NINTH EDITION

COUNTERPOINT APPLIED

In the Invention, Fugue, Canon
and Other Polyphonic Forms

An Exhaustive Treatise on the Structural and Formal Details of the
Polyphonic or Contrapuntal Forms Of Music

for the use of

General and Special Students of Music

by

PERCY GOETSCHIUS, Mus. Doc.

(Royal Württemberg Professor)

author of

"The Material Used in Musical Composition." "The Theory
and Practice of Tone-Relations," "The Homophonic
Forms of Musical Composition." "Models of
the Principal Musical Forms," "Exer-
cises in Melody-Writing, etc."

This Digital Edition by Jonathan Kulp

Price, net, $3.00

NEW YORK

G. Schirmer, Inc.

Copyright, 1902

By G. SCHIRMER, INC.

Printed in the U. S. A.

dedicated to

HORATIO W. PARKER

In Cordial Recognition of His
Achievements in the Serious
Forms of Musical
Writing.

PREFACE.

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This book is a sequel to the Homophonic Forms, and the system pursued in its preparation corresponds in every detail to that of the latter.

Experience in practical teaching has confirmed the author’s belief that no further preparation for the exercise of contrapuntal writing is necessary than the course of harmony given in the Material Used in Musical Composition (or any equally exhaustive treatise), together with the course of study prescribed in the Homophonic Forms. But these courses, especially that in harmony, must be exceedingly thorough; two years of diligent application to Material is by no means too much, pos­sibly not enough, for the acquirement of the only basis upon which practical contrapuntal facility can rest, naturally and securely.

Nevertheless, the first Division of the present book is devoted to the specific details of contrapuntal discipline, partly because of their inseparable bearing upon polyphonic form, and partly as a concession, — for the benefit of students not familiar with the method of harmonic discipline peculiar to the Material.

The other Divisions owe their design to the author’s conviction that the quickest and surest means of acquiring contrapuntal skill consists in the practical application of the contrapuntal method to the composition of polyphonic forms. Hence the title of the book.

Therefore, this volume, like the preceding, "undertakes no more than the systematic enumeration and exhaustive explanation of all the formal designs and methods of structural treatment in the polyphonic domain of music composition, as revealed in classic or standard writings."

Further, "the student must regard the conscientious analysis of all the carefully collected references, as a very significant and distinctly essential part of his study." On the other hand, it will probably not be necessary for every student to do all of each Exercise. The tasks have been made extremely comprehensive, not because they are indispensable, but rather in order to meet the wants of every class of students.

The following works, to which constant and vital reference is made, should be owned by the student:

Of Bach, the Well-tempered Clavichord, Vols. I and II; the 2- and 3-voice Inventions; the English Suites; the Organ Compositions (Peters compl. ed.), Vols. II, III, IV, V, and VI.

Of Mendelssohn, Pfte. Works, op. 35 and op. 7; Organ Composi­tions, op. 37 and op. 65.

Besides these, frequent reference is made to —

Bach, The Art of Fugue, French Suites, Partitas, and other clavichord works;

Händel, Clavichord Suites;

Klengel, 48 Canons and Fugues;

And Oratorios and similar choral works of Händel, Mendelssohn, Bach, Beethoven, Brahms, etc. These and all other cited compositions may be obtained, for inspection at least, at any large music store.

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Like its predecessor, this book is designed not only for the practical composer, but also for the general music-student. The latter, while studying and analyzing with the same thoroughness as the special student, will simply omit the prescribed Exercises.

PERCY GOETSCHIUS.

BOSTON, MASS., September, 1902.

APPLIED COUNTERPOINT.

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INTRODUCTION.

The most concise definition that may be given of good and correct Polyphony is, that it consists in the HARMONIOUS ASSOCIATION of INDIVIDUALLY PERFECT and COÖRDINATE, BUT INDEPENDENT, MELODIES. Correct polyphonic writing is, therefore, subject to the following three conditions: —

Condition 1:	Perfect Melody;
Condition 2:	Harmonious Union;
Condition 3:	Independence Of Parts;

each of which will be successively treated in the chapters of Divi­sion One.

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DIVISION ONE. 
THE FUNDAMENTAL PRINCIPLES OF THE SIMPLE (TWO-VOICE) POLYPHONIC STYLE.

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CHAPTER I.
 Condition 1: “Perfect Melody.” The Conduct of the Single Part or Voice.

Conjunct Movement.

1. The first and most comprehensive rule of polyphonic melody is, to lead each single part as smoothly and evenly as possible. Conjunct movement (that is, stepwise ascending or descending progression along the line of the prevailing scale) is therefore preferable to disjunct movement (that is, by leap or skip), as a general rule. Disjunct move­ment is, however, by no means undesirable, but should be used in moderate proportion to the stepwise movement.

* An exhaustive exposition of the fundamental laws of melodic progression may be found in the author’s "Exercises in Melody-Writing." Thorough understanding of Chapters I–V of that book will facilitate (possibly supersede) the study of the above chapter.

[Fugue No. 8 in D♯ minor (here in E♭ minor) BWV 853 from WTC, Book I, m. 1]

2. Diatonic conjunct movement is preferable to chromatic.

a. Chromatic successions are least objectionable in slow movement (with tones whose time-values represent whole beats, or at least half­beats); and are generally better in ascending than in descending direction, especially when moderately rapid.

[Chromatic Fantasy and Fugue in D minor, BWV 903, mm. 1–3 (also see Example 83-10)]

[Fugue No. 12 in F minor, BWV 857 from WTC Book I, mm. 1–3]

See also Ex. 82-1; [ex.] 26-5

b. A chromatic succession should, if possible, be approached in the corresponding direction; and requires, almost certainly, to continue In the same direction. For illustration:

c. It is generally unmelodious to separate a chromatic succession by inserting an intermediate neighboring-tone, in quick movement:

Disjunct Movement.

3. Disjunct progressions are qualified as narrow leaps (major or minor 3rds), and wide leaps (all skips beyond the intervals of the 3rd).

Permissible Skips.

a. Narrow leaps are generally permissible.

Wide leaps, or leaps in general, are always permissible when both tones are common to the momentary chord, i.e., if they occur during chord-repetition. For instance:

[Fugue No. 15 in G major, BWV 884 from WTC Book II, mm. 1–4]

See also Ex. 52-2.

b. A skip of any reasonable extent (rarely beyond an octave) may be made downward to any tone whose natural tendency is upward; or upward to any tone whose tendency is to descend; — that is, the skip may be made in the direction opposite to that of the natural tendency. (These tendencies are defined in par. 6, which see.) Thus:

[Fugue No. 1 in C, BWV 846, from WTC Book I, mm. 1–2]

[Fugue No. 15 in the G, BWV 860, from WTC Book I, mm. 1–3]

These skips are, however, objectionable in the other direction (i.e., that corresponding to the natural tendency); — unless in obvious and perfect accord with par. 3a (during chord-repetition). For example:

c. Almost any leap, no matter how unusual or awkward in itself, may be justified by sequence-progression, i.e., by the reproduction of a melodic figure upon other, higher or lower, scale-steps. Thus:

[Fugue No. 3 in C♯ (here notated in C), BWV 848, from WTC Book I, mm. 1–2]

To be feasible, such a line of sequences should start from a figure that is fault­less. The rectitude of the initial figure is the justification of all reasonable sequence-­shifts (or reproductions) of it.

d. Unusual, and otherwise doubtful, skips sometimes occur at (im­mediately after) an accented tone. For example:

[Fugue No. 17 in A♭ major, BWV 886, from WTC Book II, mm. 16–17]

This particular passage represents, simply, a continuous scale-passage, with two shifts to the next higher octave-register, — a device which is very common and effective in contrapuntal melodies, and possible in either direction. The rule at d, however, applies to other cases also (Ex. 16).

Objectionable Skips, and Exceptions.

4. On the other hand, skips are distinctly faulty

a. After any tone which is obviously inharmonic or dissonant, i.e., foreign to the prevailing chord.

To this rule there are two important exceptions:

(1) It is always possible to leap a 3rd, from a neighboring-note to the opposite neighboring-note (of the same essential tone); usually, the essential tone follows and concludes the group,—as it also begins it:

That is to say. the figures and   are always correct, in any reasonable movement (fast or slow), at any point in the measure, and whether the harmony remains the same, or is changed, during the group. The figure contains a "Double appoggiatura," and results from inserting the upper and lower neighboring-tones successively between the principal tone and its recurrence.

[ed. note: his "Double appoggiatura" is sometimes called a cambiata figure or a neighbor group (Kennan, Counterpoint, 3rd. ed., pp. 39–40), or a double-neighbor (Mark DeVoto, The New Harvard Dictionary of Music, ed. by Don Randel, s.v. "Counterpoint."]

Not infrequently, especially in 3-tone groups, the recurrence of the principal tone is dispensed with. The license then consists in leaping down a 3rd from the upper neighboring-note; it is rarely applied in the opposite direction (leaping upward a 3rd from the lower neighbor). This is called the "unresolved upper neighboring-note." [ed. note a.k.a. "incomplete neighbor tone"] For example:

(2) It is possible to make an indirect or "ornamental" resolution of a Suspension, and of similar dissonant tones. Thus:

The interposed tones (marked x x), inserted between the Suspension and its resolving-tone, usually belong to the resolving-chord, as seen in the above illustrations; but brief diatonic passing-notes may be added. Thus:

[Two-Part Invention No. 3 in D major, BWV 774, mm. 54–56]

b. A skip, narrow or wide, to any inharmonic or dissonant tone (whereby the latter is deprived of its legitimate "preparation"), is, as a very general rule, objectionable. But it is by no means unpermissible, especially in the lighter (freer) styles of polyphony. See the g♯. in the preceding illustration; and the following:

c. The leap of an augmented 4th is usually, for one reason or another, very objectionable; and the progression by an augmented 2nd, diminished 3rd, major 7th, augmented 5th or 6th, or other awkward intervals, should be avoided. They are best justified (1) by chord-repetition (par. 3a):

[Fugue No. 1, BWV 846, from WTC Book I, mm. 19–20]

[13-2: Two-Part Invention No. 4 in D minor, BWV 775, mm. 1–2]

[13-3: Two-Part Invention No. 9 in F minor, BWV 780, m. 31]

or (2) by sequence-formation (par. 3c):

[Two-Part Invention No. 7 in E minor, BWV 778, m. 16]

or (3) when occasioned by such distribution of the tones as represents the alternate appearance of two adjacent parts (correct in their respective movements):

[15-1: Two-Part Invention No. 7 in E minor, BWV 778, m. 14–15]

[15-2: Two-Part Invention No. 7 in E minor, BWV 778, m. 12]

or (4), as shown in par. 3d, by occurring at (after) an accented tone,—especially when the latter is the Tonic:

[Fugue No. 18 in G♯ minor, BWV 863, from WTC Book I, mm. 1–2]

5. After a wide leap (beyond a 3rd) the part should turn, and progress in the opposite direction. See Exs. 6a, [ex.] 7, [ex.] 8, [ex.] 12, [ex.] 13. To this very important and general rule there are a few exceptions, as follows:

a. The part may continue in the same direction after a skip, if it passes on into a tone which belongs to the same chord, whether the harmony changes meanwhile, or not. Thus:

(Correct in either direction.)

The following successive skips are all very doubtful, because their aggregate effect is not harmonious:

(Doubtful, in either direction, because these are not legitimate chord-forms.)

Compare par. 3a.

b. It is almost always correct to pass on diatonically in the same direction, after a wide leap, if the direction of the part is then changed; i.e., it is usually sufficient to change the direction at the second tone after the leap. For example:

[Fugue No. 18 in G♯ minor, BWV 863, from WTC Book I, mm. 17–18]

In this example the whole structure suggests a distribution of the tones of two adjacent parts (noted in Ex. 15), equivalent to:

[Fugue No. 18 in G♯ minor, BWV 863, from WTC Book I, mm. 17–18]

Besides, the formation is sequential (par. 3c).

c. The part need not turn, after a wide leap, if it remains, even briefly, upon the same tone; — whether the latter be reiterated,

or simply held, for a pulse equivalent to repetition,

or embellished by either neighboring-tone:

[Fugue No. 21 in B♭ major, BWV 866, from WTC Book I, mm. 2–3, 5–6

Active Tones.

6. The natural or inherent tendencies of certain scale-steps (called Active steps because of their strong natural inclination to move) are as follows:

That of the 7th scale-step (Leading-tone) is to ascend diatonically; that of the 6th scale-step to descend diatonically; and that of the 4th scale-step to descend diatonically.

