Theory and practice of musical composition

Front matter

hiyuels pie Me

SOR CARR

0, ie gi Ae, a, 8.4 fits Ey fi pI 9 Df SoH avaba) i Utes a js

Table Of Contents

MUSICAL NOTATION.

Praca _Inrnopuction nut tee ieee ter aren St Pe

‘PART FIRST.—TONES AND NOTES.

Part First.—composition For Single Parts (monophonic : Composition), 53

Cnarter I. The first Formations: 1. The Tone-chain, with its Species, 53 ; Tone Reg. ulation, 54; The Major Scale, ib.; Analysis of the Scale, 55; 2, Rhythmical form. ation of the Tone-chain, 56; Retrospection, 59.

Carter II. Invention of Monophonic Phrases, 61; 1. The Design and its Efficacy, t.; 2. Formation of Passages, 63 ; 3. Formation of Phrases, 64; 4. Periods, 66.

Cuarter III. Discovery of New Means, 67.

Part Second.—composition For Two Parts Puperonig Composition)

Cuarter I. The Duophonic Composition, derived from the Monophonic, 72.

Cuarter II. The Duophonic Composition, derived from Natural Harmony, 74; 1. Manner of arriving at it, ib.; 2. Application, 77; Melodic Application, ib.; Harmonic Application, ib. ; 3. Harmonic Designs, 78; 4. The Cadence, 79; 5. The Half-Cadence, ib. ;

Cuarter III. The Duophonic Composition, 81.

10 TABLE OF CONTENTS,

Cuapter ITV. Compositions of two and three parts, 84; Retrospection, 87 ; Compositions of three parts, 89. ‘ CuHarterR V. The Double Duophonic Composition, 90 ; Application, 93.

Part Third.—harmony Of The Major Scale

Cuarter I. Discovery of the necessary Harmonies, 94.

Cnapter IJ, Examination and Justification of the Harmony, 99; A. The Four Voices, id.; B. The Connection-of Chords, 100; C. Harmonic Designs, 7.; D. Faulty Pro gressions, 101; 1. Octave Succession (Consecutive Octaves), ib.; 2 Quint or Fifth Succession (Consecutive Fifths), 102; E. The Dominant Chord, 103; F. The Triad of the Dominant, 105.

Cuarter [I]. The Accompaniment of given Melodies, 107; A. Limitation to those means which were found in the Ascending Scale, ib.; B. The Descending Scale, 109.

Part Fourth.—the Freer Use Of The Chords In Our Possession, 113

Cuarrer I. Harmonic Designs, 114; A. Development of a Single Chord, ib.; B. Com bination of Major Triads, 115; 1. Designs of Nearest Connection, 1. ; 2. Designs of Remote Connection, ib.;.C. The Combination of Minor Triads, and of Minor and Major Triads, 116; D. Harmonic Designs from adding the Dominant Chord, 117; 1. The Dominant Chord preparing the end, éb.; 2. Other Chords in connection with the Dominant Chord, 118; E. Extension of the Harmonic Designs by means of Rhythm, 118; F. Formation of Harmonic Passages or Sequences, 119; Prelude, 120.

Cnuapter Il. Freer Harmonization of given Melodies, 122; A. Freer use of Triads ib.; B. Free introduction of the Domnant Chord, 125; Freer Treatment of the Dominant Chord, 127; Doubling of intervals in the Dominant Chord, 128 ; Covered Octaves and Fifths, 129.

Part Fifth.—inversion Of Chords, 131

Cuarter J. Enumeration and Appellation of the Inversions, 132; Figuring, 134.

Cuarter II. Free use of the Inversions, 136; A. New Designs and Passages, 2. ; B. Combination of Inversions with Fundamental Chords, 138; C. Preludes and Final Cadences, 140; D. Avoiding faulty progressions, 141; E. The Diminished Triads,

Cuarter II]. Employment of Inversions, &c, 143.

