D. = D. IV. Body front, head front, 2 Ms. = V. Body turned from empty side, head same way, 10 Ms. + D. =
This is also in order of less complete balancing of the original elements. The principal characteristics of the different divisions are as follows:--
A. I. (Symmetrical.) Most used element, L.; least used, V.
II. (Balanced, D. = D.) Most used element, L.; least used, V.
III. (D. = .) Most used element, Ms., in 74 per cent, of cases opposed to D.; in 30 per cent, of cases, D. of glance opposed to D. of body; least used, V. (1 per cent.).
IV. One case only.
V. (D. = .) Most used element, Ms., in 73 per cent. of cases opposed to D.; in 40 per cent. of cases, D. of glance opposed to D.; in 28 per cent. Ms. + D. of glance opposed to D.; least used element, V. (15 per cent.). I. 39 per cent.; L. 38 per cent.
B. I. (Balanced, Ms. + I. = D.) Most used element (not counting those already included in equation), I., 55 per cent.; least used, V., 2 per cent.; L., 50 per cent. In 44 per cent., D. of glance opposed to D.
II. (Ms. + I. = D.) Most used element (not in equation), I., 52 per cent. Least used, V., 26 per cent. L., 43 per cent. In 21 per cent., D. of glance opposed to D.
III. (Ms. + I. + D. = D.) Three cases. Two cases V. on empty side.
IV. (Ms. + I. = .) Two cases. One case V. on empty side.
V. (Ms. + I. + D. = .) Most used element, L., 60 per cent.; least used, V., 10 per cent.; 33-1/3 per cent., D. of glance to empty side.
The portrait class is an especially interesting object for study, inasmuch as while its general type is very simple and constant, for this very reason the slightest variations are sharply felt, and have their very strongest characteristic effect. We shall, therefore, find that the five principal factors in composition express themselves very clearly. The general type of the portrait composition is, of course, the triangle with the head at the apex, and this point is also generally in the central line--in 73 per cent. of the whole number of cases, as is seen from the table. All cases but one are longer than they are wide, most are half-length or more. Nevertheless, great richness of effect is brought about by emphasizing variations. For instance, the body and head are, in the great majority of cases, turned in the same way, giving the strongest possible emphasis to the direction of attention--especially powerful, of course, where all the interest is in the personality. But it is to be observed that the very strongest suggestion of direction is given by the direction of the glance; and in no case, when most of the other elements are directed in one way, does the glance fail to come backward. (Cf. A. II., V., and B. I., II., V.)
A. It is of especial value for our conclusions that that division in which the constant elements are least balanced (V.) is far the most numerous. Comparison of this with III. shows that the principal element, direction of movement of head or body, is balanced by the larger mass of the body or accessories. Very significant, also, is the great increase in the use of V. in this most irregular class (15 per cent. as against 1 per cent. in III.). Three cases (214, 1087, 154, all A.V.,) fail to show substitutional symmetry.
B. With the head on one side of Cn., of course the greatest interest is removed to one side, and the element of direction is brought in to balance. Again, with this decrease in symmetry, we see the significant increase in the use of the especially effective elements, V. and L. (Cf. B. I., II., III., IV., and especially V.) In fact, the use of the small deep vista is almost confined to the class with heads not in the middle. The direction of the glance also plays an important part. It is to be noted that in B. I. and II., I. appears as the most frequently used element, exclusive of the general equation, which is, of course, between the mass of the body and interest of the face, on one side, and the direction of suggested movement on the other. This means that very often the direction of movement alone is not sufficient to balance the powerful Ms. + I. of the other side, and that the eye has to be attracted by a definite object of interest. This is usually the hand, with or without an implement--like the palette, etc., of our first examples--or a jewel, vase, or bit of embroidery. This is very characteristic of the portraits of Rembrandt and Van Dyck.
In general, it may be said that (1) portraits with the head in the center of the frame show a balance between the direction of suggested movement on one side, and mass or direction of attention, or both together, on the other; while (2) portraits with the head not in the center show a balance between mass and interest on one side, and direction of attention, or of line, or vista, or combinations of these, on the other. The hypothesis of substitutional symmetry is thus completely confirmed.
Genre.
Still more unsymmetrical in their framework than portraits, in fact the most unfettered type of all, are the genre pictures. Being so irregular, they admit of no complete classification based on constant elements in the framework, such as was possible for the types already dealt with. A grouping, based on types of composition, is indeed possible, as of triangles, diagonals, etc., but as this begs the question of the relative importance of line and direction of attention, and assumes that the shape is all-important, it will not be made use of here. The broad divisions and the relative use of the elements are given as follows:
S.C. 63. Most frequent form (I. = or I. + D. =). Most used element, I., 89 per cent.; least used, L., 44 per cent.; D., 57 per cent.; Ms., 57 per cent.; V., 46 per cent.