Besides these, there are a number of acquired tendencies, as follows (all diatonic):

That of all chord-sevenths, chord-ninths, and diminished 5ths and 7ths to descend; that of all raised (altered) scale-steps to ascend; that of all lowered scale-steps to descend; and that of Suspensions to pass into their respective resolving-tones.

Rule. — These natural and acquired tendencies should be respected, as far as is consistent with reasonable freedom of melodic movement.

For illustration of the natural tendencies (these being the most significant in the conduct of single melodic parts):

[21-1: Fugue No. 7 in E♭ major, BWV 876, from WTC Book II, mm. 1–3]

[21-2: Fugue No. 20 in A minor, BWV 865, from WTC Book I, m. 1]

See also Ex. 1; Ex. 6a, Nos. 1 and 3.

As indicated, the regular resolution of all active tones is effected diatonically (i.e., stepwise). To the above rule there may be, both as concerns direction and distance, the following

Exceptions.

a. An active tone may leap to any tone that belongs (or might belong) to the same chord; compare par. 3a. The leap may be made either upward or downward, though always best in the proper direction (that corresponding to the resolution). Thus:

[22-1: Fugue No. 16 in G minor, BWV 861, from WTC Book I, m. 1]

[22-2: Fugue No. 2 in C minor, BWV 847, from WTC Book I, m. 1–2]

[22-3: Fugue No. 5 in D major, BWV 874, from WTC Book II, m. 1–2]

[22-4: Fugue No. 15 in G major, BWV 884 from WTC Book II, mm. 2–4]

Such disjunct movements from the active tones constitute, often, examples of the indirect (or "deferred") resolution, referred to in par. 4a, (2). That is, the unexpected tone or tones are simply interposed between the active tone and its resolution. Thus:

As a rule, if only one tone of the same chord intervenes, the obligation remains, and the resolving-tone should follow; though this depends largely upon whether the interposed tone lies in the direction of the resolution or not, — if the active tone progresses in the proper direction, its obligation is at least partly canceled. For illustration:

If two tones of the same chord follow the active tone, its resolution may be evaded; or if the active tone passes to another active tone, the resolution of the latter is sufficient. Thus:

b. The natural tendency of these active scale-steps may be counteracted by approaching them stepwise in the corresponding direction (i.e., that in opposition to their tendency); in which case they may continue in the (false) direction, along the scale.

[26-2: Fugue No. 2 in C minor, BWV 871, from WTC Book II, m. 1–2]

[Fugue No. 23 in B major, BWV 868, from WTC Book I, mm. 1–2]

[Fugue No. 13 in F♯ major, BWV 858 from WTC Book I, mm. 1–2]

[Fugue No. 6 in D minor, BWV 875, from WTC Book II, m. 1–2]

N.B. — This is merely an obvious corroboration of par. 1, in its broadest application.

c. An active scale-step, when approached thus in the "opposite" direction, has the option either of passing onward (as in Ex. 26), or of turning and fulfilling its natural obligation. But, if approached in the direction corresponding to its tendency, it is very difficult indeed for the active tone to turn and progress incorrectly. The most natural exception (possibly the only defensible one) is when mere melodic embellishment, or deferred resolution, is involved, — i.e., when one of the tones is a neighboring-note, or obviously an interposed tone. For example:

[Fugue No. 1 in C major, BWV 870 from WTC Book II, mm. 1–2]

[Fugue No. 13 in F♯ major, BWV 858 from WTC Book I, mm. 1–2]

[Fugue No. 21 in B♭ major, BWV 866, from WTC Book I, mm. 1–3]

[Fugue No. 17 in A♭ major, BWV 862, from WTC Book I, mm. 1–2]

[Fugue No. 11 in F major, BWV 856, from WTC Book I, mm. 1–2]

7. Care must be taken to avoid any awkward conditions at the transition from one beat into the next. In approaching an accented fraction of the (following) beat, with a fairly rapid figure, the latter must be so calculated as to reach the desired point at precisely the right moment, — not too soon (so that awkward anticipation results), nor too late (so that an equally awkward leap is necessary). Supposing c to be the tone to be reached, in a rhythm of four tones to the (preceding) beat:

In measure 1 the run is faulty because it reaches the c too soon; in measure 2 it is calculated to reach c too late; measure 3 is correct.

As a rule, after moving stepwise toward the desired tone (at the beginning of the next beat), it is necessary to continue and enter the new beat stepwise, — not with a leap. If a leap be necessary, it should be made earlier in the figure, according to the prevailing harmonic conditions:

In the last measure, the awkward leap into b is avoided by inserting an accented passing-note; this is a very common and excellent device.

While it is usually better to continue thus, and enter the next beat diatonically in the same direction, there is no objection to turning at the transitional point:

8. The reiteration of a tone should be avoided in rapid rhythmic succession. It is, however, entirely permissible in slow movement; i.e., after a tone of full-beat value or more, — more rarely after one of half-beat value; always good after a tie.

[29-2: Fugue No. 5 in D major, BWV 874, from WTC Book II, m. 1]

[29-3 Fugue No. 12 in F minor, BWV 881 from WTC Book II, mm. 1]

[Prelude No. 7 in E♭ major, BWV 852, from WTC Book I, mm. 50–51]

a. Rapid reiterations are justified when occurring several times in succession, especially in sequences:

[30-1: Fugue No. 13 in F♯ major, BWV 858 from WTC Book I, m. 7]

[30-2: Fugue No. 21 in B♭ major, BWV 890, from WTC Book II, mm. 40–44]

[30-3: Fugue No. 6 in D minor, BWV 851, from WTC Book I, m. 9–11]

b. The most natural remedy, in case of objectionable reiterations, is to leap up or down an octave, — always an effective and permissible progression:

9. The tie is one of the most effective devices for obtaining the desirable rhythmic independence of the several parts; it serves to procure time-values of an extent — and at locations — not provided for by the ordinary characters of notation. The tie extends the duration of a tone from one beat into the next, or, with still more striking effect, from the last beat or beats of one metric group into the first beat of the following group (i.e., at, or over into, the accented pulses).

a. A long tie — from a long or heavy note, of at least a whole (or possibly half) beat value — is everywhere possible.

b. On the contrary, a short tie — as a rule, from any value less than a half-beat of the prevailing meter, in moderate tempo, — should be avoided.

Both of these rules coincide, in rhythmic principle, with par. 8.

c. As a general rule, the second tone (the one into which the tie extends) should not be of longer duration than that of the first (preceding) tone.

d. A brief tie, from a tone of less than half-beat duration (see b), is best justified when it gives rise to a Suspension:

[Prelude No. 12 in F minor, BWV 857 from WTC Book I, m. 12]

or when several such (brief) ties occur in succession, as syncopated form of an entire passage:

[Fugue No. 23 in B major, BWV 868, from WTC Book I, mm. 22–23]

[Fugue No. 4 in C♯ minor, BWV 873, from WTC Book II, m. 34–35]

e. After a tie of fairly long duration, the part may progress either quickly or deliberately; if the tie is brief, however, the part should progress with corresponding promptness, as indicated at c.

f. A tie may be followed:

1. by the same tone (reiteration, par. 8);
2. by the next higher or next lower tone (which progression provides for any "resolution" that may be necessary, — for example, in case of a Suspension);
3. by the tone a 3rd above or below, either as harmonic skip, involving no further obligation, or as opposite neighboring-note of the resolving-tone, in case such be necessary. See par. 4a (1);
4. or by any still more remote tone, belonging to the momentary chord, — again either as harmonic skip, or as interposed tone before resolution. See par. 4a (2).

The choice of these possible, and equally good, progressions depends principally (often solely) upon the location of the essential tone required or desired at the beginning of the next beat, and is governed in any case by the rules of par. 7, which see.

Given the tied note c, followed in the next beat by c:

10. Brief rests () may be inserted at the beginning (generally only at the beginning) of almost any beat, but especially any accented beat. The rest should not occur, as a rule, after any inharmonic tone (on account of the resolution); nor after any very short tone, — occupying the last unaccented fraction of the preceding beat; nor in the course of a beat, in such a manner as to impair the rhythm:

Longer rests (, , etc.) are good almost anywhere, but under precisely the same limitations:

[Fugue No. 7 in E♭ major, BWV 852, from WTC Book I, mm. 23–24]

[Fugue No. 12 in F minor, BWV 857 from WTC Book I, mm. 13–14]

See also Ex. 37, No. 2.

11. The influence of harmonic laws upon the conduct of each single part (even when isolated, — temporarily unattended by other parts), is obvious from many passages in the foregoing rules; especially par. 3a, [par.] 4, 5a, 6a, 9f. The next chapter will demonstrate in detail the manifest necessity of basing the polyphonic complex upon a harmonic fundament, and of regarding the polyphonic style simply as an advanced stage in the manipulation of the self-same original factors of Harmony, — characterized by that superior freedom and independence which advanced growth brings. But, aside from the controlling influence exerted by harmonic law upon the co-operation of two or more simultaneous parts, the same influence is present even in the conception and movements of the single, unaccompanied part; for example, the direct derivation of a melody from a harmonic source, or its dictation by a harmonic purpose, is plainly shown in such motives as the following (all from Bach):

[Fugue No. 23 in B major, BWV 892, from WTC Book II, mm. 1–4]

[37-2: Fugue No. 20 in A minor, BWV 889, from WTC Book II, mm. 1–3]

[37-3: Fugue No. 17 in A♭ major, BWV 862, from WTC Book I, mm. 1–2]

[Fugue No. 18 in G♯ minor, BWV 887, from WTC Book II, mm. 1–5]

See also Exs. 5, [ex.] 7, [ex.] 14, [ex.] 15, [ex.] 22, Ex. 30-1, etc.

Such evidences of harmonic design are most palpable in melodies in disjunct movement (i.e., with many skips); but are more vague in melodies in preponderantly conjunct movement. Hence it is that, according to the rule of par. 1, conjunct or stepwise progression is a characteristic distinction of the polyphonic style of composition, in which the parts are more emancipated from the governing power of harmonic bodies; the homophonic style, in which this power constantly prevails, being distinguished, on the contrary, by greater frequency of skips, and disjunct movement generally.

12a. The above rules apply, with no essential modifications, to the minor as well as the major mode. The only noteworthy addition is, that in the ascending scale-progression in minor the 6th step (as defined by the signature) is generally raised; and in the descending scale-progression, the 7th step is generally lowered. See par. 20.

b. Further, all of the given rules are most binding in prominent parts, namely, the uppermost and lowermost of the polyphonic complex; but are subject to a certain degree of license in the inner part or parts.

c. All reasonable violations of the rules are palliated (and even completely justified) by "thematic authority," — that is, when called forth by deference to, or confirmation of, any perfectly apparent and recognizable thematic design, involved by the Imitation of a motive or figure (par. 24), by the Sequence (par. 3c), or any other sufficiently obvious and plausible melodic purpose.

Summary.

13a. Conjunct movement is almost invariably good.

Principal exception, Ex. 27, measures 1–3.

b. Skips are good between chord-tones, and justifiable by correct harmonic conditions.

Principal exceptions, Ex. 6b, par. 4a, 4c.

c. Any essential (harmonic) tone may be preceded by its two (upper and lower) neighbors. Par. 4a, (1).

d. After a wide skip, the part turns, either immediately or at the second next tone.

Principal exception, par. 5a.

e. Any progressions are possible which represent the successive (or alternate) distribution, in one part, of tones which would constitute two (or possibly more) strictly regular adjacent parts.

Ex. 15, Ex. 19.

f. The tendency of active tones should be respected, and all "resolutions" properly effected.

Principal exceptions, par. 6a and [par.] 6b.

g. The direction of comparatively rapid figures must be governed by the essential tone (or first tone) of the. following beat. Par. 7.

h. The movements of a melodic part must corroborate some rational harmonic purpose; especially applicable to disjunct movement. Par. 11.

i. Cause for almost any irregularity is afforded by the Sequence, or any other entirely obvious and defensible thematic purpose. Par. 3c, Ex. 14. Ex. 30; Par. 12c.

EXERCISE 1.

A. Analyze, thoroughly and minutely, the progressions of the solo part at the beginning of every Fugue in the Well-tempered Clavichord of J. S. Bach, for about 5 or 6 measures (even after another part may have joined the first). Every movement, from tone to tone, and the collective relations from measure to measure, are to be tested and demonstrated with reference to the above rules.

B. Write a large number of original melodic sentences (40 or 50), of from one to three or four measures in length, illustrating each rule and exception given in Chapter I., successively. Terminate each sentence upon the first unit of the final measure; employ every variety of measure (from to ), and all the keys, major and minor alternately. Imitate the rhythm and style of the Bach models.