Cuarren IV. Cluse and dispersed Harmony, 144; Retrospection—Modulation, 147

Part Sixth.—harmony Of The Minor Scale

Cuarter I. Formation of the Minor Scale, 149.

Cuarter Ii. Harmonization of the Minor Scale, 151; NoraChord (Chord of the Ninth), 152.

Cuarrer III. Nona-Chord, continwed, 154; Inversions of the Nona-Chord, 155; Diminished Septime Chord, ib.

Cuarter IV. Freer use of the New Chords, 157; 1. Major Melodies, 158; 2. Minor Melodies, 7b. ; 3. Licenses of the Dominant Chord, 160.

Part Seventh.—modulation Into Foreign Keys, 161

Cnarter I. Modulation from one Key into another, 162; 1. The Dominant Chord, 163; 2. Thé Nona-Chords, 168; 3. The Septime Chord, ib.; 4. The Diminished

TABLE OF CONTENTS. 11

Septime Chord, 169; 5. The Diminished Triad, i.; 6. The Dominant Triad, 1703 7. The Minor Triad, 171.

Cuarter II. Introduction of new means to the Harmonization of Melodies, 173; A. Ascertainment of Digressive Melody, id.; 1, External Characteristics, ib.; 2. In ternal Characteristics, 174; B. Discovery of all eligible Chords, 175 ; C. Application of these means to Indigenous or Digressive Melodies, 177.

Cuaprter III. Formation of new passages with the aid of Foreign Chords, 186; 1. Pas. sages of Dominant Chords, 189; 2. Indigenous Passage, 190 ; 3. Successions of Nona Chords, 191; 4. Indigenous Passage of Nona-Chords, 192; 5. Successions of derivea Septime Chords, 192.

Cnarter IV. Variable modulations, 196; A. The Diminished Septime Chord, 1b. ; B. The Dominant Chord, 199. ¢

Cuarter V. General Order of Construction, 201; A. The first perfect Construction of a two-part Composition, 7b.; B. Second two-part Construction, 203; C. Further extension of Modulation, 204; D. The Interrupted Cadence, 205.

Cuarter VI. Abrupt Modulation, 207. ;

Cuarter VII. Order of Modulation for more extended Compositions, 211; Passages of Phrases, 213.

CuartTerR VIII. The Pedal-point, 215.

Cnarter IX. Retrospection, 220; A. Development of Harmony, #.

*

Part Eighth.—displacement Of Chords, 298

Cuarter I. Suspensions from above, 228 ; Suspensions of fundamental Tones, 234.

Cuapter II. Suspensions from below, 236; A means of Connection, 238 ; Fifths miti gated by Suspensions, 244; Octaves covered by Suspensions, 245.

Cuarter III. Anticipated Tones, 246.

THE ACCOMPANIMENT OF GIVEN MELODIES, IntTRopUCTION, 281.

Part First.—the Accompaniment Of The Choral, 283

Cuartrr I General Conception of the Melody, 285; A. Confirmation of the Key, and the principal points of Modulation, i. ; B. Summary of Cadences, 290. Cuarter II, Disposition 0? the Harmony, 297.

{2 TABLE OF CONTENTS.

Cuarter III. Simple treatment of the Choral, 305.

Cuarter IV. Higher treatrent of the Choral, 310; A. Character of the Voices, 311; B. Application to the Choral, 314; 1. Technical Difficulties, 318; A. Tone-repetition, 7b.; B. Phrase-repetition, 2b. ; 2. Artistic aim of Choral treatment, 319.

CHAPTER y. The Cantus Firmus in other Voices, 321; A. The Cantus Firmus in the Alto, 322; B. The Cantus Firmus in the Tenor, 323 ; C. The Cantus Firmus in the Bass, 324.

. Carter VI. More and less voiced treatment of the Choral, 327; A. The Choral with less than four Voices, 1%3.; 1. The Duophonic treatment, 7.; 2. The Triphonic treatment, 328 ; B. The Choral with more than four Voices, 330.

Crarrer VII. How to acquire facility in the Harmonization of the Choral, 331.