D.C. 19. Most frequent form (I. + D. = I. + D.) Most used element, I. (all cases); least used, L., 31 per cent.; V., 47 per cent.; Ms., 63 per cent.; D., 42 per cent.
S.&S. 11. Most frequent form (I. or I. + Ms. = V. or V. +). Most used element, I., 100 per cent.; least used, L., 20 per cent.; V., 82 per cent.; Ms., 72 per cent.; D., 27 per cent.
As these are pictures with a human interest, and, therefore full of action and particular points of interest, it was to be expected that I. would be in all forms the element most frequently appearing. In compositions showing great variations from geometrical symmetry, it was also to be expected that V. and L., elements which have been little used up to this point, should suddenly appear in very high percentages; for, as being the most strikingly 'heavy' of the elements, they serve to compensate for other variations combined. In general, however, the balance is between the interesting side, which is also often the most occupied (I. + Ms.), and the direction of suggestion to the other side.
For the first time in this investigation the S. & S. and D.C. types appear in appreciable numbers. It is of some significance that the most irregular type of all, S. & S., in which the weight of interest and of mass is overwhelmingly on one side, should be invariably balanced by the third dimension (V.). As these somewhat infrequent cases are especially enlightening for the theory of substitutional symmetry, it is worth while to analyze one in detail.
286. Pieter de Hooch, The Card-players, in Buckingham Palace, portrays a group completely on the Right of Cn., all facing in to the table between them. Directly behind them is a high light window, screened, and high on the wall to the extreme Right are a picture and hanging cloaks. All goes to emphasize the height, mass and interest of the Right side. On the Left, which is otherwise empty, is a door half the height of the window, giving on a brightly lighted courtyard, from which is entering a woman, also in light clothing. The light streams in diagonally across the floor. Thus, with all the 'weight' on the Right, the effect of this deep vista on the Left and of its brightness is to give a complete balance, while the suggestion of line from doorway and light makes, together with the central figure, a roughly outlined V, which serves to bind together all the elements. This matter of binding together of elements is reserved for further discussion--the purpose of this detailed description is only to show the extraordinary power of a single element, vista, to balance a whole composition of others, and its significance in the tables as an increasing accompaniment of increasing variations from symmetry.
The D.C. cases, inasmuch as they always present a balance of interest at least, are less valuable for our theory; among the variations the larger side, Ms., is often balanced by a vista, or, combining with the usual equation for genre pictures, Ms. + I. + D. = V. + I. + D. There is only one picture which cannot be schematized (263).
Landscape.
The landscape is another type of unfettered composition. As it represents no action or single object or group of objects, its parts are naturally more or less unconnected. It should, therefore, be said that no picture was taken as D.C. unless there was a distinct separation of the two sides. The typical examples are analyzed in detail.
S.C. 912. J. van Ruysdael, Forest Landscape, in the London National Gallery. In the Cn. is a stagnant pool, backed on the Right by thick woods. A dead tree, white, very prominent in the Right foreground, another at its foot sloping down to Cn. On the Left a bank sloping down to Cn., a tree at its foot; behind both, and seen also between the two central trees, bright sky and clouds. Thus, there is on the Right, Mass and Direction to Cn.; on the Left, Vista and Direction to Cn.; Ms. + D. = V. + D.
D.C. 642. Hobbema, The Watermill, in Buckingham Palace. On the Right, a bank sloping upward, a large cluster of trees, a path leading down to Right lower corner. On the Left, somewhat lower, the mill, and water in front of it, flowing down to Left; clearest sky between mill and trees. Thus Mass and Direction out are placed over against Interest (in mill) and Direction out, plus possibly a hint of Vista, or Ms. + D. = I. + D + V.
S.C. 65. Most frequent form, Ms. + I. = V. + L. Most used element, V., 98 per cent.; least used, D., 22 per cent. I. 73 per cent.; Ms. 66 per cent.; L. 31 per cent.
S. & S. One case. Ms. + I. + V. = V.
D.C. 22. Most frequent form, Ms. + I. or Ms. = V. or V. + (almost invariable). Most used element, V., 100 per cent.; least used, D., per cent. Ms. 82 per cent.; I. 73 per cent.; L. 23 per cent.