CHAPTER II.
 Condition 2: “Harmonious Union.” The Association of Two Parts (Voices).

14. The simultaneous conduct of two parts must, naturally, yield a harmonious result; not necessarily wholly, but preponderantly so. The consonant intervals must, therefore, dominate all Essential tones, while the equally desirable and necessary dissonant intermixtures must be limited to the Unessential tones.

The fundamental distinction between Essential and Unessential tones is partly a question of harmony, but more largely (at least in the present connection) one of rhythm, or, rhythmic prominence. Hence, the Essential tones are those which represent and obviously govern an entire metric unit of moderate duration, that is, the full beats in somewhat rapid tempo, and the half-beats in ordinary or deliberate tempo, — possibly the quarter-beats in decidedly slow tempo. The essential tones, in order thus to govern their beats or half-beats, will usually appear at the beginning, or upon an accented fraction, of the same; but not necessarily, as the harmonic quality of the tones (their relation to the momentary chord) is decisive in all doubtful cases.

The Unessential tones are those whose relation to the chord, or the beat, render them manifestly secondary to the essential tones.

Rules for Exclusively Essential Tones.

15. The consonant, or at least harmonious, intervals which are to govern the association of Essential tones, are of three grades: Primary consonances, secondary consonances, and mild dissonances.

a. The primary consonances are:

1. The 3rds, major and minor; and
2. the 6ths, major and minor.

The quality (major or minor) depends upon the momentary key; and the choice between 3rd and 6th is dictated by the harmonic demands or preference. They are not affected by the enlargement (through an octave of double-octave separation) to 10th, 13th, etc.

These intervals are invariably permissible, at any point, during notes of any reasonable time-value, in practically any order and connection.

An unbroken succession of 3rds (or of 6ths), while inevitably harmonious, and therefore desirable in moderation, nevertheless militates against the necessary independence of the two parts, and should, for that reason, not be protracted beyond 3 or 4 (5) at a time, as a rule.

For illustration (adapted from Bach, with omission of the unessential tones contained in the original):

[38-1: Fugue No. 15 in G major, BWV 860, from WTC Book I, mm. 5—6]

[38-2: Fugue No. 6 in D minor, BWV 875, from WTC Book II, m. 4–5]

[Gottes Sohn ist kommen (fughetta), BWV 703, mm. 4–7]

The complete form of these illustrations is given in Ex. 44, Nos. 1, 44-2, 44-3.

b. The secondary consonances are:

1. The perfect 8ve, or unison; and those
2. perfect 5ths which represent strong triads (those of the Tonic and Dominant).

The octave is useful, and quite common; it may represent the duplication of any scale-step excepting the Leading-tone (step 7), but is best as Tonic, Dominant, or Subdominant; if it occurs at the weaker steps (2nd, 3rd or 6th) its effect must be carefully tested. The perfect 5th is rare, and always requires to be tested.

Neither of these intervals can occur in succession (8–8, or 5–5), nor should they be interchanged (8–5, or 5–8), as a rule, when the tones are Essential.

Neither of them should be approached in parallel direction, when the upper part makes a wide leap, — always excepting during chord-repetition. A wide leap in either direction, in connection with the perfect 5th, is objectionable, especially in the upper part.

For illustration:

See also Ex. 40, B; Ex. 44, Nos. 4, 44-5.

c. The mildly dissonant intervals, permitted to dominate occasional Essential tones, are:

The diminished 5th;	} In V7—
the augmented 4th;
the diminished 7th;	} In V9 Incomplete (Dim. 7th chord)—
the augmented 2nd;

and those minor 7ths and major 2nds which represent good chords of the seventh.

The diminished and augmented intervals are by no means infrequent; but the major 7ths are very rare.

None of these intervals can be used in succession, nor, as a rule, interchanged; i. e., they should occur only in connection with the primary consonances (3 or 6), or, more cautiously, with secondary ones (par. 15b).

They must not be introduced abruptly; the wide leap, in either part, toward any of them should be avoided, — excepting during chord-repetition. If a chord-7th or 9th is involved, it must be properly resolved.

For illustration:

[Sinfonia No. 13 in A minor, BWV 799, mm. 1–4]

See also Ex. 44, No. 2, and [ex. 44] Nos. 6–9.

d. Additional general rules:

It is mainly important that each part, alone by itself, should constitute a perfect, well-designed melody; therefore the rules of melodic conduct, given in Chap. I., must be strictly regarded.

And the use of the Sequence, or any other factor which imparts design and purpose to the melody, is of great importance. See par. 17c; and par. 21b.

Further, a good harmonic result must also be achieved, and for that reason the fundamental principles of chord-succession (detailed in par. 18, to which reference should be made) must be respected. Wide leaps, particularly, are to be tested chiefly with reference to these principles.

It is very difficult to justify a wide leap in both parts at the same time, excepting during chord-repetitions.

The two parts should be led, generally, in opposite directions, though by no means necessarily. One part may, at almost any time, remain upon the same tone (reiteration, par. 8) while the other part progresses. See par. 17f.

EXERCISE 2.

Unessential Tones.

16. The unessential tones may constitute any interval, harmonious or dissonant. But every exceptional interval (not enumerated in the preceding paragraph) must appear as obvious modification of an unobjectionable one, — as transient (passing) note, neighboring-note, or suspension; and must be employed in such a manner as to confirm the distinction between unessential and essential tones. That is, the objectionable interval must be followed immediately, or very soon, by one or another of the perfectly good intervals; thus, 4–3, or 4–6, or 4–5–6; possibly 4–2–6, or 4–2–3; but not 4–2–5–7, or any similar succession. For example:

Concisely stated: some good interval (par. 15) must "govern" the ordinary beat, or half-beat, of moderate duration (par. 14, last clauses). If, for any reason, an exceptional interval governs the beat, the effect will be poor. No reasonable interval-association is impossible, but all exceptional intervals must be palpably unessential, and less prominent than the good ones. The operation of this principle may be tested in the examples which follow, — or in any models of good counterpoint in standard literature.

Further, of the two tones which form an objectionable interval, that one which is obviously non-harmonic (foreign to the chord) should generally enter without leap, though this is not strictly necessary (Exs. 12, [ex.] 32); but it must progress conjunctly (stepwise); excepting the two leaps of a 3rd shown in Ex. 9a ("double-appoggiatura") and Ex. 9b (unresolved upper neighboring-note); and the "ornamental resolutions" of the suspension, Exs. 10, [ex.] 11.

[ed. note: The figure he marks as “wrong” here in Ex. 42-2 is typically called an “escape tone” or an “incomplete neighbor” tone, and is not considered incorrect now.]

But an unessential tone that might be regarded as harmonic, as a part of the momentary chord, may leap along that chord-line without objection; or may make any reasonable leap even during a change of chord.

Review par. 3a, and par. 4a and [par.] 4b.

For general illustration (unessential tones in parenthesis):

[44-1: Fugue No. 15 in G major, BWV 860, from WTC Book I, mm. 5–6]

[44-2: Fugue No. 6 in D minor, BWV 875, from WTC Book II, m. 4–5]

[44-3: Gottes Sohn ist kommen (fughetta), BWV 703, mm. 4–7]

[Sinfonia No. 1 in C major, BWV 787, m. 1]

[Sinfonia No. 10 in G major, BWV 796, m. 1–3]

[Fugue No. 6 in D minor, BWV 875, from WTC Book II, m. 3–5]

[Fugue No. 4 in C♯ minor, BWV 849, from WTC Book I, m. 4–7]

[44-8: Fugue No. 5 in D major, BWV 850, from WTC Book I, m. 3–4]

[44-9: Fugue No. 13 in F♯ major, BWV 882 from WTC Book II, mm. 4–5]

[44-11: Fugue No. 8 in D♯ minor (here in E♭ minor) BWV 853 from WTC, Book I, mm. 3–7]

17a. The interval most to be shunned, between two essential (or even semi-essential) tones, is the perfect 4th. It is tolerated, as a rule, only between strictly unessential, and brief, tones.

[Fugue No. 6 in D minor, BWV 851, from WTC Book I, mm. 3–4]

[Fugue No. 8 in D♯ minor, BWV 877 from WTC, Book II, mm. 3–4]

b. Each part must progress in a strictly correct melodious manner (see par. 15d). In perfectly good 2-part polyphony it must be entirely feasible to dissociate the parts and obtain a perfectly good and intelligible melodic result in each alone. So important is this principle, that it sometimes overpowers the otherwise rigorous rules of part-association (detailed in par. 15, 16, etc.). That is to say, if each one of two associated parts pursues a definite and obviously justifiable melodic purpose, they may be conducted with a certain degree of indifference to their contrapuntal details. In the conscious fulfillment of a broader melodic aim, the mind of the hearer may waive the demands of euphony to a certain (limited) extent. (Compare par. 13i.) For example:

[Sinfonia No. 6 in E major, BWV 792, mm. 35–36]

The lower of these two parts has the original Motive (par. 38a); the upper one has, simultaneously, the same Motive in "contrary motion" (par. 29a); — each, therefore, moves according to manifest "thematic authority."

c. For this very reason, it is eminently desirable that each part (but especially the more rapid part, in protracted uniform rhythm) should exhibit well-defined and regular formation, i.e., should be compounded of more or less lengthy and regularly recurring symmetrical figures, that impart recognizable design to the tone-succession, and prevent it from being a shapeless, rambling, unintelligible, and apparently aimless melodic line.

This emphasizes the importance of the Sequence, without which truly good and intelligible polyphony can scarcely be imagined. But it refers also to all other means by which the evidence of clear form and broader melodic design may be established, and which are quite as necessary as the sequence, — especially at those places where the sequence itself threatens to become tiresome from overuse. The beginner should never employ, at a time, more than three (four?) sequences of a figure (unless the figure be a very brief one). For example:

[Two-Part Invention No. 5 in E♭ major, BWV 776, mm. 3–5]

The succession of figures in the lower part forms a thoroughly intelligible and coherent melodic line; but the groups differ from exact Sequence just sufficiently to avoid monotony. See also Exs. 88, [ex.] 92.

d. As stated in par. 15b and [par.] 15c, it is a part of the limitation of the secondary intervals, that they can only appear singly, — not in succession. Thus, perfect octaves cannot appear in immediate succession under any circumstances; and even when separated by one tone, they are quite as objectionable as immediate octaves, if the intermediate tone is distinctly unessential:

But an "oblique" succession of perfect octaves is generally permissible, if one of the tones of the octave itself is obviously unessential; or better, if it is evident that the two parts maintain their respective melodic independence:

[49-1: Fugue No. 22 in B♭ minor, BWV 867, from WTC Book I, mm. 4–5]

[49-2: Pastorale in F major, BWV 590, IV (mm. 28–29)]

[49-3: Fugue No. 24 in B minor, BWV 869, from WTC Book I, m. 6]

A succession of perfect 5ths is not permitted between essential tones, unless one semi-essential tone, or at least two unessential tones, intervene. When each 5th embraces an unessential tone, or when one of the tones of the second 5th alone is plainly unessential, the succession is not objectionable. Thus:

[50a-3: Two-Part Invention No. 1 in C major, BWV 772, m. 3]

A wide leap to or from a tone that is obviously the Fifth of the momentary chord, must be made with caution. It is generally bad when the chord-fifth forms the interval of a perfect 5th with the lower part (and is taken by wide leap, — especially parallel with the other part). But is harmless:

1. During chord-repetition; and
2. When the chord is so inverted that the interval of a perfect 5th disappears:

[Two-Part Invention No. 8 in F major, BWV 779, mm. 1–2]

e. The direct succession of any other secondary intervals (i.e., parallel 7ths, 2nds, 4ths, etc.) is permissible only when at least one of the tones involved is distinctly unessential, and very brief. Thus:

* Par. 4a, (1).

f. Partly because of the risk of such disagreeable successions as those involved by parallel movement of the two parts; and partly because such parallel conduct deprives both parts of a certain degree of their respective melodic individuality; it appears desirable to lead the parts in contrary directions, as a very general, though by no means binding, rule. Illustrations of wholly or largely opposite motion (at the points where both parts move) are found in Ex. 42-1; Ex. 44-2; 44-4; 44-6; Ex. 46; — of almost totally parallel motion, in Ex. 44-3; — of largely parallel motion, in Ex. 38-2; 44-7.