Part Second.—chorals In The Ecclesiastical Keys, 338

Carter I. The Ecclesiastical Keys, 341; A. The Melodic Point, %.; B. The Harmonic Point, 342; C. The Essential Tones of every Key, 344; D. Admissibility of foreign Tones, ib.; E. Traysposition and Signature, ib,; F. Modulation into other Keys, 346.

Carter JI. The Jonian Key, 347.

Crarter III. The Mixolydian Key, 349.

Cuarter IV. The Dorian Key, 350.

Cuapter V. The Molian Key, 352.

CuHarter VI. The Phrygian Key, 354.

Cuapter VII. The Lydian Key, 356.

Part Third.—the Secular National Song, 358

Cuarter I. General Conception of the Melody, 360; 1. Consideration of Voice-region, ib. ; 2. Character of Keys, ib.

Cuarter II. Plan of the Harmony, 361; 1. The Measure or the Quantity of the Harmony, i.; 2. Number of accompanying Voices, 364; 3. The Form of the Harmony, 366.

Cuarter III. Harmonic’Figuration, 367; Discovery of its Designs, ib, ; 1. Monophonic Designs, ib.; 2. Duophonic and Polyphonic Designs, 363,

Cuarter IV. Execution of the Harmonic Figuration, 370; A. The Harmonic Point of View, ib.; 1. Retarded Resolution, 1.; 2. Octave and Quint-Succession, 371; 3. Passing-tones, 372; B. The Melodic Point of View, ib. ; 1. Consistency of Execution, 373; 2. Firm Connection, ib.

Cuapter V. The Exercise of Harmonic Figuration in Passages and given Melodies, 375; 1. Passages reduced to Harmonic Figuration, 1b. ; 2. Accompaniment of giver Melodies, 377.

Cuarter VI. Passing-Tone and Bye-Tone, 379 ; Help Tones, 381; Trills, Turns, &e., 382 ; Passing or Transient Chords, 384.

Cuarter VII. Introduction of Passes and Help-tones into Figuration, 385; A. Figuration of the Upper Voice, ib.; B. Figuration of the Bass, 387; C. Figuration of a Middle Voice, 389; Application, 390.

Cuarter VIII. Application of these means to Artistic Accompaniments, 392.

APPENDIX, The Figural Prelude, 401.

ELEMENTS OF MUSICAL NOTATION.

BY THE

TRANSLATOR, ©

Preface To The Elementary Part

THE indefiniteness of the English language, in everything concerning Music, makes it a task of extreme difficulty to write an Elementary Treatise, corresponding to a theoretical work of any foreign, and particularly German author. The German musicians have made Music so thorough a study, that it is absolutely impossible to do them justice in translating their works with general terms, which at every step are subject to modifications and contradictions.

It is this consideration which has induced the Translator of this work to prepare the student by an Elementary Treatise, the chief object of which is to give exact definitions of such terms as may occur in this or other works of the same author, and the exact meaning of which it is absolutely necessary for the student to know.

In order to avoid the introduction of indefinite terms, or arguments upon them, as much as possible, the Translator has thought it best to convey the necessary information in regular didactic form; and if comparisons and arguments cannot be absolutely avoided, they will be made at least as brief as possible.

Introduction

* Mosic is the art of combining sounds agreeable to the ear,’’ is the general definition given of the word.

Not every sound, however agreeable to the ear, is a musical sound ; nor is a combination of such sounds always Music. It follows, then, that our first task must be to distinguish musical sounds, or sounds agreeable to the ear, from such sounds as constitute Music.

We know that the ear is the organ which is most directly affected by Music. Every vibration of air caused by a colfision of bodies, or other means, sufficient to affect the ear, we designate by the general name of

SOUND.

We know, also, that Music is produced by the human voice, as well as by instruments of various kinds—F utes, Trumpets, Violins, &c. These instruments distinguish themselves from each other by the quality of their sounds.