It was, of course, to be expected that in pictures without action there should be little suggestion of attention or of direction of movement. What is less evident is the reason for the high percentage of I. Of course, figures do appear in many examples, and in most pictures some inanimate object is emphasized--as, for instance, the mill in our second example. But the most remarkable point of difference in these tables from the preceding is the presence of V. in practically every example. It is, of course, natural that somewhere in almost every picture there should be a break to show the horizon line, for the sake of variety, if for nothing else--but what is significant is the part played by this break in the balancing of the picture. In about two thirds of the examples the vista is enclosed by lines, or masses, and when near the center, as being at the same time the 'heaviest' part of the picture, serves as a fulcrum or center to bind the parts--always harder to bring together than in the other types of pictures--into a close unity. The most frequent form of this arrangement, as seen by the table, is a diagonal, which just saves itself by turning up at its far end. Thus the mass, and hence usually the special interest of the picture, is on the one side, on the other the vista and the sloping line of the diagonal. In very few cases is the vista behind an attractive or noticeable part of the picture, the fact showing that it acts in opposition to the latter, leading the eye away from it, and thus serving at once the variety and richness of the picture, and its unity. A pure diagonal would have line and vista both working at the extreme outer edge of the picture, and thus too strongly--unless, indeed, balanced by very striking elements near the other edge.
This function of the vista as a unifying element is of interest in connection with the theory of Hildebrand,[16] that the landscape should have a narrow foreground and wide background, since that is most in conformity with our experience. He adduces Titian's Sacred and Profane Love as an example. But of the general principle it may be said that not the reproduction of nature, but the production of a unified complex of motor impulses, is the aim of composition, and that this aim is best reached by focusing the eye by a narrow background--i.e., vista. No matter how much it wanders, it returns to that central spot and is held there, keeping hold on all the other elements. Of Hildebrand's example it may be said that the pyramidal composition with the dark and tall tree in the center effectually accomplishes the binding together of the two figures, so that a vista is not needed. A wide background without that tree would leave them rather disjointed.
[16] A. Hildebrand, 'Das Problem der Form in der Bildenden Kunst,' Strassburg, 1897.
Another interesting observation concerns the use of water in landscapes. In nearly all appears an expanse of water, and in four fifths of the cases it is either on the same side as the vista, or in the same line with it. This is no doubt partly due to the light-effects which can be got on the water, but it also greatly reinforces the peculiar effect of the vista. That effect, as has been repeatedly said, is to concentrate, to hold, to fixate vision. The same thing is true of the horizontal line, as was shown by some preliminary experiments not here reported. The contrast to the ordinary trend of lines--particularly in a landscape--together with the strong suggestion of quiet and repose, serve to give the same concentrating effect to the horizontal lines as to the vista.
In general, it may be said that balance in landscape is effected between Mass and Interest on one side and Vista and Line on the other; and that unity is given especially by the use of Vista and the horizontal lines of water.
A survey of the subject-types remaining on the list of page 514 shows that they may quite well be grouped together with those already examined; that is, the Holy Families, Adorations, Crucifixions, and Annunciations are very symmetrical in type, and present the same characteristics as the Altarpieces. The Miscellaneous (mostly religious) pictures, the Descents, and the Allegorical are, for the most part, freely composed, irregular, full of action, and resemble the genre pictures. The Single Figure pictures, Religious, Allegorical and Genre, and the Portrait Groups, resemble the portraits. Therefore, it may be considered that the existence of a perfect substitutional symmetry has been established, inasmuch as it has been shown to be almost invariably present in the types examined.
The experimental treatment of the isolated elements determined the particular function of each in distributing attention in the field of view. The object of large size claims attention, but does not rivet it nor draw it out powerfully; the intrinsically interesting object does excite it, but limits it to a comparatively small field; the suggestion of movement or of attention on the part of pictured objects carries the attention through the field of its operation; the vista rivets the attention without powerfully exciting it, and the line extending in a certain direction carries the attention in the same way as does the suggestion of movement. But the preceding statistical analysis has shown that while all are possibly operative in a given picture, some are given much more importance than others, and that in pictures of different types different elements predominate.
The following table gives the distribution of the elements in the single-center pictures already examined. The numbers represent the per cent. of the whole number of balanced pictures in which the given element appears once or more.
S.C. Ms. I. D. V. L.