For illustrations of unusually protracted parallel motion, see Bach, 2-voice Invention, No. 8, meas. 5, 6; 2-voice Invention, No. 14, meas. 14–16. See, also, 2-voice Invention, No. 9, meas. 1, 2, 4 (contrary), meas. 3 (parallel).

Harmonic Influence.

18. Strict observance of the above detailed rules must lead to a thoroughly acceptable musical result; but inasmuch as these details themselves are very largely dictated by the principles of harmony and correct chord-progression (without which no style of music can be faultlessly constructed), it follows that constant regard of fundamental harmonic laws must facilitate the application of the detailed contrapuntal rules. As already stated (par. 11), the influence of the original harmonic principles is chiefly exhibited wherever disjunct movement is employed; but it is never absent, and is the remote power which directs even conjunct movements. The laws of harmonic (chord) succession may be summarized as follows:

I. Diatonic (within one key).

a. Tonic chords (I or VI) can progress into any other chord of the same key, or of a different key (usually related by adjacent signature).

b. Dominant chords (V–V7–V9–₀V7–₀V9, the ₀ indicating incomplete forms *) pass, legitimately, into Tonic chords. Other progressions are, however, possible, through the agency of Inversion (i.e., into inverted forms of the otherwise inaccessible chords).

c. Second-dominant, or sub-dominant chords (the II–IV–II7 –IV7 **) pass, naturally, into Dominant chords. But their progression into Tonic chords is entirely permissible; best, however, into inverted forms of the latter.

* Triad and 7th-chord on the Leading-tone. See the Author’s "Mat. of Mus. Comp.," par. 187 par. 198.

** Idem, par. 206, 407.

f. Any chord may be repeated within the same rhythmic group, but, as a rule, not into a unit which is more accented than that upon which the chord began. This rule, however, is also moderated somewhat by inversion, i.e., change of bass tone at the accent.

II. Chromatic.

g. If the chromatic inflection is employed, any reasonable chord-succession is feasible, subject to par. 2a, and [par.] 2b.

The most vital of these rules are a, b, and c, — particularly b. For illustration:

[Two-Part Invention no. 1 in C major, BWV 772, mm. 2–4]

[Two-Part Invention no. 4 in D minor, BWV 775, mm. 3–7]

[Fugue No. 18 in G♯ minor, BWV 887, from WTC Book II, mm. 5–7]

[Fugue No. 12 in F minor, BWV 881, from WTC Book II, mm. 5–8]

[52-5: Fugue No. 17 in A♭ major, BWV 862, from WTC Book I, mm. 2–4]

[52-6: Two-Part Invention no. 9 in F minor, BWV 780, mm. 3–4]

h. In the conduct of the lowermost part, the treatment of the chord 5th (as obvious 6–4 chord) should be guarded. The established rules apply here also:

1. Avoid leaping either to or from a bass tone that is obviously the 5th of the momentary chord, always excepting during chord-repetition. (Comp. Ex. 50, B.)
2. Avoid a succession of 6–4 chords. These are always betrayed by parallel fourths between the upper and lowermost parts, when the 4ths are both essential. (Comp. par. 17e.)
3. Further, it is unwise to place any 6–4 chord in a very conspicuous position; hence, it should not appear as very first, or as last, chord of a sentence.

See also par. 62, where these rules are more exhaustively illustrated.

EXERCISE 3.

EXERCISE 4.

* The tie must be omitted here, for an obvious reason.

(4) It is generally very undesirable to reverse the rule of clauses 1 and 2 above; namely, to tie a poor interval over into a good one:

Modulation.

19. The rules of harmonic progression, given above, also govern the movements of the parts in modulation, i.e., in passing from one key into another.

a. It is always safe, generally necessary, to close each key upon some form of its Tonic harmony (I or VI); to pass from this into some Dominant or Second-dominant chord of the desired key, and from this into its Tonic harmony. Comp. par. 18a, and [par.] 18b and [par. 18]c. This modulatory formula is the most common and reliable, whether effected exclusively by diatonic successions, or involving a chromatic inflection (see par. 19). It is least binding for modulation into the Relative key (i.e., the key with the same signature); and, of course, it is subject to numerous modifications, especially upon the grounds of par. 17b, — unconstrained melodious conduct of the individual parts. For example:

[Two-Part Invention no. 1 in C major, BWV 772, mm. 3–4]

[Two-Part Invention no. 4 in D minor, BWV 775, 7–10]

*1) From a Tonic chord of the first key into a Dominant chord of the desired (next-related) one.

*2) From a Tonic chord of old key, into a Second-dominant, and then Dominant chord of new key.

[Two-Part Invention no. 7 in E minor, BWV 778, 9–11]

[Fugue No. 16 in G minor, BWV 861, from WTC Book I, mm. 21–22]

*3) From the VI (subordinate Tonic chord), into Second-dominant and Dominant chord.

*4) Chromatic inflection in Bass.

*5) The f♯ is a raised fourth scale-step only,— not the index of a Modulation; it is evident that no other key than c-minor is present.

b. The principal exception to this fundamental rule of modulation is occasioned by the chromatic inflection; this melodic device, as stated in par. 18g, if properly applied (par. 2a, [par. 2]b), renders every rational harmonious succession possible and acceptable.

For illustration:

[Two-Part Invention no. 11 in G minor, BWV 782, mm. 1–3]

[Fugue No. 12 in F minor, BWV 857, from WTC Book I, mm.5–7]

[Prelude No. 19 in A major, BWV 864, from WTC Book I, 1–2]

c. Another somewhat exceptional, though highly effective, modulatory device consists in introducing an unexpected accidental in the course of a part-progression, whereby the essential tone involved receives an unpremeditated chromatic inflection (not affecting the letter); or, in other words, a foreign tone is substituted for the expected one, so as to divert the melody and lead abruptly, but perfectly smoothly, into a new (usually closely related) key. Such a "Substitution" may take place at almost any point; but, of course, only where either tone (with or without the accidental) constitutes an equally correct and natural melodic progression from the preceding ones. It is usually safest at accented beats, or accented fractions of beats, and after a Tonic impression of the former key has been imparted — no matter how brief. The parts must be conducted, after the substitution, in a manner calculated naturally to confirm the new key. For illustration:

[Fugue No. 6 in D minor, BWV 851, from WTC Book I, 4–5]

[Two-Part Invention no. 8 in F major, BWV 779, 14–15]

[Two-Part Invention no. 2 in C minor, BWV 773, 21–22]

How peculiarly prolific and potent this seductive little device may prove to be when skilfully employed, and how perfectly natural and justifiable its operations may be when prudently conducted, is shown by the following test, in which, it is true, the best possible conditions are provided by the sequential formations (comp. par. 13i):

Original form without Modulation:

Modified by Substitutions (accidentals):

or, if the most extreme treatment be justified or demanded:

*1) The accidentals suggested in the brackets above are doubtless too "extreme"; though they might, perhaps, be justly adopted in slower movement.

*2) The comparison of these two widely different terminations of one and the same series of letters, with the same starting-point, proves that any modulatory design may be speedily realized by judicious application of this principle of "substitution." Still, as with all other somewhat irregular factors of musical texture, its best results are emphasized with peculiar effectiveness by moderation. A very striking, almost startling, example of substitution occurs in Bach, Well-tempered Clavichord, Vol. I, Fugue 20 (a minor), measure 14, beat 3, g♯ in tenor, which abruptly follows g♮ in the soprano. This change is due to the modulatory design as a whole.

d. Finally, any reasonable irregularity with regard to the method of modulation, or the choice of key, is justified at a Cadence, or at any obvious point of separation between members of the structural design (i.e., between Sections, Phrases, Motives or Figures; the latter, especially, when sequential in arrangement; compare par. 13i). For illustration:

[Two-Part Invention no. 4 in D minor, BWV 775, 37–39]

[Two-Part Invention no. 7 in E minor, BWV 778, 13–14]

[Two-Part Invention no. 6 in E major, BWV 777, 27–29]

[Two-Part Invention no. 15 in B minor, BWV 786, 2–3]

[Fugue No. 24 in B minor, BWV 869, from WTC Book I, mm. 4–5]

[Fugue No. 2 in C minor, BWV 847, from WTC Book I, mm. 18–19]

20. The notation of the minor scale depends chiefly upon the harmony, and is subject to the following rules:

a. The harmonic form (lowered 6th step and legitimate leading-tone) is rarely used, though possible during the Dominant harmony. — See Ex. 52, Note *9). —

b. The melodic forms, with raised 6th scale-step in ascending and lowered 7th step in descending, are used during Tonic harmonies. Thus:

[Sinfonia No. 2 in C minor, BWV 788, 25–26]

(An illustration in three-part counterpoint is given, because of the superior distinctness of the harmony.)

c. The "ascending" form (with raised 6th step) is used in preference to the harmonic form, in descending also, when the harmony is Dominant; this is because of the proper leading-tone (7th scale-step), which is characteristic of the Dominant harmony, and not to be altered. Thus:

[Sinfonia No. 2 in C minor, BWV 788, mm. 26, 27, 19–20]

d. Inversely, the "descending" form (with lowered 7th scale-step) may be used in ascending also, when the harmony is Sub- (or Second-) Dominant; or when it is Tonic, immediately followed by Subdominant. This, however, is far rarer than the foregoing.

For illustration:

[Prelude No. 7 in E♭ major, BWV 852, from WTC Book I, 52–53]

*1) In both of these cases the notation is influenced by the coming Subdominant harmony. See par. 20e.

e. These exceptional regulations will be seen to corroborate the general rule that the notation of all passing-notes usually conforms to the scale represented by the chord upon the momentary beat, — or by the chord upon the next-following beat (if near enough to be affected by the latter rather than by its own beat).

Illustrations are very numerous, in classic writings, of this rational principle of defining the notation of all passing-notes which fall within the limits of a certain chord, as if that chord were, for the time being, a "Tonic" chord. Apparently, it is most commonly the coming chord that exercises this dominating power. Exceptions are found, where the influence of the momentary chord is weighty enough to overpower that of the coming one; and, further, at cadences and other points of separation (alluded to in par. 19d), where abrupt effects are desired.

General Illustrations:

[Mozart: Piano Sonata in F major, K. 547a, I, mm. 187–189]

[Two-Part Invention no. 4 in D minor, BWV 775, mm. 41–43]

f. The same rule applies also to the upper one of the two neighboring-notes which attend each chord-interval. The notation of the lower neighbor may either correspond, likewise, to the momentary scale, or it may be a half-step (minor second) below its principal tone; the former notation is generally chosen in stately, more serious polyphony; the latter in lighter, more lively, music. For example:

[Fugue No. 5 in D major, BWV 850, from WTC Book I, m. 24]

[62-2: Fugue No. 5 in D major, BWV 850, from WTC Book I, mm. 17–18]

[62-3: Prelude No. 2 in C minor, BWV 871, from WTC Book II, mm. 13–14]

Summary.

21a. In two-part Polyphony, the intervals of the 3rd and 6th prevail, and govern the majority of simultaneous essential tones.

The perfect 8th and 5th, — diminished 5th and 7th, — augmented 4th and 2nd, — govern occasional essential tones, when they represent rational harmonies.

All positively objectionable intervals must be the obvious modification of some permissible interval (defined by the harmony).

b. Each part must be so conducted as to constitute, by itself, a perfect, interesting, and well-formulated melody, independent of its fellow-part. In order to verify this, the student must play or sing his added part alone, after each melodic task is completed.

Further, the parts are conducted, generally, in opposite directions.

c. The concerted operations of the two parts must be in manifest keeping with the laws of harmonic (chord-) progression, and modulation.

Principal exception: par. 18g.

d. Smooth and effective modulatory inflections (transient or definite) may be made by the substitution of an inflected tone (by an unexpected accidental) for the expected scale-tone, at the appropriate time and place.

e. The notation of passing-notes, within a certain narrow harmonic range, is defined upon the assumption that the chord which governs that range is temporarily the representative of the corresponding key (usually as Tonic chord), irrespective of its actual name in the prevailing tonality.

f. Sequential (or generally symmetrical) formations justify any not unreasonable dissonance, irregularity of melody, harmonic succession, or modulation.

EXERCISE 5.

CHAPTER III.
 Condition 3: “Individuality of Parts.”

The Rhythmic Relation of One Part to Another.

22. The fundamental rule is, diversity and contrast between the rhythms of the separate parts. But the collective effect of the rhythm of two associated contrapuntal parts is generally that of uniform movement.

a. A certain grade of tone-values is adopted as the uniform basis of motion (most commonly the 8th- or 16th-note, sometimes as triplet), and this fundamental rate is sustained with predominating regularity. It is rarely pursued in either part alone, or in both parts at once, for many successive beats; but alternates more or less regularly between the parts,—the part not conducting the fundamental rhythm relaxing, meanwhile, to tone-values of any reasonable length.