Finally, we perceive on one and the same instrument, that the sounds produced upon it vary in regard to pitch. Thus, for instance, are the sounds produced on the shorter strings of a Harp more acute than those produced on a longer string. When we consider a sound in this respect, we must call it

TONE.

We have, therefore, many different tones. The tones of the longer or thicker strings are called low ; those of the shorter or thinner strings are called high. Thus of human voices, we say that the tones of a man’s voice, in general, are lower than those of a boy’s or girl’s voice ; the tones of the Flute, Violin, Trumpet, we say, are higher than those of the Bassoon, Double-bass, and Horn. We say “‘ in general ;”’ for since every voice and every instrument can produce many tones, it can occur that the highest tenes of a ‘man’s voice, for instance, are higher than the lowest tones of a girl’s voice, &c.

Every tone or sound to be produced, must be produced within a certain time, therefore must fill a certain space of time,—a longer or shorter space, definite or indefinite. This time, or space of time, accorded to a tone or sound, is . called its

DURATION.

We say, therefore, of a tone: it has a definite or inde. finite duration.

If we cause the gradual production of a series of tones or sounds of certain duration, according to some regulating law, in any fixed and continued, i.e. repeated, time-moments, we call this regulation of time-succession,

RHYTHM.

Where such regulation does not take place, the tones hare either no certain duration, or follow in no regular succession; we say that such tone-succession is unrhythmical.

A succession of tones, which is formed according to any ie particular plan, and at the same time rhythmically regulated, (whether agreeably, expressively, &c., or not,) is called a

MELODY.*

A piece of Music can consist of a single tone-series,—it

is then called Monophonic, (for one voice.)

Or it can consist of two, three, four, or more, simultaneously* progressing tone-series ; it is then called

Duophonic (for two voices) ; Triphonic (for three voices) ; Tetraphonic (for four voices); or Polyphonic (for many

Voices. ) Each series of tones, however, whether sung or produced upon some instrument, is called a VOICE.

The simultaneously-meeting tones of different voices must stand to each other in some reasonable, corresponding rela.

tion. This relation is called HARMONY.

And of all these essentials : tones and sounds, tone-succession and rhythm, melody and harmony, does

MUSIC consist.

* A mpre concise definition of Melody will be given at a later periog,

FIRST PART.

TONES AND NOTES.

Chapter I. The Tone System

Tone is a sound of certain height or depth, (pitch.)

We know already that there are many tones; the mass of the various tone-gradations is absolutely innumerable. In Music, however, not all these tone-gradations are made use of. A part merely of these tones are actually and fixedly employed. These tones constitute what is called the

TONE SYSTEM.

This tone-system contains above one hundred tones. It would have occasioned much difficulty to fix 3 particular name for each of them; and this has been the cause of the classification of these tones under seven

DEGREES.

These degrees have been named C—D—E—F—G—A—B.

And all tones have one of these names, or one derived from them.

Chapter II. The Note System

For the designation of tones, we make use of a series of characters, called

NOTES.

It would be tedious for us to enter into the history of Musical Notation. We must content ourselves with communieating the facts, that after many changes and modifications, five lines have been fixed upon, on which, or between which, the tones are indicated by open or:filled circles, or ovals, according to their pitch and duration.

Where these five lines are not sufficient, additional lines, called LEGER LINES are introduced, which, not being continuous, are easily distinguished from the lines of the stave. Here

So Sa ee a 23S Sea = we have introduced the leger lines, in order to designate

20 those high or low tones, which are above the highest or the lowest tones capable of being designated within the stave. We might now read and write all notes, if we only knew what meaning to attach to any particular note. In other words, we must fix upon some point, or some note corresponding to a certain tone, by which we can be guided in the designation of the others.

For this purpose we have certain characters, called CLEFS, which indicate the tone represented by them. Of such clefs there are three in use :— The G-clef, or Treble-clef ; The C-clef, and The £-clef, or Bass-clef.