Alt. p. 26 100 91 13 31 Mad. 21 100 96 27 64 Port. 80 63 98 17 61 Genre 57 89 57 46 44 Lands. 66 73 22 98 31
It is seen that in those classes with a general symmetrical framework, the altar and Madonna pictures, the elements of interest and direction of attention are overwhelmingly predominant--which is the more to be expected as they appear, of course, as variations in a symmetry which has already, so to speak, disposed of mass and line. They give what action there is, and when they are very strongly operative, we see by page 516, (8) and (9) and note, that they are opposed by salient lines and deep vistas, which act more strongly on the attention than mass; compare further Mad., V. 27 per cent., L. 64 per cent., as against Alt., V. 13 per cent., L. 19 per cent., as confirming the view that they are used in the more irregular and active pictures. But I. keeps its predominance throughout the types, except in the portraits, where, indeed, we should not expect it to be so powerful, since the principal object of interest must always be the portrait head, and that is in most cases in the Cn., and therefore not counted. Yet I. has a respectable representation even in the portrait table, showing that such objects as jewels, embroideries, beautiful hands, etc., count largely too in composition. Its greatest is in the genre table, where, of course, human interests constitute the subject matter.
It is among the portraits that the direction of suggestion is most operative. Since these pictures represent no action, it must be given by those elements which move and distribute the attention; in accordance with which we see that line also is unusually influential. As remarked above, the altarpieces and Madonna pictures, also largely without action, depend largely for it on D., in the form of direction of attention (D. 91 per cent.).
The vista, as said above, rivets and confines the attention. We can, therefore, understand how it is that in the genre table it suddenly appears very numerous. The active character of these pictures naturally requires to be modified, and the vista introduces a powerful balancing element, which is yet quiet; or, it might be said, inasmuch as energy is certainly expended in plunging down the third dimension, the vista introduces an element of action of counterbalancing character. In the landscape it introduces the principal element of variety. It is always to be found in those parts of the picture which are opposed to other powerful elements, and the 'heavier' the other side, the deeper the vista. This is especially to be noted in all pictures of the S. & S. type, where the one side is very 'heavy' and the deep vista practically invariable on the other. Also in D.C. pictures it serves as a kind of fulcrum, or unifying element, inasmuch as it rivets the attention between the two detached sides. (Cf. D.C. among Alt. and Mad.)
The direction of suggestion by means of the indication of a line (L.), quite naturally is more frequent in the Madonna-picture and Portrait classes. Both these types are of large simple outline, so that L. would be expected to tell, but more or less irregular, so that it would not appear on both sides, thus neutralizing its action, as often in the symmetrical altarpieces. This neutralizing explains why it has a comparatively small per cent. in the landscape table, it having appeared in minor form all over the field, but less often in large salient outline. It is worth noticing that for the D.C. of both genre and landscape, the per cent. drops appreciably. As it is, in a decided majority of cases, combined with V.--the shape being more or less a diagonal slope--it is clear that it acts as a kind of bond between the two sides, carrying the attention without a break from one to the other.
The element of mass requires less comment. It appears in greatest number in those pictures which have little action, portraits and landscapes, and which are yet not symmetrical--in which last case mass is, of course, already balanced. In fact, it must of necessity exert a certain influence in every unsymmetrical picture, and so its percentage, even for genre pictures, is large.
Thus we may regard the elements as both attracting attention to a certain spot and dispersing it over a field. Those types which are of a static character abound in elements which disperse the attention; those which are of a dynamic character, in those which make it stable. The ideal composition seems to combine the dynamic and static elements--to animate, in short, the whole field of view, but in a generally bilateral fashion. The elements, in substitutional symmetry, are then simply means of introducing variety and action. As a dance in which there are complicated steps gives the actor and beholder a varied and thus vivified 'balance,' and is thus more beautiful than the simple walk, so a picture composed in substitutional symmetry is more rich in its suggestions of motor impulse, and thus more beautiful, than an example of geometrical symmetry.
B. Principles of Composition.
The particular function of the elements which are substituted for geometrical symmetry has been made clear; their presence lends variety and richness to the balance of motor impulses. But the natural motor response to stimulation has another characteristic which belongs to us as individuals. The motor response must be balanced, but also unified. In a picture, therefore, there must be a large outline in which all the elements are held together, corresponding to this requirement of unity. Now this way of holding together, this manner of combination, may vary; and I hope to show that it not only varies with the subject and purpose of the picture, but bears a very close relation thereto--that, in short, it is what determines the whole character of the picture. Just what this relation is will appear in the study of our material.