Distinction in rhythmic formation must be regarded as the most powerful means of realizing the necessary independence and individuality of the several parts of a polyphonic complex. Hence, the fundamental law of Contrasting Rhythm, and Alternation. Similar rhythm in both parts at once (as in Ex. 46), or persistent uniform rhythm in either part (as in the examples made in Exercise 3, etc.), militates against this vital principle of rhythmic individuality, and must be used sparingly, as an exception to the rule. For example (correct rhythm):

[Two-Part Invention no. 1 in C major, BWV 772, mm. 15–16]

See, further, Ex. 44-2 (16th-triplets at first in lower, and then in upper part). Ex. 52-1, — the rhythm of 16th-notes in alternating parts during two measures; then maintained for a time in upper part alone. — Ex. 52-2, similar. — Ex. 55-3.

In Ex. 46 the fundamental rhythm is maintained in both parts at once; in Ex. 53-2, it is uniform in each part for some time; both cases are somewhat exceptional, as already stated. In Ex. 54-1, the upper part is uniform, but the lower one diversified.

b. Modifications of the fundamental rate of motion, for the sake of variety, in either or both of the parts, conform usually to the laws of regular rhythm; i.e., comparatively heavy (long) tones should occupy the heavier beats, and lighter (short) tones the light beats. In other words, relaxation to longer tone-values should generally occur at accented pulses, and acceleration to shorter tone-values at unaccented pulses.

See Ex. 44, No. 1 (lower part, 16th-notes on beats 2–3, 5–6; the 8th-notes on accented beats 1 and 4). Ex. 44, No. 1, the change of rhythm from 16ths to 8ths takes place at the accented unit (lower part). Ex. 45, No. 1, heaviest note at beginning of measure. Ex. 45-2, fundamental rhythm of 8th-notes, accelerated to 16ths on unaccented fractions of 2nd and 4th beats. Ex. 57-3, fundamental rhythms of 16th-notes, accelerated to 32nds on unaccented fractions.

c. Still, as long as either one of the two parts is conducted in uniform rhythm, it appears easy to justify irregularities of rhythm in the other part.

See Ex. 44, No. 6; the upper part is practically uniform (8ths), while the lower, near the end, is distinctly irregular. Ex. 47, lower part uniform 16ths, upper part irregular. Ex. 52-3, lower part uniform, upper part irregular. Ex. 52-5 similar. Ex. 54-1, and 3. Ex. 57-5, end of measure 1. Ex. 40, B.

d. The importance of the tie must here again be emphasized. By no other means can an equally effective and legitimate result be obtained, as tending toward the mutual independence of the parts. All forms of syncopation are simply the consequence of ties (actual, or—according to their location in the measure — implied), and therefore serve the same important end. The treatment of the tie is defined in par. 9, which review.

An especially felicitous illustration of the tie is given in Ex. 44, No. 11. See also Ex. 45-2. Ex. 50-1 (syncopation). In each of these cases the general rhythmic effect is regular, and preponderantly uniform, because of the correct alternation of the parts, as shown in par. 22a. Ex. 64-3 (syncopation).

The absence of ties will be observed most frequently in two-part counterpoint of a somewhat lively character and movement, where but little opportunity is afforded for the check which ties naturally occasion (comp. par. 9b). See Ex. 47; Ex. 52-1, 52-2, 52-4.

Of barely less importance is the occasional rest, which, in the proper place, and in judicious proportion, is quite as valuable as any tone, often far more so. See par. 10. Its use is exemplified in Ex. 63; Ex. 64, No. 2; Ex. 91.

e. Distinctly irregular rhythmic formations are justified by sequences, or any other form of symmetrical successive recurrence; comp. par. 21f. For example:

[Prelude No. 20 in A minor, BWV 865, from WTC Book I, mm. 1–2]

[Prelude No. 10 in E minor, BWV 879, from WTC Book II, mm. 3–4]

[Two-Part Invention no. 6 in E major, BWV 777, mm. 1–3]

EXERCISE 6.

CHAPTER IV.
 The Development of Thematic Resources. The Various Modes of Imitation.

23. The necessary co-ordination of two associated contrapuntal melodies is due largely, it is true, to contrasting rhythmic formation, whereby mutual independence of melodic effect is achieved. See par. 22a, second clause.

But, besides this independence or individuality, another condition, that of thematic (or melodic) equality, is vitally essential to a proper co-ordination of the parts; and this condition of thematic equality is obtained by the device known as Imitation, — a device peculiarly characteristic of true polyphonic style.

24. Imitation is the highest of the three progressive species of melodic recurrence.

The first grade, (1) simple "Repetition," is the recurrence of a melodic figure in the same voice, and upon the same scale-steps. This has its natural types in the echo, bird-calls, and other preponderantly physical manifestations.

The second grade, (2) the "Sequence," is the recurrence of a melodic figure in the same voice, but upon other scale-steps. This, unless purely accidental, implies the exercise of a certain degree of mental power, and therefore enters actively and significantly into the processes of artistic music.

The third grade, (3) "Imitation" proper, is the recurrence of a melodic figure in some other voice, either literally or with modifications. This involves the unanimous co-operation of different individuals, and therefore calls forth still more comprehensive faculties, enters more deeply into the artistic methods of composition, and becomes the most vital factor of Polyphony. For illustration:

[65a: Prelude No. 1 in C major, BWV 846, from WTC Book I, m. 1]

[65b: Fugue No. 15 in G major, BWV 860, from WTC Book I, m. 1]

[65c: Fugue No. 15 in G major, BWV 860, from WTC Book I, mm. 51–52]

25. The Imitation of a given melodic figure or motive may occur either above or below the latter; and at any time, — though, as a rule, the temporal relation is regular, i.e., the Imitation appears at the same part of the (next) metric group, so that the arrangement of accented or unaccented units is not disturbed (see Exs. 66, [ex.] 67, etc.).

Further, the Imitation may be effected in a great variety of ways, affecting both the temporal and interval relations. These various modes of Imitation, which constitute an important part of so-called thematic resources, are explained in detail below.

The principal general distinction is that made between Strict (or Rigid) Imitation, and Free Imitation.

Strict Imitation.

26. An Imitation is strict when it adheres exactly to the successive interval-progressions of the initial figure (or motive). This is certain to be the case when it is made upon the same steps of the same scale, i.e., with the selfsame tones, either in the same register (in which case it is called an Imitation in Unison) or, as is far more common, in the next higher or next lower register (called an Imitation in the Octave); possibly in a more distant register, for which, however, no special designation is necessary.

a. The 8ve-Imitation, because of its perfect agreement with, and confirmation of, the motive (par. 38a), is the most natural, simple and frequent, especially for the beginning of a polyphonic section. For illustration:

[66-1: Two-Part Invention no. 13 in A minor, BWV 784, mm. 6–7]

[66-2: Two-Part Invention no. 8 in F major, BWV 779, mm. 1–2]

[66-3: Two-Part Invention no. 4 in D minor, BWV 775, mm. 3–6]

[66-4: Fugue No. 13 in F♯ major, BWV 858, from WTC Book I, mm. 13–14]

b. It is also possible to imitate a motive upon other, higher or lower, steps of the scale, without altering any of the given intervals (i.e., strictly):

[67-1: Sinfonia No. 6 in E major, BWV 792, mm. 1–2]

[67-2: Sinfonia No. 4 in D minor, BWV 790, mm. 1–2]

c. But, as seen already in the second of the above illustrations, the Strict Imitation in any other interval than the octave, is quite likely to call for inflections of the original scale, equivalent to more or less pronounced modulations. Thus:

[Two-Part Invention no. 10 in G major, BWV 781, mm. 16–17]

[Two-Part Invention no. 1 in C major, BWV 772, m. 18]

Free Imitation.

27. The precision of interval-succession observed in all the above examples of Strict Imitation, is, however, too whimsical and irksome to be insisted upon; and, therefore, such desirable licenses, or intentional modifications, as come under head of Free Imitation, are not only-sanctioned but required, as conducing to greater freedom of manipulation, and to more complete development of the possibilities latent in the adopted thematic material (Motive).

These licenses may affect either the melodic or rhythmic form of the motive to be imitated; they may be either essential or unessential in nature (according to the extent and quality of the changes); or they may even assume complex forms by associating different varieties of modification. The extent to which the licenses of Imitation may be carried, is subject to but one limitation, namely, the ready recognizability of the original motive; that is, all the essential, or striking, characteristics of the motive should be preserved. Upon this unquestionable recognizability of the leading figure (motive), the argument of par. 23 depends.

Unessential Melodic Changes.

28. In Free Imitation with Unessential melodic changes, the modifications may affect

a. The quality of one or more of the original interval-successions.

That is, a perfect interval may be altered to its augmented or diminished form; or a major one to its minor form, or vice versa; etc.

These qualitative changes are illustrated in the following:

[Sinfonia No. 6 in E major, BWV 792, mm. 19–20]

[Sinfonia No. 14 in B♭ major, BWV 800, m. 1, 7]

[Variation 9, mm. 1–2, "Canone alla Terza a 1 Clav.," from the Goldberg Variations, BWV 988]

[Variation 21, mm. 1–2, "Canone alla Settima," from the Goldberg Variations, BWV 988]

[Klengel, Canon XVII from Canons and Fugues, Book I, mm. 1–3]

b. Further, the unessential melodic changes may affect the quantity of one or more of the original interval-successions.

That is, the interval of a 3rd may be enlarged to a 4th or 5th, or contracted to a 2nd, etc.

For illustration:

[Sinfonia No. 14 in B♭ major, BWV 800, m. 1, m. 8]

[Two-Part Invention no. 10 in G major, BWV 781, mm. 1–2]

c. As important as these alterations of the melodic and harmonic form of the original motive may appear to be, in themselves, the particular object of the unessential melodic changes will be found to consist, chiefly, in facilitating the adjustment of the motive (upon its periodic recurrences) to the prevailing modulatory conditions, or to any immediate or general requirement of the total design.

When the motive is imitated in any other interval than the 8ve, — that is, when it is shifted to other steps of the scale than those which it originally occupied, — the melodic conditions are changed, of course, and possibly seriously disturbed. To counteract this, two things may be done:

(1) A modulation may be made (into any next-related key), changing the scale in such a way that the new location of the motive shall represent correct step-progressions. Or,

(2) The above quantitative melodic changes may be undertaken in the Imitation itself, so that the otherwise faulty successions are removed.

For example, the following motive, in C major:

[would, if imitated thus in the 4th,] assume an awkward and defective form, if retained in C major without change of interval-quantity; but it may be redeemed, either by changing the key:

or by altering the size of the first interval:

or by resorting to both devices; if transferred to a minor or d minor, without further change, the result would again be faulty [but would be rectified by the following]:

Essential Melodic Changes.

29. In free Imitation with Essential melodic changes, the following distinctions of species are made:

a. Imitation in contrary motion. Here, the direction of each tone-succession of the Motive is reversed in the Imitation; i.e., all ascending progressions are changed to descending ones, and vice versa. As these changes, though radical in their nature, affect each and every tone alike, the result is a legitimate uniform modification; though turned "upside down," it is the same melodic line, and invariably recognizable as such.

The term "inverted motive" is permissible; but it is judicious to restrict the word "inversion" rigidly to the local relation of two or more parts to each other, as involved in so-called double-counterpoint (see par. 55).

For illustration:

[Prelude No. 23 in B major, BWV 892, from WTC Book II, m. 1]

[Two-Part Invention no. 1 in C major, BWV 772, mm. 8–9]

The size of the interval-progressions may be in "strict" accordance with those of the Motive, but this is by no means necessary, or even desirable. The "interval of Imitation" cannot be defined as in par. 26, obviously, because the melodic lines are not parallel, but contrary; but they appear to revolve, in opposite directions, about a certain mutual axis, or corresponding tone, and the choice of this tone is significant in determining the degree of coincidence, both harmonic and melodic, between the Motive and its Imitation.

If, for instance, every Mediant (3rd Scale-step) in the Motive is answered by a Mediant in the Imitation, the several tones of the Tonic chord and also of the Incomplete Dominant 9th chord (the most important fundamental harmonies) will reappear, in reverse order. Thus:

The harmonic similarity is therefore complete.

This coincidence may also be defined as tonic note responding to dominant note for that is the natural consequence of Mediant responding to Mediant.