1—THE G-CLEF has this form, ts and indicates that upon the line inclosed by its lower circle, the tone g, (the lowest g of the Oboe, or the fourth g of a six-octave Piano-forte, counting from the left to the right,) shall be represented. French composers of former times, placed this clef upon the first line of the stave, thus making it imperative to consider the note upon it as the representative of the tone g. At present the G-clef is invariably placed upon the second line of the stave, and the notes preceded by it would accordingly be named thus :— vise ese wttens CDEFGAB CDEFG

By means of additional leger-lines, we might designate many additional tones upon this stave ; but since the reading of,such notes would be a very troublesome task, another character has been invented, in the shape of a wave, oralotted line :—

8 sad or See eee ee eeee eoe8 va which, with the figure 8 before it, and the % succeeding it, indicates that the passage thus marked is to be played or sung an octave higher than it is written. :

The leger lines below the stave can be avoided, if necessary, by substituting another clef. More of this, however, anon. 2.—THE C-CLEF.

Its most usual form is this = , and its use 1s a threeit is used— fold one. Indicating the tone i ; -@- Al, as Soprano-clef ; im which case it is placed upon the first line of the stave, and the names of the notes succeeding it are fixed ue es: fas Arar a ra ma AS siper Peeceiseseeee|

EF GAB CDEFGAB C Ag such it is placed upon the third line of the stave, and

B, as Alto-clef.

the notes succeeding it are called :—

C, as Tenor-clef.

As such it is placed upon the fourth line of the stave, and the notes succeeding it are called :— iS pep rooe : Eas ertetth

It 1s ee necessary to add, that additional leger-lines can be employed in the C-clef, as well as in the G or F-clef.

8.—THE F-CLEF.

It has generally this oF or some other similar form,

4. and indicates the tone f ll It is now placed exclusively upon the fourth line of the stave, and thus gives to the notes succeeding it the following names :— 7s

See =

Setar Oe, = GAB C

The attentive student will have divined, ere this, what these differtnt clefs are used for. Tigss and Treble clefs even are not sufficiently convenient for all tone-series and voices. The F-clef, for instance, would be too low for a Tenor or Alto voice, while the Treble, or G-clef, would be just as much too high. The former would require, at least, four leger-lines above the stave, and the latter just as many below the stave. How much more convenient in this respect is the Alto and the Tenor clef :—

The above passage, if aire in the Treble-clef, would ;

appear thus— 9.

These different clefs are also used in passages of extensive corapass, for which a single clef would not be sufficient.

Here, for instance, 11.

is a passage, which, by means of eee the clefs, has been made readable; while the use of a single clef would have made it almost unintelligible. .

When several voices combine in one composition, they are written upon separate, parallel staves, and each voice is preceded by its proper clef; for instance, the G-clef for the higher voices, the F-clef for the lower ones. In such case each clef is valid until replaced by another.

CHAPTER Il.

ABBREVIATIONS AND OTHER ACCIDENTAL CHARACTERS IN MUSIC.

WE have already mentioned the character which transposes a tone-series to the octave above. ‘The same character is used for the transposition of a passage into a lower octave. In such case the wave-line is placed below the notes to be transposed. For single notes the figure 8 will be sufficient.

A similar facilitation consists in employing the words all’-ottava, or all’8%*, which, if placed above the notes, indicates that the higher octave is to be added to the notes thus marked; if placed below the notes, the lower octave is intended. Thus the following passages.

might be expressed in this manner :— all’8va.

= all’8va.

Other abbreviations, like alla 3za (ter2*), alla 6% (sista), &c., will need no further explanation.

Finally, there are certain characters intended to save the notation of a passage partly.

If a passage is to be repeated two, three, or four times, it is written but once, and the words—

bis,—ter,—quater, are placed above it. In addition to the above, the passages to be repeated are often inclosed by curves, or dots :—

14. Bis. WN AV VAAN OA ati once eee =| i. Roe se ee See ae

If a more extensive passage, or perhaps a distinct part of a composition, is to be repeated, THE REPEAT, consisting of two perpendicular lines, with dots on one or both sides, is made use of :-—

If the dots are placed on both sides, the repeat refers to the part just played, as well as to the succeeding part, which latter must be terminated by another repeat with dots on one side.