Examples of these types of composition may best be found by analyzing a few very well-known pictures. We may begin with the class first studied, the Altarpiece, choosing a picture by Botticelli, in the Florence Academy (746). Under an arch is draped a canopy held up by angels; under this, again, sits the M. with the C. on her lap, on a throne, at the foot of which, on each side, stand three saints. The outline of the whole is markedly pyramidal--in fact, there are, broadly speaking, three pyramids; of the arch, the canopy, and the grouping. A second, much less symmetrical example of this type, is given by another Botticelli in the Academy--Spring (140). Here the central female figure, topped by the floating Cupid, is slightly raised above the others, which, however, bend slightly inward, so that a triangle, or pyramid with very obtuse angle at the apex, is suggested; and the whole, which at first glance seems a little scattered, is at once felt, when this is grasped, as closely bound together.
Closely allied to this is the type of the Madonna of Burgomaster Meyer, Holbein (725), in the Grand-Ducal Castle, Darmstadt. It is true that the same pyramid is given by the head of the M. against the shell-like background, and her spreading cloak which envelops the kneeling donors. But still more salient is the diamond form given by the descending rows of these worshipping figures, especially against the dark background of the M.'s dress. A second example, without the pyramid backing, is found in Rubens' Rape of the Daughters of Leucippus (88), in the Alte Pinakothek at Munich. Here the diamond shape formed by the horses and struggling figures is most remarkable--an effect of lightness which will be discussed later in interpreting the types.
The famous Bull of Paul Potter (149), in the Royal Museum at the Hague, furnishes a third type, the diagonal. High on one side are grouped the herdsman, leaning on a tree which fills up the sky on that side, and his three sheep and cow. The head of the bull is turned toward this side, and his back and hind leg slope down to the other side, as the ground slopes away to a low distant meadow. The picture is thus divided by an irregular diagonal. Somewhat more regular is the diagonal of the Evening Landscape, by Cuyp (348), in the Buckingham Palace, London. High trees and cliffs, horsemen and others, occupy one side, and the mountains in the background, the ground and the clouds, all slope gradually down to the other side.
It is a natural transition from this type to the V-shape of the landscapes by Aart van der Neer, Dutch Villages, 245 and 420, in the London National Gallery and in the Rudolphinum at Prague, respectively. Here are trees and houses on each side, gradually sloping to the center to show an open sky and deep vista. Other examples, of course, show the opening not exactly in the center.
In the Concert by Giorgione (758), in the Pitti Gallery, Florence, is seen the less frequent type of the square. The three figures turned toward each other with heads on the same level make almost a square space-shape, although it might be said that the central player gives a pyramidal foundation. This last may also be said of Verrocchio's Tobias and the Archangels in the Florence Academy, for the square, or rather rectangle, is again lengthened by the pyramidal shape of the two central figures. The unrelieved square, it may here be interpolated, is not often found except in somewhat primitive examples. Still less often observed is the oval type of Samson's Wedding feast, Rembrandt (295), in the Royal Gallery, Dresden. Here one might, by pressing the interpretation, see an obtuse-angled double-pyramid with the figure of Delilah for an apex, but a few very irregular pictures seem to fall best under the given classification.
Last of all it must be remarked that the great majority of pictures show a combination of two or even three types; but these are usually subordinated to one dominant type. Such, for instance, is the case with many portraits, which are markedly pyramidal, with the double-pyramid suggested by the position of the arms, and the inverted pyramid, or V, in the landscape background. The diagonal sometimes just passes over into the V, or into the pyramid; or the square is combined with both.
It is, of course, not necessary at this point to show how it is that such an apparently unsymmetrical shape as the diagonal, alone or in combination with other forms, nevertheless produces an effect of balance. In all these cases of the diagonal type the mass or interest of the one side, or the direction of subordinate lines backward to it, balances the impulse of the line descending to the other side. The presence of balance or substitutional symmetry is taken for granted in this treatment, having been previously established, and only the modifications of this symmetry are under consideration.
Now, in order to deal properly with the question of the relation of the type of composition to the subject of the picture, complete statistical information will be necessary. A table of the pictures, classified by subjects and distributed under the heads of the six major types, is accordingly subjoined.