The same is true of the corresponding minor (c minor). And it applies to these tones either in their simple harmonic form, or embellished, — as basis of an ornate melodic motive.

If, further, each Mediant in the Motive be answered by a Tonic note, the result will be:

which constitutes very nearly the same degree of harmonic coincidence as above. Consequently, these two varieties of melodic relation,— Mediant responding to Mediant (= Tonic to Dominant) and Mediant responding to Tonic, — are the best for the Imitation in Contrary motion. These, and other conditions, are illustrated in the following:

[Fugue No. 6 in D minor, BWV 851, from WTC Book I, mm. 1–3, 27–28]

[74-2: Fugue No. 15 in G major, BWV 860, from WTC Book I, mm. 1–4, 20–24]

[74-3: Two-Part Invention no. 1 in C major, BWV 772, mm. 17–18]

[Fugue No. 14 in F♯ minor, BWV 859, from WTC Book I, mm. 1–4; 32–35]

b. Retrograde Imitation (cancrizans), in which the motive is reproduced backward. This alteration so seriously endangers the recognizability of the motive, that it may scarcely be regarded as a legitimate or permissible mode of Imitation; and, in truth, its adoption in modern Polyphony is extremely rare. See par. 27, last clause.

[Mozart: Symphony No. 41 in C major, K. 551, IV, mm. 1–4; 227–230 (vla & vc)]

An extraordinary example of Retrograde Imitation may be found in Beethoven’s Pfte. Sonata, op. 106, in B♭ major, last movement. The long and unique Subject at the beginning of the Allegro risoluto reappears in reversed order (i.e., backward) at very nearly its full length, in the first nine measures of the section with the 2♯ signature,— in the lower part; the same form follows immediately in the upper part, and then in the lowermost part. It is characteristic of Bach’s conception of pure Polyphony, that this device does not appear at all in his "Art of Fugue," a work replete with all the legitimate devices of contrapuntal texture.

Unessential Rhythmic Changes.

30. In Free Imitation with Unessential rhythmic changes, the following licences occur:

a. The value of the final tone of the motive may be either increased or reduced. This utterly harmless modification is illustrated in Ex. 67, No. 1; Ex. 68, No. 2; Ex. 69, No. 1; Ex. 70A, No. 3; and Ex. 74, No. 3, — which see.

b. The value of the first tone of the motive, also, may be increased or decreased (by beginning the Imitation correspondingly earlier or later). Neither of these modifications is purely arbitrary, but will, in the majority of cases, be dictated by the necessity of adjusting the thematic figure, at either of its extremities, to the general design, — especially as concerns the harmony and modulation. For illustration:

[Sinfonia No. 10 in G major, BWV 796, mm. 3–5, 11]

[Two-Part Invention no. 3 in D major, BWV 774, mm. 1, 9–10]

c. More rarely, the value of certain tones in the course of the motive may be modified, — generally in such a manner that what is added to one beat is subtracted from the neighboring beat, so that the rhythm of the remaining tones, and the effect as a whole, is not disturbed. These changes are largely arbitrary, and are made more for the sake of variety and heightened effect, than from necessity of adjustment. For illustration:

[Fugue No. 2 in C minor, BWV 871, from WTC Book II, m. 1, 8]

[Fugue No. 8 in D♯ minor, BWV 853, from WTC Book I, mm. 1–3, 20–22]

[Prelude No. 4 in C♯ minor, BWV 849, from WTC Book I, mm. 8–9, 26–27]

Essential Rhythmic Changes.

31. Free Imitation with Essential rhythmic changes involves the following modifications:

a. Imitation in Augmentation. Here the time-value of each tone and rest is multiplied in uniform ratio. Thus, the length of the motive is usually exactly doubled, although three-fold and even four-fold augmentation sometimes occurs. This applies naturally to motives in duple rhythm; whereas in triple time it is often necessary to resort to uneven proportions of augmentation, in order to preserve the original arrangement of accented and unaccented tones. This change, though essential, does not jeopardize the recognizability of the motive, for it has usually simply the effect of decreasing the tempo without affecting any of the melodic or rhythmic proportions of the original tones. For illustration:

[Fugue No. 2 in C minor, BWV 871, from WTC Book II, m. 1; mm. 14–16]

[78-2: Fugue No. 8 in D♯ minor (here in E♭ minor) BWV 853 from WTC, Book I, m. 1; mm. 62–67]

[78-3: Art of Fugue, Contrapunctus 7, mm. 1–2; mm. 24–29]

[78-4: Beethoven: Piano Sonata no. 31 in A♭ major op. 110, IV: mm. 26–29; mm. 160–168]

b. Imitation in Diminution. This is exactly the reverse of the above, and has the effect of increasing the tempo without changing the design of the motive. It is hardly feasible in any other than duple measure. For example:

[Fugue No. 9 in E major, BWV 878, from WTC Book II, mm. 1–2, 27]

[179-2: Art of Fugue, Contrapunctus 6, mm. 1–4, 3–5]

[179-3: Beethoven: Piano Sonata no. 31 in A♭ major op. 110, IV (Fuge): mm. 26–29; mm. 156–157, 168]

c. Imitation in Shifted rhythm; that is, the reproduction of the motive at a different part of the measure, so that the original arrangement of accented and unaccented tones is more or less completely changed.

In 4-4 measure, a shift of two beats simply produces an exchange of accents, without appreciable change of prosodic effect. This is illustrated in Ex. 66, No. 1 (the motive begins in the 3rd beat, the Imitation in the 1st); Ex. 68, Nos. 2, [no.] 3, [no.] 4, and [no.] 7; Ex. 69, No. 4; Ex. 71, Nos. 1 and [ex. 71, no.] 2.

In 4-4, or any other variety of duple measure, an entirely new arrangement is obtained by shifting the motive one beat, forward or backward; or, as is more rarely the case, by shifting it a fraction of one or more beats, so that the original full beats fall between the pulses, and the Motive assumes a syncopated form. For example:

[80-1: Sinfonia No. 14 in B♭ major, BWV 800, mm. 1, 12–13]

[80-2: Fugue No. 22 in B♭ minor, BWV 867, from WTC Book I, mm. 1–3, 68–70]

[Fugue No. 5 in D major, BWV 874, from WTC Book II, mm. 1–2, 27–29]

In 3-4, or any other variety of triple measure, the prosodic transformations are still more numerous, because the accented tones may be shifted to either of the two unaccented units, with totally different results. Besides this, syncopated Imitation is also possible, as above. For illustration:

[Brahms, Piano Quartet No.2, Op.26, III, mm. 1–4]

*1) This phrase is borrowed from the pianoforte-quartet in A (3rd movement), merely to illustrate, in a peculiarly effective manner, the two-fold transformation possible in triple measure. At *2) the motive is shifted forward, and at *3) backward, one beat.

32. Complex forms of Imitation, such as Contrary motion, and, at the same time, unessential melodic or rhythmic changes; or simultaneous Contrary motion and Augmentation, Diminution, or Shifted rhythm, and so on, — are possible and not uncommon. But it must be remembered that the more these licences are multiplied, the more likely they are to endanger, or destroy, that recognizability of the original motive designated in par. 27 as the inexorable limit, beyond which it would be inconsistent to pass. For example:

[Fugue No. 6 in D minor, BWV 875, from WTC Book II, mm. 1–2, 17–18]

[Fugue No. 9 in E major, BWV 878, from WTC Book II, mm. 1–2, 35]

[Art of Fugue, Contrapunctus 7, mm. 1–2; 2–6]

*1) Imitation in Contrary motion and Diminution; the value of the first tone abbreviated. — A few other cases of slight complication are shown in Ex. 74, No. 2: Ex. 78, No. 3; and Ex. 79, No. 2.

33. Finally, more exceptional forms of modified Imitation are occasionally encountered in the polyphony of Bach and others, consisting, (1) in the addition of intermediate embellishing tones; (2) in the contrary motion of some single interval; (3) the transposition of a portion of the motive to a higher or lower octave; and (4) the partial application of certain essential modifications (i.e., to certain figures, only, of the motive). Such miscellaneous changes are most justifiable when made for the sake of adjusting the Imitation to some legitimate and obvious thematic purpose; or to facilitate obstinate and awkward, but manifestly necessary, contrapuntal movements. (Comp. par 12c.) And, as usual, they should not infringe upon the recognizability of the original motive. For illustration:

[Sinfonia No. 11 in G minor, BWV 797, 1–3]

[Fugue No. 4 in C♯ minor, BWV 849, from WTC Book I, mm. 1–4, 59–62]

[Fugue No. 11 in F major, BWV 856, from WTC Book I, 1–3, 65–67]

[Two-Part Invention no. 9 in F minor, BWV 780, mm. 1–3, 9–11]

[Two-Part Invention no. 7 in E minor, BWV 778, m. 1, 15–16]

[Fugue No. 8 in D♯ minor, BWV 853, from WTC Book I, mm. 1–3, 77–79, 39, 24–27]

[Fugue No. 9 in E major, BWV 878, from WTC Book II, 1–2, 23–24]

[Art of Fugue, Contrapunctus 3, mm. 5–9; mm. 23–27]

[Art of Fugue, Contrapunctus 12, mm. 1–5; mm. 21–25]

[Chromatic Fantasy and Fugue in D minor, BWV 903, mm. 1–8, 76–83, 107–113]

The Contrapuntal Associate.

34. After the leading part has terminated its Motive, and the Imitation of the latter is annunciated in the other part, the leading part does not discontinue its movement, or even pause briefly, but carries its melodic line along, apparently independent of the Imitation. This projection of the motive-melody must, however, constitute a harmonious contrapuntal associate of the Imitation, and therefore its conduct must be defined according to the rules of two-part polyphony, detailed in Chapter II. It is usually called the "Counter-motive," or, briefly, the "Counterpoint."

35. To the general details of contrapuntal association given in the second chapter, the following special rules must be added:

a. The "Counterpoint" must be a perfectly natural continuation of the Motive-melody which precedes it, — as if the imitatory appearance of the other part were rather accidental than intentional, and did not concern the progressive movement of the leading part.

This rule is of the utmost moment in genuine polyphonic texture. For illustration:

b. The beginning of the Imitation must be properly adjusted (as regards harmony and modulation) to the termination of the motive. This will influence the choice of the interval of Imitation (par. 26a, [26]b, [26]c); may induce the employment of the unessential rhythmic changes noted in par. 30b and will possibly necessitate the unessential melodic changes given in par. 28a and [28]b, at the beginning of the Imitation.

For example:

c. It suffices, as a rule, to provide thus for harmonic agreement at and during the first beat or two of the Imitation. The subsequent beats may easily be so manipulated, — either by unessential modification of the Imitation itself (par. 28a, [28]b), or by consistent and careful conduct of the "Counterpoint," — as to achieve good harmonic conditions.

The Imitation once correctly launched, the succeeding movements of the contrapuntal associate are determined, as already stated, by the principles of two-part polyphony, but with more particular regard of the primary rule given at a above (par. 35).

Examine the methods of adjusting the beginning of the Imitation to the termination of the motive, in Exs. 66, [ex.] 67, [ex.] 68, [ex.] 69, [ex.] 70A, [ex.] 71; 74, No. 3; 83, No. 1.

The Stretto.

36. The Imitation is said to be in "stretto" when it overlaps a portion of the motive; i.e., when the Imitation sets in before the motive is finished.

The section of the motive thus covered by a section of the Imitation is, consequently, at the same time the contrapuntal associate of the latter; and, therefore, the practicability of the Stretto is conditional upon reasonable contrapuntal agreement between these sections. This depends

(1) upon the choice of Strict or Free Imitation (pars. 26, [par.] 27); if Strict, — if no concessions are to be made, — then but few Stretti will be found feasible, though the rules of par. 12c and par. 17b (which see) provide an excuse, at least, for some harshness of effect; if Free, then the judicious application of the unessential licences of par. 28a, [28]b, will make almost any Stretto possible. It depends, further,

(2) upon the length of the overlapping section.

The earlier the Imitation appears, the longer will the overlapping section be, and, consequently, the more protracted the risk of disagreement. Hence, fewer Stretti will be practicable after only one or two beats (i.e., from the beginning of the motive) than after a longer period, nearer the end of the motive. But, here again, slight alterations in interval-quantity will facilitate even such extreme Stretto-Imitations.

Specimens of incipient forms of the Stretto are seen in Ex. 66, No. 3, and Ex. 67, No. 1, where the Imitation begins simultaneously with the final unit of the motive; this brief interlinking of the two parts (not strictly "overlapping") involves no more than the rule of par. 35b. See also Ex. 68, Nos. 1, [68]-5, [68]-6; Ex. 69, Nos. 1, [69]-3, [69]-5.

