A quantitative study of rhythm : the effect of variations in intensity, rate and duration

Front matter

Class Book-

SMITHSONIAN. DEPOSIT

THE EFFECT OF VARIATIONS IN INTENSITY, RATE AND DURATION

Contents

I. Historical 5

II. Apparatus and Procedure 12

III. Intensity 30

CHAPTER I HiSTOEICAL

To produce an impression of rhythm, it is necessary to have a series of stimuli. These stimuli may be sounds, as in the ease of poetry and music, muscular contractions, as in dancing and beating time, or lights and electrical shocks, as in some laboratory experiments. The stimuli which give the impression of rhythm, whatever their nature, may vary in intensity, in duration, and in quality, and may be separated by intervals of varying length. A fundamental task of the experimental investigation of rhythm is to investigate the part played by each of these factors. Only after each of them has been studied separately, may we study the effect when two or more of them are simultaneously involved, and when more complicated factors are introduced, as in melody and harmony.

The aim of the present study is to examine quantitatively the dependence of the rhythmical impression on the intensity and duration of the stimuli. Such an investigation is evidently along the same lines as much of the experimental work of Meumann, Bolton, R. McDougall, and others, who have studied the objective conditions of rhythm. It is necessary, therefore, to review the work that has already been done on the perception of rhythm as influenced by variations in the intensity and the duration of the stimuli.

Meumann^ found that in listening to a series of sounds, some of which were louder than others, there was a strong tendency towards the formation of rhythmical groups. He studied the effect of accented sounds on the intervals preceding and following them. The most general conclusion at which he arrived is that the effect of the more intense sound may be very different according to its position in the rhythmical group. ^ He found that sometimes the interval following the accented sound is overestimated and sometimes underestimated, and also that sometimes the interval preceding the accented sound is overestimated and sometimes underestimated, and in the cases in which he used more than one subject, he gets quite different results under the same objective conditions. Meumann states, also, that, with most subjects, the sudden introduction of a loud sound into a series of weaker ones causes an underestimation of the interval preceding, and an overestimation of the interval following, the loud sound ;^ but he does not

say how many observers gave this introspection, what was the introspection of those who did not give it, how many judgments were made by each observer, or how they were instructed. Meumann made no investigation of the effect of duration in rhythm.

Bolton^ presented sets of sounds of different intensities and durations, which recurred always in the same order, and asked the subject to point out where the series was grouped. In this way, he sought to determine what was the most natural order in which the different intensities and durations occurred in the group. These experiments led him to state the following general principle: "In a series of auditory impressions, any regularly recurrent impression which is different from the rest, subordinates the other impressions to it, in such a way that they fall together in groups. If the recurrent difference is one of intensity, the strongest impression comes first in the group and the weaker ones after. If the recurrent difference is one of duration, the longest impression comes last."^

Bolton calls attention, further, to the long interval which appeared between the groups, the intervals being objectively equal. The pause seemed to be due to the fact that a long interval generally preceded the accented sound. At the same time some subjects, especially 10 and 15, make a short interval after the strongest sound. But in another place, Bolton writes: "The accented long sound frequently appeared more prolonged than the unaccented of the same length: the accent had the effect both to increase the length of sound and of the interval which followed." And consulting his table of results,^ we find that his subjects often found the interval preceding the accented sound longer than the others, but more often did not. As regards the effect of duration, most of Bolton's subjects remarked upon the long interval or pause which seemed to follow the long sound, and for this reason it was found difficult to make the close of the group come at any other place.

Ettlinger^ has criticized Bolton for his tendency to generalize his results on duration, which, being limited to the single case in which one sound is twice the duration of the other, do not permit of much generalization. So far as they go, however, his results indicate that the effect of increasing the length of any regularly recurrent sound is to produce an overestimation of the followdng

HISTORICAL 7

interval, while the effect of increasing the intensity is uncertain. To most of Bolton's subjects, the strongest sound seemed longer than the rest, and the long sound frequently seemed accented.

Schumann^ asked his subjects to compare the second of two intervals enclosed within a series of three sounds with the first interval. He found, in the case of four subjects, that when the third sound was louder than the preceding, the second interval was underestimated as compared with the first. Three of those same subjects were also tested with regard to the effect of a loud sound which was unexpectedly introduced in a series of weaker sounds. In the case of all three, the interval preceding the louder sound was apparently shorter than the other intervals. Two subjects, on the other hand, obtained the opposite result in both experiments, that is, the interval preceding the accent was overestimated as compared with the other intervals. Schumann explains this apparent contradiction on the ground that the two last mentioned subjects perceived the sounds rhythmically. He made no investigation of the effect of the regular recurrence of a more intense sound every second or every third time in a long series, nor did he study the effect of variation in the durations of sounds on rhythm or on the judgment of intervals.