Pyramid. Double-Pyr. Diagonal. S.C. D.C. S.S. S.C. D.C. S.S. S.C. D.C. S.S. Altarpieces, 49 0 1 10 4 0 1 0 0 Mad. w. C., 40 0 0 7 0 0 0 0 0 Holy Family, 25 0 4 0 0 1 2 2 2 Adorations, 19 0 0 0 0 0 0 0 0 Crucifixions, 11 0 0 7 0 1 0 0 1 Desc. fr. Cross, 12 0 0 3 0 0 1 0 0 Annunciations, 0 8 0 0 4 0 0 0 0 Misc. Religious, 55 16 3 4 4 0 10 7 5 Allegorical, 20 2 1 4 0 0 4 0 2 Genre, 25 4 4 5 0 0 18 2 1 Landscape, 8 2 1 3 0 0 25 6 0 Port. Group, 20 4 2 9 0 0 3 3 2 Rel. Single Fig., 20 0 0 2 0 0 2 0 0 Alleg. S.F., 7 0 0 2 0 0 3 0 0 Portrait S.F., 179 0 0 28 0 0 0 0 0 Genre S.F., 15 0 0 1 0 0 1 0 0
V-shaped. Square. Oval. S.C. D.C. S.S. S.C. D.C. S.S. S.C. D.C. S.S. Altarpieces, 6 1 0 4 1 0 0 1 0 Mad. w. C., 0 0 0 0 0 0 0 0 0 Holy Family, 13 3 6 0 0 0 0 0 0 Adorations, 0 0 0 0 0 0 0 0 0 Crucifixions, 0 0 0 3 0 0 0 0 0 Desc. fr. Cross, 5 0 1 3 0 0 2 0 0 Annunciations, 0 1 0 0 8 0 0 0 0 Misc. Religious, 20 14 2 9 12 1 2 2 3 Allegorical, 3 2 1 3 1 0 3 1 0 Genre, 10 7 6 4 4 0 1 3 0 Landscape, 20 12 0 4 0 0 5 2 0 Port. Group, 10 7 1 0 3 0 0 0 0 Rel. Single Fig., 3 0 0 1 0 0 0 0 0 Alleg. S.F., 0 0 0 0 0 0 0 0 0 Portrait S.F., 0 0 0 0 0 0 0 0 0 Genre S.F., 1 0 0 0 0 0 0 0 0
What types are characteristic of the different kinds of pictures? In order to answer this question we must ask first, What are the different kinds of pictures? One answer, at least, is at once suggested to the student on a comparison of the pictures with their groupings according to subjects. All those which represent the Madonna enthroned, with all variations, with or without saints, shepherds or Holy Family, are very quiet in their action; that is, it is not really an action at all which they represent, but an attitude--the attitude of contemplation. This is no less true of the pictures I have called 'Adorations,' in which, indeed, the contemplative attitude is still more marked. On the other hand, such pictures as the 'Descents,' the 'Annunciations,' and very many of the 'miscellaneous religious,' allegorical and genre pictures, portray a definite action or event. Taking together, for instance, in two groups of five each, the first ten classes in the table, we find that they fall to the six types in the following proportion:
P. D.P. Dg. V. Sq. Ov. I. 66 13 05 13 03 0 II. 43 07 14 20 12 04
Inasmuch as II. contains also many 'contemplative' pictures, while I. contains no 'active' ones, the contrast between the proportions of the groups would really be sharper than the figures indicate. But as it is, we see that the pyramid type is characteristic of the 'contemplative' pictures in a much higher degree. If the closely allied double-pyramid type is taken with it, we have 79 per cent of the 'contemplative' to 50 per cent, of the 'active' ones. This view is confirmed by contrasting the 'Adoration,' the most complete example of one group, with the genre pictures, the most complete example of the other--and here we see that in the first all are pyramidal, and in the second only 26 per cent. A class which might be supposed to suggest the same treatment in composition is that of the portraits--absolute lack of action being the rule. And we find, indeed, that no single type is represented within it except the pyramid and double-pyramid, with 86 per cent. of the former. Thus it is evident that for the type of picture which expresses the highest degree of quietude, contemplation, concentration, the pyramid is the characteristic type of composition.
But is it not also characteristic of the 'active' pictures, since, as we see, it has the largest representation in that class too? Perhaps it might be said that, inasmuch as all pictures are really more 'quiet' than they are 'active,' so the type par excellence is the pyramidal--a suggestion which is certainly borne out by the table as a whole. But setting aside for the moment the pyramid and its sub-variety, we see that the diagonal V-shaped and square types are much more numerous in the roughly outlined 'active' class. Taking, again, the genre class as especially representative, we find 23 per cent. of the diagonal type, and 25 per cent. of the V-shaped. We have seen how closely allied are these two types, and how gradually one passes over into the other, so that we may for the nonce take them together as making up 47 per cent. of the whole. The type of picture which expresses the highest degree of activity, which aims to tell a story, has, then, for its characteristic type the V and its varieties.