Illustrations of the genuine Stretto: —

EXERCISE 7.

This exercise is to be limited to par. 26a, — Strict Imitation in the Octave.

The student is expected to manipulate this (No. 1) again, in his own way. Then Exercise 6B (page 58), Nos. 3, 4, 5, 2, 6, 7, 8. Then the following: —

B. A number of these motives (as specified below) to be manipulated according to par. 26b,— Strict Imitation in the 5th.

Each motive, as before, imitated both above and below. Especial attention to par. 35b ([par.] 35c) will be necessary.

EXERCISE 8.

EXERCISE 9.

EXERCISE 10.

DIVISION TWO. THE INVENTION-FORMS.

Introductory.

37. Polyphonic styles of composition are divided into three classes, distinguished chiefly by the degree of severity with which the principles of polyphony, or contrapuntal writing, are applied; namely: the Invention, the Fugue, and the Canon.

In the Canon the utmost rigor of thematic treatment prevails. In the Fugue, the contrapuntal methods are applied with less insistence, but with reference to certain specific conditions, peculiar to this class. In the Invention, the polyphonic principles (Imitation, etc.) are applied in a general way only, with much freedom of detail; and with almost, if not quite, equal regard of the broader considerations of form (structural design), and of general external effect.

The "Invention" (a term adopted from one of the musical practices of the 17–18th centuries) is, then, the simplest and least constrained of the three principal classes of Polyphonic Form.

38. The factors which enter into the construction of an Invention are: (1) The Motive; (2) The Imitations or recurrences of the Motive; (3) The Contrapuntal Associates; and (4) The Episodic passages (including the Cadences).

The Motive.

a. The Motive is a brief melodic sentence, calculated to be (and adopted as) the basis and source of the evolution, construction (or "invention"), of the polyphonic composition in view. It is the "theme" of the structural task.

To this end, it should be simple and regular in its harmonic design, and faultless in melodic formation; but, at the same time, sufficiently characteristic and suggestive to invite manipulation, and to sustain interest. For this reason, somewhat striking melodic features may be admitted, and moderate rhythmic irregularities are appropriate, if not necessary, — hence the frequency of the tie, in effective Motives.

The most important rule for the Motive is, that its first tone, or tones, should impart an unmistakable Tonic impression: —

See Exercise 6B, Nos. 2, 3, 6, 8, — beginning with the Tonic note; also Exercise 7A, Nos. 1, 4, 5, 6, 7, 9, 12, 13, 14, 15, 21, 23, 24. Further, Exercise 7A, Nos. 2, 3, 8, 10, 11, 17, 22, 26, — beginning with the Dominant note, followed immediately, or soon, by the Tonic. In Exercise 7A, Nos. 19 and [no.] 25, the Tonic note follows quite late, but the Tonic impression is clear. Exercise 7A, No. 18, is misleading, as the Tonic note is entirely absent. In Exercise 6B, Nos. 5 and [no.] 7 begin upon the Mediant, followed soon by the Tonic, — this is perfectly clear. Exercise 7A, No. 16, is again misleading, because of the long absence of the Tonic, after the initial Mediant (which imparts the impression of e minor, instead of G major). Exercise 6B, No. 4, begins with the lower neighbor of the Tonic, and is entirely clear. Exercise 7A, No. 20, is misleading, because the upper neighbor of the Mediant, though unaccented, imparts a B♭ major impression where F major is intended.

The Imitations, or Thematic Components.

b. The Imitations, or successive recurrences of the Motive, constitute the so-called thematic texture of the polyphonic fabric. Compare par. 38d, and review Ex. 69, Note *2). The details of this factor are given in Chapter IV.

The Counterpoint.

c. This term is applied (possibly a little loosely) to all the passages that are invented as contrapuntal associates of the motive, upon each of its successive Imitations or recurrences See par. 34.

The Episodic Components.

d. To all those portions of the polyphonic fabric where the motive is not present in either part, or is represented by only one of its fractional figures, the term Episodic passage is applied. The necessity for such elements in effective polyphony, as a foil to the thematic portions, is obvious; for the monotony of persistent motive-imitation must be relieved from time to time. But it is equally manifest that episodic passages should, as a rule, be neither too frequent nor too extended; and that they must be in close keeping with the character of the thematic portions.

For the latter reason, the episodes are usually derived (1) directly from the motive itself, by using some fraction of the same; or (2) indirectly, by utilizing the whole or some portion of any of the contrapuntal associates of the motive; or, possibly (3), an entirely new figure may be adopted, on condition that it be conceived strictly in the spirit of the motive, or of the general context, and that it reappear at intervals during the composition. Finally (4), it is also possible that an episodic passage, after beginning in touch with the motive, may, by gradual and consistent stages, develop into a more or less independent character, — though it can scarcely be justified in becoming quite foreign. For illustrations of the episodic components, see Exs. 89, [ex.] 90, [ex.] 91.

CHAPTER V.
 The Two-Voice Invention.

39. An Invention may be constructed, like any homophonic composition, according to the design of the so-called Part-forms, or Song-forms. But it is somewhat inconsistent with the polyphonic style to check the current of thematic development with the emphasis necessary for the Cadence of a genuine and well-defined Part;^[*] and it is, therefore, more common for the structural design of Inventions to consist in a kind of group-form, or chain-form, the several divisions of which may most appropriately be called "Sections."

a. The Section of polyphonic designs differs from the Part of homophonic forms in being, as a rule, less regular and definite in character; in terminating with a brief, and less distinct, form of cadence; and in maintaining less obvious formative relation (with regard to general melodic design) to its fellow-divisions. For these reasons, the number of Sections, also, is entirely optional.

b. Generally, each successive Section undertakes a somewhat different method of manipulation, or the development of some special resource of the Motive. But, notwithstanding the comparative independence thus effected, it is necessary to preserve a certain measure of logical connection and relation between the Sections, and therefore it is customary to revert, from time to time, to some structural feature of an earlier Section; thus the idea, at least, of the Homophonic designs^[*] prevails in the polyphonic designs as well — especially in the Invention, which, in contents and purpose, is more closely akin to the ordinary (homophonic) Song-forms than are the more advanced grades of polyphony.

The First Section.

40. The 1st Section, or "Exposition," of the Invention, will exhibit, as a rule, all of the structural factors enumerated in par. 38.

a. The Motive may be first announced by either the upper or (more rarely) the lower of the two parts; generally it appears alone, though it is sometimes accompanied by a few unimportant auxiliary tones, the better to establish chord, key and rhythm.

Compare Bach, 2-voice Inventions, Nos. 1, 3, 4, 8, with Nos. 7, 13 — the first measures of each.

b. The first Imitation, in an Invention, is almost always made in the octave; though occasionally the fifth is chosen, or some other interval which adjusts itself readily to the harmonic design, — any interval being permissible.

In Bach, 2-voice Inventions, Nos. 1, 3, 4, 7, 8, and 13, the first Imitation is in the lower 8ve; in No. 10 it is in the 5th; in Bach, English Suite No. 6, 2nd movement of the "Prélude," it is in the 4th; the same in Bach, Partita II, 3rd movement of the "Sinfonia" (3-4 time).

c. The details of the Exposition up to this point have been thoroughly exemplified in the work of Exercise 7, etc. The next step in the development of the thematic design is, usually, another immediate recurrence of the motive, in the first (i.e., leading) part, as re-imitation of the preceding announcement. The interval of this new Imitation is optional, though 8ve or 5th is the most usual. Meanwhile the other (second) part continues its movement, as contrapuntal associate of the Motive, according to par. 35. See, also, par. 41a. For example:

*1) This "Counterpoint" to the second recurrence of the Motive closely resembles the first contrapuntal associate (measures 3–4). It is so natural and tempting to adhere thus to the first Counterpoint, that the student must be reminded of the monotony it involves, and be warned against making it a rule. The recurrences of the Motive provide amply for the necessary condition of consistency and symmetry; the equally necessary condition of variety devolves largely upon the contrapuntal associates, which may assume more or less different forms at the successive recurrences of the Motive. On the other hand, to guard against excess in this respect, it is advisable to adhere to a certain counter-motive during two (or three) consecutive announcements of the Motive, and to return, from time to time, in the following Sections, to such former Counter-motives (i.e., "counterpoints").

See further: Bach, 2-voice Invention No. 1, first six beats; the second recurrence of the Motive (meas. 2) is a Re-imitation in the 5th. The same is the case in No. 7, first six beats (Ex. 91). In No. 8, measures 1–3, it is in the 3rd.

d. What follows, after this second recurrence (i.e., the third announcement) of the Motive, cannot be determined in detail, but only with reference to the general purpose of the entire first Section, which involves the following contents: —

• The announcement of the Motive;
• The Imitation and successive recurrence, as necessary thematic basis;
• The exhibition of variety (episodic and otherwise);
• A modulation into the key in which the Section is to terminate;
• The establishing of this key; and
• A palpable Cadence in the same.

e. Perhaps the most imperative condition, at the juncture reached in the above example, is that of variety. This may be obtained, (1) by substituting the principle of the Sequence for that of Imitation, — i.e., reproducing the Motive once or twice in the same part instead of the opposite part; or (2) by dropping the thematic thread, and proceeding episodically.

The first alternative, the Sequence (see par. 41c), is illustrated in the following:

The second alternative, the Episode (see par. 38d), is illustrated in the following:

f. On the other hand, these specific modes of obtaining variety are sometimes not resorted to until the alternating Imitations have been extended still farther. For illustration:

g. The modulatory design of the First Section of an Invention corresponds to that of the First Part in homophonic forms, namely: if in major, the Section generally terminates in its Dominant key; if in minor, usually in its Relative (major) key. Exceptionally, these relations may be exchanged (i.e., the Dominant key from minor, and the Relative key from major). Or some other next-related key may be chosen; especially the Relative of the Dominant, — rarely the Sub-dominant keys.

The influence of this modulatory purpose will probably be evinced as soon as the original key is sufficiently established; generally during the first or second episodic passage; or during a line of sequential announcements of the motive.

In Ex. 88, the latter is clearly illustrated; in measures 78 (of the entire Invention) the lines of d minor waver, and in measures 9–10 the transition into F major is complete. In Ex. 91, precisely the same course is pursued: measures 1–3 are in e minor, measures 4–5 in G major. See also Bach, 2-voice Invention No. 1; measures 1–3 in C major; during the following sequences of the Motive (in contrary motion) in the upper part, the digression into G major is initiated, and is confirmed in the following (5th) measure.

And the remainder of the Section consists, probably, in a comparatively brief confirmation of the new key, and a cadence in the latter. For example:

When the Section is extended to an unusual length, the corresponding breadth of design will probably induce (or necessitate) transient modulations into various next-related keys; and the prescribed modulatory aim of the whole may not assert itself until the Section approaches its cadence. In this case, further, the cadence is apt to be proportionately stronger.

See Bach, Well-tempered Clavichord, Vol. II, Prelude 10, first twenty or thirty measures; — to be analyzed solely with reference to the changes of key.

h. The Cadences of polyphonic Sections are generally, as implied in par. 39a, much less decisive than those of homophonic forms, both in harmonic and rhythmic respect. Still, they assume the aspect of the Perfect cadence (only excepting a few rare instances where the formal purpose demands the effect of a Semi-cadence), and, therefore, the distinctive traits of the former are usually preserved, — especially as concerns the lower part (the Bass).*

But the rhythmic interruption (or pause) is brief; so much so as to create the impression of an Elision;** for the thematic thread is taken up so promptly that the cadence-group of one Section is, almost always, at the same time the initial group of the next.

For illustration (from Bach):

* "Homophonic Forms," par. 3, par. 6. ** Idem, par. 60.

The material of the cadence is very likely, in view of its special object, to be episodic, and may even be entirely independent of all anterior figures. It is, however, also possible, by ingenious treatment, to interweave thematic figures with the cadence, — especially when more than two parts are used.

See Bach, W.-t. Clav., Vol. I, Fugue I, measure 19; — cadence on 3rd beat, during thematic announcements (in Stretto) in Tenor and Alto. See also Ex. 96. Note *1). Ex. 116, last measure.

Additional General Principles.

41a. Influence of harmonic bent. In determining the progressive conduct of polyphonic parts, the harmonic and modulatory inclinations must be respected, and even anticipated.