McDougalP found that a loud sound introduced into a uniform series of six beats causes a considerable underestimation of the interval following the loud sound, while it less often and less considerably lengthens the preceding interval. As regards the overestimation of the interval preceding the accent, of the four tables^ of results which are presented to prove this, one^ shows an uDderestimation; another^ shows practically no constant error, but an underestimation rather than an overestimation, while a third^ does not show that accent has any effect on the interval immediately preceding, but that a longer interval causes overestimation of the interval preceding that longer interval. As regards underestimation of the interval following the accented sound, we find one table^ which shows that when the interval following was 20 per cent, shorter than the interval preceding the accent, and 10 per cent, shorter than the remaining intervals, it was judged less than the remaining intervals 26 times,

^ Harvard Psychol. Stud., i; Monog. Sup. Psychol. Rev., 4, 309-412, 1903.

4 Table XXIX. s Table XXXI.

« Table XXXII. 7 Table XXIX.

but as equal to them 31 times, and greater six times. The table shows, therefore, that the interval following the accented sound, which was 10 per cent, less than any of the other intervals, was judged either equal or greater in 59 per cent, of the cases. This is about as strong evidence of overestimation as the other three tables give of underestimation. Still more doubt is thrown upon McDougall's conclusion in this connection from the fact that, though five subjects are said to have participated in the experiments represented in these four tables, no separate record is kept of these individuals, and even then the total number of judgments on anyone set of intervals is very often not over six. These experiments were made as already stated with series of six sounds, one of which was louder than the others. Other experiments were made by McDougall in which series which might be called rhythmical were presented to the subject, that is, series in which the accented sound recurred regularly every other time or every third time. In these, it is quite evident that the interval preceding the accented sound is overestimated as compared with the other intervals. McDougall moreover determines the magnitude of this relative overestimation of the interval preceding accent in rhythmical groups of both two and three sounds. To accomplish this, he ascertained at what temporal spacing the grouping disappeared, that is, what relative length of the intervals before and after the accented sound was necessary to produce the impression of temporal uniformity in the series. He refers to the point at which temporal uniformity takes the place of rhythmical grouping as the indifference point. Concerning this point, he writes: "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."^ As regards the effect of duration, McDougall made no investigations corresponding to those on intensity.

Miner^ investigated the effect of intensity and of duration in visual rhythms, using lights in place of sounds. His subjects mistook a difference in the duration of the lights for one of intensity. The more intense light regularly recurred every second or every third time. The intervals between the lights were always equal. The subjects were asked to group the lights first, in groups in which the brighter came first, and second, in groups in which the brighter came second. While doing this, they had, further, to judge which interval was the longer, and which the shorter. We have no guaran-

* Monog. Sup. Psychol. Rev., 5, No. 4, 1903.

HISTORICAL 9

tee that the subjects actually held to this forced rhythm while observing the relative length of the intervals. In fact, Miner, himself, distinguishes two attitudes on the part of these subjects, though all were similarly instructed. These attitudes he calls the rhythmical and non-rhythmical. He reports no introspections, however, on the part of the subjects, on which to base this division of them into rhythmical and non-rhythmical, and it is made merely as an explanation of the disagreement between the results of different individuals. His results do not admit of much generalization. The following statements, however, can be made. The interval which was most often judged the longest, no matter how the sounds were grouped, was that which separated the groups. The interval next most frequently judged the longest was that before the brighter light. Like Meumann, Schumann, and Mc- Dougall, Miner also investigated the effect of only one intense stimulus in a longer series of less intense. He found that twelve out of seventeen subjects judged the interval after the bright flash to be the longer.