The landscape picture presents a somewhat different problem. It cannot be described as either 'active' or 'passive,' inasmuch as it does not express either an attitude or an event. There is no definite idea to be set forth, no point of concentration, as with the altarpieces and the portraits, for instance; and yet a unity is demanded. An examination of the proportions of the types shows at once the characteristic type.
P. D.P. Dg. V. Sq. Or. Landscapes, 13 03 35 36 05 08
It is now necessary to ask what must be the interpretation of the use of these types of composition. Must we consider the pyramid the expression of passivity, the diagonal or V, of activity? But the greatly predominating use of the second for landscapes would remain unexplained, for at least nothing can be more reposeful than the latter. It may aid the solution of the problem to remember that the composition taken as a whole has to meet the demand for unity, at the same time that it allows free play to the natural expression of the subject. The altarpiece has to bring about a concentration of attention to express or induce a feeling of reverence. This is evidently brought about by the suggestion of the converging lines to the fixation of the high point in the picture--the small area occupied by the Madonna and Child--and by the subordination of the free play of other elements. The contrast between the broad base and the apex gives a feeling of solidity, of repose; and it seems not unreasonable to suppose that the tendency to rest the eyes above the center of the picture directly induces the associated mood of reverence or worship. Thus the pyramidal form serves two ends; primarily that of giving unity; and secondarily, by the peculiarity of its mass, that of inducing the feeling-tone appropriate to the subject of the picture.
Applying this principle to the so-called 'active' pictures, we see that the natural movement of attention between the different 'actors' in the picture must be allowed for, while yet unity is secured. And it is clear that the diagonal type is just fitted for this. The attention sweeps down from the high side to the low, from which it returns through some backward suggestion of lines or interest in the objects of the high side. Action and reaction--movement and return of attention--is inevitable under the conditions of this type; and this it is which allows the free play--which, indeed, constitutes and expresses the activity belonging to the subject, just as the fixation of the pyramid constitutes the quietude of the religious picture. Thus it is that the diagonal composition is particularly suited to portray scenes of grandeur, and to induce a feeling of awe in the spectator, because only here can the eye rove in one large sweep from side to side of the picture, recalled by the mass and interest of the side from which it moves. The swing of the pendulum is here widest, so to speak, and all the feeling-tones which belong to wide, free movement are called into play. If, at the same time, the element of the deep vista is introduced, we have the extreme of concentration combined with the extreme of movement; and the result is a picture in the 'grand style'--comparable to high tragedy--in which all the feeling-tones which wait on motor impulses are, as it were, while yet in the same reciprocal relation, tuned to the highest pitch. Such a picture is the Finding of the Ring, Paris Bordone (1048), in the Venice Academy. All the mass and the interest and the suggestion of attention is toward the right--the sweep of the downward lines and of the magnificent perspective toward the left--and the effect of the whole space-composition is of superb largeness of life and feeling. With it may be compared Titian's Presentation of the Virgin (107), also in the Academy, Venice. The composition, from the figure moving upward to one high on the right, to the downward lines, waiting groups and deep vista on the left, is almost identical with that of the Bordone. Neither is pure diagonal--that is, it saves itself at last by an upward movement. Compare also the two great compositions by Veronese, Martyrdom of St. Mark, etc. (1091), in the Doge's Palace, Venice, and Esther before Ahasuerus (566), in the Uffizi, Florence. In both, the mass, direction of interest, movement and attention are toward the left, while all the lines tend diagonally to the right, where a vista is also suggested--the diagonal making a V just at the end. Here, too, the effect is of magnificence and vigor.
If, then, the pyramid belongs to contemplation, the diagonal to action, what can be said of the type of landscape? It is without action, it is true, and yet does not express that positive quality, that will not to act, of the rapt contemplation. The landscape uncomposed is negative; and it demands unity. Its type of composition, then, must give it something positive besides unity. It lacks both concentration and action; but it can gain them both from a space composition which shall combine unity with a tendency to movement. And this is given by the diagonal and V-shaped type. This type merely allows free play to the natural tendency of the 'active' picture; but it constrains the neutral, inanimate landscape. The shape itself imparts motion to the picture: the sweep of line, the concentration of the vista, the unifying power of the inverted triangle between two masses, act, as it were, externally to the suggestion of the object itself. There is always enough quiet in a landscape--the overwhelming suggestion of the horizontal suffices for that; it is movement that is needed for richness of effect; and, as I have shown, no type imparts the feeling of movement so strongly as the diagonal and V-shaped type of composition. It is worth remarking that the perfect V, which is of course more regular, concentrated, quiet, than the diagonal, is more frequent than the diagonal among the 'Miscellaneous Religious' pictures (that is, it is more needed), since after all, as has been said, the final aim of all space composition is just the attainment of repose. But the landscapes need energy, not repression; and so the diagonal type is proportionately more numerous.