If a part is to be repeated from the beginning of a composition, a repeat with dots on one side only is necessary :— 15.

i= et heeetel

26°

If a passage is to be repeated, the end of which expe. riences an alteration in its repeat, the part to be altered is enclosed by a curve, and the words 1™2 (prima volta), are placed above it. In the repetition of such part, the passage marked 1™2 is omitted, and the player has to pass on beyond the repeat, where the words 2% (seconda), should be placed to guide him. The words prima volta, and seconda volta, stand here for [st and 2d time, and thus explain the mystery.

The words Da capo, (D. C., or D.c., or d. c.,) have a similar meaning,—1. e., “‘ to repeat.”

If the repetition goes merely to a certain point, where the piece is to be ended, the point is marked by the word— Fine, (end,)

and for the sake of clearness a pause : feN

is placed above the end note; and instead of the simple D. C., the words D. C. al fine (from the commencement to the end), are placed at the point where the repetition is to take place.

If the repetition is to begin at a certain point in the middle of the piece, that point is marked thus:

and instead of d. c., the words d. s., (dal segno,) from the sign, are used.

There are in use still more characters of abbreviation and facilitation, we might say, but these not being absolutely necessary for our immediate purpose, we shall g:ve their meaning when they occur.

Chapter IV. Elevation And Depression

WHEN we compare our notes and tones, as far as we know them at present, with the key-board of a Piano-forte, we find that we do not know yet all the tones of our system, and that consequently we cannot represent them by notes. We have reference to the upper keys, or black keys of the Piano-forte. We have permitted this temporary incompleteness, in order to obtain a basis from which we can easily arrive at the wanting tones and characters.

Our tones, thus far, if succeeding each other in regular rotation, are by no means equidistant from each other. Beginning from c, for instance, we arrive at the next toned ; between the two, however, there is room for another tone. The same relation exists between d ande, f and g, g anda, a and b.

A diagram of these relations will aid us materially in achieving our object. Wehave here accidentally mentioned c as the first tone ; and on examination the series from ¢ to its octave, will be found so satisfactory to the ear, that we shall adopt it at once as the normal tone-series for our analysis, being, in addition to the above, the only one of the seven tone-series at present within our reach, which is completely satisfactory. Here, then, is a diagram in which the possible intermediate tones are marked by a mere dot, for the simple reason that, at present, we have no other means of designating them : i 6 | C—d—e f—g—a—b ¢

We repeat, again, that this succession of tones is perfectly satisfactory to the ear; and since we ascend, as it were, from one c to the other, we will call the whole diagram a ladder, or to use a technical expression derived from the Latin word for “* Ladder,”’ (scala,) we will call it

A SCALE.

Having onge adopted the term ‘“‘ scale,” it is but natural that we should call the intermediate tones DEGREES ; and the distances from tone to tone, or from degree to degree, STEPS.

When we now compare the different steps, we find that those admitting of an intermediate tone are larger, must be larger, than those which do not admit of an intermediate tone. We will distinguish these different species of steps by the terms “‘ whole steps,” or ‘* steps,”’ and ‘‘ half steps.”

We find, further, that our scale contains five steps, and two half steps, distributed in such a manner, that from the first to the second, from the second to the third, from the fourth to the fifth, from the fifth to the sixth, and from the sixth to the seventh degree, are steps; and from the third to the fourth, and from the seventh to the eighth degree, are half steps, as in the following diagram : 7 1

Oe Sas a! a Pa 16, c—d—e—f—g—a—-b-c.

We stated in a former paragraph that our taking ¢ as the basis of a scale, was.merely accidental. We will remember that a succession of tones, in order to be a scale, must be a regular succession, in which the steps and half steps are distributed according to the above diagram. And now we will attempt to form a-scale from any other tone.