Miner says that the discrepancy between his own results and those of McDougall may be due to the difference in the quality of the stimulus or the length of the intervals. But this would not explain the discrepancy between Meumann's statements and those of McDougall. Of more importance, probably, is the fact that, in Miner's experiments, the subjects did not know at what point in the series to expect the intense stimulus, whereas, in McDougall's, they did. Miner says that the bright flash was brought in at an unexpected time. Moreover, the subjects were told to notice any difference in the appearance of the interval or the light that followed the bright flash, that is, their attention was directed to the interval and stimulus following the more intense stimulus. With such instructions, we do not know whether the interval following the brighter light appeared longer because of the brighter light or because the subject's attention had been specially directed to the interval and light following the bright flash. McDougall's subjects, on the other hand, knew when the loudest sound was to appear. He writes: "As a single hearing very commonly produced but a confused impression due to what was reported as a condition of unpreparedness the method adopted was

to repeat each series before asking for a judgment

In order to define the direction of attention on the part of the ob- :server, 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."^ This difference in the instructions given the subjects may account for the difference in the results. In other words, the disagreement between the results of Miner and McDougall may be interpreted as merel}^ a piece of evidence of the importance of the direction of attention in the estimation of intervals. The results of both investigations agree in that they find an overestimation of the interval preceding that stimulus which, there is reason to suppose, is the object of the greatest amount of expectant attention, namely, the more intense, when the subject knows when to expect it,^ or the one after the more intense, when they are not informed when to expect the more intense, but have had their attention especially directed, as a result of their instructions, to the stimulus following the more intense. The apparent discrepancy between the results of Miner and McDougall, therefore, goes to confirm Schumann's theory concerning the effect of strain of attention in the estimation of small intervals.

Whether Miner's results are to be considered as contradicting those of Bolton on the effect of an increase in duration is not very clear. Miner found that his subjects mistook an increase in the duration of a light for an increase in intensity, and finds that this apparent increase in intensity has about the same effect on the rhythmical grouping as an actual objective increase in the intensity of the stimulus. But as we have already pointed out. Miner's experiments do not permit us to generalize concerning this effect. And, in fact, we have no way of being sure which of the large number of varieties of effect he mentions were due to apparent intensity and which to the attempt of the subjects to group the sounds in the way that they were instructed to group them.

Notwithstanding many apparent contradictions among the investigations I have reviewed, it is yet possible to indicate the general trend of results so far obtained concerning the effect of variations in the duration and intensity of certain stimuli in a series. There

^ G. F.°Arps und O. Klemm, "Der Verlauf der Aufmerksamkeit bei rythmischen Reizen." Psychol. Stud., 4, 518-528, 1909. These authors, using the sensitivity to temporal displacements of each of the members of a dactylic group (every 3rd sound of the objective series being accented and the intervals all equal) as a measure of the degree of attention bestowed on each of the members, conclude that the greatest degree of the attention occurs at the accented sound and the least at the second unaccented sound. The greatest change in the level of attention occurs therefore during the interval preceding the accented sound. Apart from this work we have the generally recognized fact that intensity is one of the "objective conditions" of attention.

HISTORICAL 11

can be no question but that the effect of a more intense stimulus in a series of less intense is different, according as the more intense occurs unexpectedly, or at a time when it is expected, as when the more intense stimulus regularly recurs. The general conclusion indicated, if I may neglect, for the sake of simplicity, the special conditions of the above-mentioned researches, is that a more intense stimulus, if unexpected, causes a relative underestimation of the interval preceding it; if expected (or regularly recurrent), a relative underestimation of the interval following it.

As regards duration, about all that can be said, neglecting special conditions again, is that in the case of regularly recurrent differences, one investigator has found an overestimation of the interval preceding the longer stimulus, another, indications of an overestimation of the interval following the longer stimulus.

Chapter II

The following experiments were performed in the psychological laboratory of the University of Michigan, under the guidance of Professor Pillsbury and Dr. Shepard, whom I am glad to thank for their advice and aid. The work was done mostly during the summer vacations of 1907 and 1908. The subjects used, thirteen in all, were, with one exception, advanced students doing original work in experimental psychology. I take this occasion to express to all those who acted as subjects my appreciation of their patience and conscientiousness.

The first question to be solved, in an investigation of this sort, is how to produce a series of sounds in which it is possible to make accurately measurable variations in the absolute and relative length of the intervals between the sounds, their absolute and relative intensity, their absolute and relative duration, and the relative proportion of sound and silence. I will describe, first, the disposition of apparatus for work in which the effect of intensity was studied and then point out the changes that were necessary for the study of variations in the duration of the sounds and their rate of succession.

Part of the apparatus used in the production of the series of intensively changeable sounds is shown in the cut, opposite page 13, which represents the operator's room. In addition, there was in the subject's room a telephone, head-rest, and a microscope for reading the amplitude of vibration of the telephone plate. This reading was not used in the final estimate of the intensity of the sound, but merely as a preliminary guide.