The square and oval types, as is seen from the table, are far less often used. The oval, most infrequent of all, appears only among the 'active' pictures, with the exception of landscape. It usually serves to unite a group of people among whom there is no one especially striking--or the object of whose attention is in the center of the picture, as in the case of the Descent from the Cross. It imparts a certain amount of movement, but an equable and regular one, as the eye returns in an even sweep from one side to the other.
The square type, although only three per cent. of the whole number of pictures, suggests a point of view which has already been touched on in the section on Primitive Art. The examples fall into two classes: in the first, the straight lines across the picture are unrelieved by the suggestion of any other type; in the second, the pyramid or V is suggested in the background with more or less clearness by means of architecture or landscape. In the first class are found, almost exclusively, early examples of Italian, Dutch and German art; in the second, pictures of a later period. The rigid square, in short, is found only at an early stage in the development of composition. Moreover, all the examples are 'story' pictures, for the most part scenes from the lives of the saints, etc. Many of them are double-center--square, that is, with a slight break in the middle, the grouping purely logical, to bring out the relations of the characters. Thus, in the Dream of Saint Martin, Simone Martini (325), a fresco at Assisi, the saint lies straight across the picture with his head in one corner. Behind him on one side, stand the Christ and angels, grouped closely together, their heads on the same level. Compare also the Finding of the Cross, Piero della Francesca (1088), a serial picture in two parts, with their respective backgrounds all on the same level; and most of the frescoes by Giotto at Assisi--in particular St. Francis before the Sultan (1057), in which the actors are divided into parties, so to speak.
These are all, of course, in one sense symmetrical--in the weight of interest, at least--but they are completely amorphous from an æsthetic point of view. The forms, that is, do not count at all--only the meanings. The story is told by a clear separation of the parts, and as, in most stories, there are two principal actors, it merely happens that they fall into the two sides of the picture. Interesting in connection with this is the observation that, although the more anecdotal the picture the more likely it is to be 'double-centered,' the later the picture the less likely it is to be double-centered. Thus the square and the double-center composition seem often to be found in the same picture and to be, both, characteristic of early composition. On the other hand, a rigid geometrical symmetry is also characteristic, and these two facts seem to contradict each other. But it is to be noted, first, that the rigid geometrical symmetry belongs only to the Madonna Enthroned, and general Adoration pieces; and secondly, that this very rigidity of symmetry in details can coexist with variations which destroy balance. Thus, in the Madonna Enthroned, Giotto (715), where absolute symmetry in detail is kept, the Child sits far out on the right knee of the Madonna. Compare also Madonna, Vitale di Bologna (157), in which the C. is almost falling off M.'s arms to the right, her head is bent to the right, and a monk is kneeling at the right lower corner; also Madonna, Ottaviano Nelli (175)--all very early pictures. Hence, it would seem that the symmetry of these early pictures was not dictated by a conscious demand for symmetrical arrangement, or rather for real balance, else such failures would hardly occur. The presence of geometrical symmetry is more easily explained as the product, in large part, of technical conditions: of the fact that these pictures were painted as altarpieces to fill a space definitely symmetrical in character--often, indeed, with architectural elements intruding into it. We may even venture to connect the Madonna pictures with the temple images of the classic period, to explain why it was natural to paint the object of worship seated exactly facing the worshipper. Thus we may separate the two classes of pictures, the one giving an object of worship, and thus taking naturally, as has been said, the pyramidal, symmetrical shape, and being moulded to symmetry by all other suggestions of technique; the other aiming at nothing except logical clearness. This antithesis of the symbol and the story has a most interesting parallel in the two great classes of primitive art--the one symbolic, merely suggestive, shaped by the space it had to fill, and so degenerating into the slavishly symmetrical, the other descriptive, 'story-telling' and without a trace of space composition. On neither side is there evidence of direct æsthetic feeling. Only in the course of artistic development do we find the rigid, yet often unbalanced, symmetry relaxing into a free substitutional symmetry, and the formless narrative crystallizing into a really unified and balanced space form. The two antitheses approach each other in the 'balance' of the masterpieces of civilized art--in which, for the first time, a real feeling for space composition makes itself felt.
* * * * *
THE ÆSTHETICS OF UNEQUAL DIVISION.
BY ROSWELL PARKER ANGIER.