We take g, which the student may again consider merely accidental; the reason, whereof, however, will soon become apparent to him. The regular succession is attended to when we take the degrees, as they follow from g to g, thus:

g—a, b, c, d, e, f, g 3 or thus, * but on striking these notes on the Piano, and comparing them with our last diagram (No. 16), we soon discover that the . steps from the sixth to the seventh, and from the seventh to the eighth degree, are different from our diagram. The e and g are correct, but the f is not what we want. Yet the f degree is necessary to make our scale complete.

And now we return to those intermediate tones, for which we could find no name. There is the very tone we need between the fand g. The f degree being absolutely indispensable, we place this new tone upon it; and in order to distinguish it from the original f, we place this mark— before it. This character is called a “ sharp,’? and conveys the idea, that the tone before the represeutative of which it is placed, has been made more acute, elevated—shar pened, as it were.

The scale of G, with this amendment, would present the following appearance :

It is now a correct scale in every particular, differing from the scale of C in but one point, that of pitch.

It is time now to give the reasons for taking the tone g to experiment upon. The student will perceive that one tone only required an alteration. G was the fifth tone of our original scale, and in taking again the fifth tone of our new scale, d, one more sharp will be all that is requisite to make the scale of D correspond with that of G. Thus the student may pursue his course, adding sharp to sharp, while we begin at a different point, probably to meet him at some point where we can explain his doubts, or remove his indecision. We have simply to add, that in the course of his labors, if he pursues the plan we indicated,—~. e., always resuming his task from the fifth tone of the Jast scale, he will soon discover tones which are not in our original scale; but in following the above directions, he cannot fail in completing his scale.

We have succeeded so well in constructing a scale upon g, the fifth tone above c, that we are warranted by it, at least, in attempting the formation of a scale upon f, the fifth tone below c.

Let us again write our degrees in regular succession, beginning with f,

Comparing the steps of this tone-succession with our diagram No. 16, we find that while in the scale of G, it was the seventh tone which required being replaced by another, it is now the fourth tone which demands a modification. We bear again in mind, that we must preserve the regular succession of the degrees, and 5 being too high, we have recourse to the intermediate tone below it, and in order to distinguish it from the original b, we place a b before it. This character is called a ‘“‘ flat,’ and conveys the idea, that the tone before the representative of which it is placed has been lowered, depressed—/flattened, as it were.

With it the scale of F would present the following appearance :

The elevated tones have the word “‘ sharp”? affixed to them, as f sharp, g sharp, &c.

The depressed tones have the name “ flat’? affixed to them, as 0 flat, a flat, &c.

Taking fifth above fifth tone to construct our scales upon, would give us the scales of C, G, D, 4, FE, B, Ft, Ci. &c.

Taking fifth below fifth, would give us the scales of C, F, Bb, E>, Ab, D>, Gb.

That some of these scales should be alike in sound, yet different in appearance, need not trouble us. Enough that we know when to use the one or the other, and enough to remember that we issued from the same point in two different directions, and that our impulse has carried us over ground previously gone over from the other point. ai. :

In order to avoid the unnecessary accumulation of characters in the notation of a piece of music, the sharps or flats incident to the scale or key in which a composition has been written, are merely placed at the beginning of the piece, or at the beginning of each stave, and are called the signature of ascale or key. This si gnature is valid until it is recalled by certain characters, (of which we shall speak directly,) or until another signature occurs. During the course of a piece of music, we have then to remember how many sharps or flats its key requires, and what tones have been thus modified. 9*

The fact of there being in existence incidental flats and sharps, leads us to suppose that there are also accidental flats and sharps. These occur in almost every piece of music, and arise when the composer leaves the key in which the piece is written, either temporarily or permanently, without changing the signature, or when a tone of a foreign scale is introduced without affecting the regular key. In such case the sharp or flat is always placed before the tone, and holds good until it is recalled—+z. e., until the modified tone is replaced by the original one, or until the end of the measure in which the accidental occurs. The character used for neutralizing a sharp or flat is calleda ‘