The sound used for producing the rhythm was that made by a telephone receiver, through which passed an alternating current of 60 alternations per second (a branch from the city lighting circuit), which current, in turn, was interrupted 250 times per second by a tuning fork. The object in having the current interrupted by a tuning fork was to get rid of a click which otherwise occurred at the moment of breaking the current. It was found that, if a current which produced an approximately pure tone was used, there was a very slight click, both at the instant of making the circuit and of breaking it, especially, however, at the break. One could not be sure in judging by the ear alone that this click was not an illusion due to contrast with the preceding or following silence; but Professor Pillsbury succeeded in demonstrating its existence objectively through the aid of a string galvanometer set up in circuit with a microphone placed in front of the telephone. I tried many methods of eliminating this click, suggested by officers of the departments of physics and of electrical engineering, but they all failed. Finally, I noticed that in some experiments in which I was using an induction coil in order to get a telephone sound, there was no click at the break and make. As the ordinary inductorium is not absolutely reliable as regards the regularity

T

Fig. I

M = Meumann's machine.

C1C2 = contacts.

S1S2 = adjustable shunt resistances.

RjRj = adjustable resistances.

WW = wall.

T = telephone.

F = 250 fork.

of vibration and resistance of its interrupter, at the suggestion of Dr. Shepard, a tuning fork with a vibration frequency of 250 per second was substituted. The platinum plate of the fork was provided with a specially devised micrometer screw arrangement, which made it possible accurately to control the closeness of the contact. Needless to say, this contact, as well as all others, were kept bright as new throughout the investigation and frequently renewed. The sound produced in this manner, according to all the subjects who took part in the investigation, was perfectly even and uniform, and was absolutely free from a click at either the beginning or ending.

For the purpose of making and interrupting the sounds, a Meumann's time-sense apparatus' was used, on which were arranged ordinarily from 2 to 6 contacts. Each contact, at the time it was closed, formed part of a separate circuit. By changing the amount of resistance in these separate circuits, the intensity of any sound could be varied independently of that of any other. This arrangement is shown in the diagram on the preceding page.

Whenever any measurements of intensity were made, all the contacts and all circuits were arranged as in actual use. This was necessary inasmuch as part of each circuit constituted a shunt for the other circuits.

As a measure of the intensity of the sounds, the distance to which they were just audible was taken. It is not claimed that such a method of measurement is very exact, but on the whole it was considered the most satisfactory. The measurements were all made on the same day, Sunday, during the sum.mer vacation, about two weeks before the opening of college, in Ann Arbor, in an open space on the campus left by the removal of an old building. Only a few series of measurements were taken for each sound, as Sunday was the only day it was quiet enough to work, and it was found impossible in the course of about two months to get more than one good Sunday, that is, one which was free from wind or rain, or the noise of birds, crickets, etc. I obtained as many series of measurements as was possible in one day, working from early in the morning until after dark, with Mr. Dockeray, at the time assistant in psychology in the University of Michigan laboratory. Environmental conditions were constant throughout the day. The method of minimal changes was used, and from 2 to 6 series were obtained with each intensity. At each step, the sound was presented three times in succession, each time for about 1 second. The operator gave the subject a signal by waving a handkerchief a short but variable time before the first sound, and the subject indicated his judgment by raising a handkerchief whenever he thought he heard the sounds and keeping it lowered the rest of the time. The intervals between the three successive presentations of the sounds were made quite irregular. If the subject signaled at such times as to indicate that he heard all three sounds or two out of three, he was considered to have judged "sound audible;" if he signaled correctly for onlyone of the three sounds, his judgment was called "doubtful;" if he got none right, he was marked as if he had judged "sound inaudible." The method used was therefore really a combination of the method of minimal changes and the method of constant stimuli. The following measurements were made of the sounds used in this investigation, the distances being given in feet:

Distance audible

No. of series

M. v. (absolute

I.O

0.8

2.6

2.0

1.2

4-3

6.0

24.6

17-3

35-0

56.0

1 100

50.0

In the remainder of this work, whenever the intensity of a sound is indicated, what is meant is the distance to which it was audible.

The rate of rotation of the Meumann's apparatus, and so the rate of succession of the sounds, was controlled by a Helmholtz motor and two ball-bearing speed-reducers. The rate of rotation of the Helmholtz motor was kept as constant as possible through the aid of a speed counter and stop watch, and an adjustable resistance in the circuit passing through the motor. An accurate record of the rate of rotation as well as the duration of each sound and each interval could be obtained by placing in the same circuit with the telephone a time marker writing on a drum alongside another time marker of 100 single vibrations per second. It was, of course, out of the question to measure individually every one of the sounds and intervals used, as the total number was over half a million. What was done was to take several drums of records of each different rhythm used, both at the beginning and end of the hour, and to keep testing the rate of revolution of the time-sense apparatus by a stop-watch and speed counter during the hour. How great a degree of regularity of speed was obtained is indicated by the mean variation of the following measurements of the times of successive revolutions:

Duration of i revolution N. M. V. per cent.

A part of this variation is, of course, due to inaccuracies in estimating fractions of a vibration of the fork. I will show later (Chap. IV) that my results would not be changed even by very considerable variations in the rate of revolution. Such extremely small mean variations in the rate of revolution as those just indicated have, therefore, no significance for the results of this investigation, and for that reason, in the tables to follow, no mention is made of the mean variation in the rate of revolution of the time-sense apparatus. Changes in the rate were made by the aid of the speed-reducers. A range of rate was obtained from one revolution in 0.5 seconds to one revolution in 26.0 seconds.

When variations in the duration of the sounds were desired, contacts of different length were used. The accurate measurement of the duration of the sounds was accomplished in the mannerdescribed above. Finally, it was possible, within certain limits, to arrange for any desired combination of intensity and duration in the sounds composing the rhythmical series.

Given a series of sounds which may be varied in intensity and duration, the question arises, how are we to investigate the effect of these variations? The question to be solved is, what values, have intensity and duration for the impression of rhythm which is obtained in listening to the series of sounds? If the study is to take on a quantitative aspect, there must be some measure of the magnitude of the rhythmical attribute of the total impression;, there must be some index to show us whether more or less rhythm is felt, some way of telling which of two rhythms, both of which may perhaps be qualitatively alike, in the sense that they are both trochaic or both iambic, is the stronger or more emphatic. The members of a group may be thought of as being held together more or less securely, by stronger or weaker bonds; and what we desire is a measure of the force with which these members of a group are held together — a measure of what McDougall calls "the rhythmic integration of the stimuli."

A very direct method would be to ask the subject to introspect regarding the relative amount of rhythm produced by two different series of sounds. This task is similar to that required of subjects in experiments on the so-called intensity of sensation. The introspection in the case of rhythm, however, is more difficult, and I doubt if reliable results can be obtained from an investigation carried out in this way. For instance, suppose we compare two trochaic rhythms, one produced by an alternation in intensity and one by an alternation in duration. It may be very apparent that both rhythms are what we call trochaic, but the total impression is very different in the two cases, and it is very hard to isolate the intensive aspect; and consequently it is difficult to say in which case the rhythm is the stronger; and it would be still more difficult to say which is the stronger if one were trochaic and the other iambic. I found that such judgments were not impossible, but I have preferred a more indirect and more objective method, one that demands something far less difficult on the part of the subject.

The following description of the method used in this research may be found rather difficult to follow by those who are unaccustomed to the terminology of rhythm; but I believe that, if the reader will take a pencil and paper and follow out by the aid of symbols the procedure below outlined, he will find no ambiguities. It should be remembered that in all the rhythms here dealt with every second or every third sound is either louder or longer than the others. Also that rhythm is characterized by an apprehension of the sounds in groups and that when there is no grouping there is no rhythm. The method consists in taking as the measure of the amount of rhythm the amount by which, measuring from the point at which all intervals are equal, the internal intervals, or intervals within the group, must be increased or decreased with respect to the external intervals, or the intervals between the groups, in order to cause a disappearance of the rhythm, that is, a disappearance of apparent grouping. Roughly speaking, I have used as the measure of the amount of rhythm the amount of work that had to be done on the intervals to destroy the rhythm. Suppose, for instance, that a certain series of sounds in which every other one is accented, produces an impression of trochaic rhythm, the accented sound seeming to begin the group. Now, such a rhythm can be changed to an iambic one by increasing the interval following the accented sound, with respect to the interval preceding the accented sound. I have found no exception to this possibility. Moreover, as the process of increasing the interval after the accented sound is going on, just before the rhythm becomes iambic, there will be a point reached at which the rhythm can hardly be said to be more iambic than it is trochaic. This point may be called the iambic-trochaic indifference point. It is the point at which the rhythm is destroyed, or at least reduced to a minimum. If, to arrive at this point, it was necessary to produce only a very slight increase in the duration of the interval after the louder sound with respect to the duration of the interval before it, the rhythm may be said to have possessed only a slight degree of temporal segregration to begin with; and that slight degree of temporal segregation to have been in the trochaic direction. This means that, to begin with, the temporal grouping of the sounds was such that the sounds within the same group were only slightly more grouped than two successive sounds belonging to different groups.