If the harmonic progression (or, in other words, the choice of the next chord) is self-defining, or perhaps even imperative, — as, for instance, at certain urgent Dominant or Second-dominant chords, which demand resolution, — then this, the Harmony, will dictate the movement of the parts; and, if necessary, the unessential licences of Imitation (par. 28) will be summoned, to fit the thematic intention to this harmonic need.

Should the harmonic progression not be self-defining, but optional,— as, for instance, after any Tonic chord, — then the thematic design will supply the impulse and determine the choice of chord and key; and either the Motive, with or without unessential modification, or the Episode, will be chosen, as appears most convenient. Review par. 11, par. 18, and the last clause in the directions to Exercise 6B.

b. The Episodes. It would be very wrong to assume that the above episodic passages (Exs. 89, [ex]. 90, [ex.] 91) proceeded from a deliberate intention, on Bach’s part, to use just these particular fragments of thematic material, in just this manner. His purpose was a far broader one; and the episodes, while responding first of all to the demand for variety, are simply incidents in the realization of that purpose.

In general, then, the episode is rather an accidental consequence than an aim; and its details, — chosen, as they may be, from a myriad of equally consistent possibilities, — are influenced by the broad harmonic conditions noted in par. 41a, and determined by such comprehensive considerations of Form as those specified in par. 40d.

It is true, however, that the beginner must work along narrower lines, until his range of experience widens toward the master’s standard. And the student will therefore, for a time, plan his episodic passages as more or less mechanical derivations from foregoing thematic premises; making generous use of the Sequence (par. 41c); not pausing long to choose, but accepting the first reasonable suggestion; and meanwhile analyzing the methods of great polyphonic writers (as found in the given citations) with the most penetrating scrutiny,—thus enriching his experience both by experiment and by observation.

As already observed, the number and variety of episodic deductions from anterior thematic figures, is practically unlimited, and the difficulty lies, not in finding a derivative, but in choosing from among the well-nigh infinite range of possibilities. So that the student who is at first apprehensive of not knowing what to do, will soon experience the still more real embarrassment of deciding what not to do; and this latter consciousness is, in fact, the most trustworthy sign of progress in thematic musical thought. For among so many possible deductions, many grades of excellence will, of course, be represented; some episodic forms will be more appropriate, ingenious, and pregnant than others.

But, though the student may for awhile not succeed in finding the best forms, or even fairly good ones, the simple determination to adopt this deductive process, in his labors with the problem of musical composition, is, in itself, meritorious and wise. For such logical processes contribute invariably, at least in some degree, to the unity and stability of the musical structure. And as the student’s experience increases and his judgment matures, he will more and more readily and unerringly select the better and best forms. At all events, this dependence is vastly preferable to relying upon chance, or upon that most delusive of resources, personal inspiration, for the answer to the vital and constantly recurring question, "What next?" Eminent and indispensable as the impulse of emotional or intellectual ardor ("inspiration") becomes to the advanced scholar and to the master of tone-texture, it is fraught with delusion and distraction to the beginner.

c. The Sequence. One of the most essential details of effective polyphony is the Sequence. It is the chief, if not the only efficient, safeguard against the most characteristic danger that besets the polyphonic style, — that of purposeless rambling, or the uncertain, discursive pursuit of a vague thematic scheme.

The Sequence imparts at least regularity and symmetry to the operations of thematic development; and, while particularly important in the more vagrant episodic components, is even freely used in the thematic passages themselves (par. 40e). Hence, the pupil may fall back upon Sequences at almost any time, and drift with them until some higher structural condition asserts itself. The number of Sequences should, however, be limited to two or three (i.e., three or four presentations of the figure at a time, in all). A larger number is permissible only when the figure is small. See also par. 21f.

d. Unusual species of Imitation, with Essential changes (par. 29, [par.] 31), are very rarely employed in the first Section, excepting the simplest variety of Shifted rhythm (par. 31c, second clause), and Contrary Motion; and even the latter should, as a rule, be deferred to the second, or a still later, Section. Both Augmentation and Diminution, excepting when applied to fragments of the Motive, are almost entirely inappropriate in the two-voice Invention. The Stretto is most valuable in the later course of a polyphonic form.

EXERCISE 11.

The Second Section.

42. The Second Section of an Invention must be conceived mainly as a continuation of the development of the Motive and its resources, initiated in the First Section. Its structural factors correspond to those of the latter (par. 38), but their arrangement is generally less systematic. The general requirements are as follows:

a. The new section may begin after the cadence of the foregoing has had its full rhythmic value, or it may follow immediately, after an elision. See par. 40h, second clause. It may begin with an announcement of the Motive (either alone, or with a contrapuntal associate); or with an episodic member. The former is the most natural and most common. Ex. 93, Note *4).

b. A certain degree of independence is desirable, and therefore the Second Section, while adhering to the spirit and general character of the First, may contain some distinctive traits; these may be obtained, either by adopting for the new section some special resource of the Motive (for instance, Imitation in contrary motion), or by inventing more striking and characteristic counterpoints than those of the First Section, or by introducing new episodic members. In this way, too, necessary provision may be made for sustaining interest. See Ex. 94, Note *2).

c. At the same time, it is desirable (though not indispensable) to institute some points of manifest resemblance, or even exact confirmation, ~ between the sections, by reproducing some portion of the preceding section, — of course in a different key, and, if possible, with inverted parts (i.e., changing the former upper part to the lower, and vice versa). Review par. 39b. And see pars. 55 and [par.] 56.

This parallelism of design is strikingly illustrated in the 1st 2-voice Invention of Bach; — the last five measures of the Second Section (measures 11–15 of the entire Invention) almost exactly corroborate the last five measures of the First Section (measures 3–7); but they are transferred to the next higher step; the former upper part becomes the lower, and its contrapuntal associate is partly reconstructed, — near the end of the section.

d. The modulatory aim of the Second Section is, generally, the Relative minor from a major beginning, or the Dominant key from a minor beginning. In a word, the first two cadences are usually made in the keys most closely allied to the original key, that is, the Dominant and the Relative; in a major Invention the Dominant cadence comes first and the Relative next; in a minor Invention the Relative comes first, and then the Dominant. Other related keys may, however, be substituted. Review par. 40g, and [40]h.

EXERCISE 12.

The Third (as final) Section.

43. If the Invention is to embrace but three sections (perhaps the most common number), the Third Section (or final one) tends to regain and re-establish the original key. This will determine its general modulatory design, which, like all terminal sections of musical form, is very likely to include a more or less positive presentation of the Sub-dominant keys.*

a. Whether the Third Section is to constitute the climax of the form, the definite and intentional culmination of the progressive development within the preceding sections, or not, it is at least more subject than these to the demand for increased interest; and therefore the most attractive and ingenious methods of manipulation should be enlisted. These may consist in the more striking (possibly hitherto untried) species of Imitation; or in more characteristic and effective counterpoints, or in more elaborate episodic passages; or, perhaps best of all, in one or more forms of Stretto-imitation (par. 36); or in all of these together.

b. Care must be taken, however, not to diverge too widely from the prevailing character of the foregoing sections; and while it is by no means necessary to return to the beginning and corroborate the main contents of the First Section, as is done in the Third "Part" of the tripartite Song-forms* (see par. 49a), it is still desirable to employ some method of confirming one or the other of the preceding sections. Review par. 42b and [42]c.

See Bach, 2-v. Invention No. 1. The parallelism between Sections I and II, already cited, is again exhibited in almost exactly the same manner in the Third Section, which, in measures 19–20, copies measures 3 and 4 (in Section I), and measures 11 and 12 (Section II), — both parts in the Contrary motion of their former contents.

c. The final cadence is made in the original key, and, as a rule, with more emphasis than the intermediate cadences, — frequently strengthened by auxiliary (inner) tones. See Ex. 93, No. 6.

d. Sometimes, however, this cadence is evaded, by using the chord of the VIth step instead of the Tonic, in which case a brief Codetta is added. For illustration:

Additional Sections.

44. If the Invention is to be extended to four, or perhaps even more, sections, the above details of Section III will need to be modified:

(1) With regard to the adoption of the most effective and interesting resources of thematic development, which, in this case, are more likely (though not certain) to be deferred to the final section; and

(2) With regard to the cadence, which will be made in some other related key, — preferably in one of the Sub-dominant keys, — thus also influencing the general modulatory design.

The conditions of individuality and confirmation (par. 42 b and [42] c) are valid, as before; while those of par. 43 a, [43]b, [43]c, and [43]d refer, in any event, to the final section.

EXERCISE 13.

The Invention in Two-Part Song-form.

45. While the "sectional" form is most consistent with the character of such polyphonic compositions as the above, representing the continuous development of an adopted thematic germ, it is nevertheless possible to cast them in the mould of some homophonic design, like the Two- or Three-Part Song-forms.

When this is done, the treatment of the "Sections" must be modified to conform with the more definite specific conditions of the "Parts." Review par. 39a.

This will probably affect the extent, which is usually greater in the "Part" than in the "Section"; and there is generally a marked distinction in the character of the cadences. As stated in par. 40h, second clause, and illustrated at the beginning of Exs. 94 and [ex.] 95, the "Section" commonly ends with an elision; i.e., the cadence-chord (or end) of one section is at the same instant the beginning of the next.

This is more rarely the case in the "Part," which is likely to have a firmer, more decisive (i.e., longer) cadence-interruption.

Further, a certain predominance of the structural idea over the details of thematic texture will also be evident, when the Part-forms are adopted, and this will influence the general character; it may lead to greater freedom of contrapuntal treatment, in favor of the distinctive conditions of the homophonic style; a more definite melodic character, more regular succession of 4-measure phrase-groups, or even distinct period-formations may prevail.

46. The primary grade of the Two-Part Song-form. This differs, when applied to the Invention, but little from a Two-section design, the main details of which are given in par. 40 and par. 43; i.e., the First Section stands for Part I, though possibly extended slightly beyond the limit of the ordinary "Exposition," and ends with a somewhat stronger form of cadence (par. 40h). The Second Part may be a trifle longer; it should exhibit the traits of confirmation explained in par. 42c; and must close with the perfect cadence in the original key, possibly followed by a Codetta.

This form is illustrated in Bach, 2-v. Invention No. 8. The First Section, or "Part" (already analyzed), embraces the first 12 measures, — a regularity of design suggestive of the group of 3 phrases; it closes with a distinct perfect cadence in the Dominant key. Measures 12–14 (beginning of Part II) correspond to the beginning of Part I, with inverted voices; measure 15 is a new episode; the following 4 measures are a sequence of these, with inverted voices; measures 20–25 are thematic, but new in treatment, involving sequential announcements of the M. in Contrary motion; measure 26 to the end exactly corroborates the last 9 measures of Part I, but transposed one fifth lower, in order to close on the original Tonic. See par. 48a, second clause.

See further, Bach, 2-v. Invention No. 10. Part I closes in measure 14 (already analyzed as Section I); Part II in measure 30, with an evaded cadence, followed by an extension of 3 measures.

The Genuine Two-Part Form. The First Part.

47. In the genuine (broader) Two-Part Song-form,* the First Part may be still more extended; possibly (though somewhat rarely) embracing two sections, the first of which fulfils the conditions of an "Exposition," with a comparatively light cadence, while the second one carries out the modulatory design, closing with a strong perfect cadence, — always in the Dominant key (whether major or minor). More commonly, however, these details are all contained in one single (long) section, which in some cases (e.g., in old Dance-forms) assumes the character of a Period or Double-period. See par. 45, last clause.

The First Part is very frequently repeated; generally with "1st and 2nd ending," the second one with a more complete check of the rhythmic movement.

The Second Part.

48. The Second Part of a genuine Two-Part Song-form is usually much more distinctly individualized than any "section" of the smaller forms. Its thematic basis may be defined in the following ways:

a. Most commonly, the same Motive (that of the First Part) is employed in Part II. It may preserve its original form exactly; or may possibly be slightly modified or reconstructed (as already witnessed in Bach, 2-voice Inventions, No. 3, meas. 12–13; and No. 7, meas. 13–14). Usually the Motive is announced first alone, or accompanied only by unessential auxiliary tones, as at the beginning.

In this case (when the same M. is retained) the characterization of the Part devolves largely upon the contrapuntal associates, which may be new and more striking than in Part I.

The condition of confirmation still demands fulfilment, as shown in par. 42c. This is most effectually realized by the very common device of ending the two Parts with the same member, — extending through an optional number of measures (from one up to ten or more). The member thus employed must reappear in a different key (Part I closing, probably, on the Dominant, and Part II on the Tonic*); and frequently the voices are inverted.

The Second Part may also consist of two (rarely more) sections, and is sometimes repeated.

b. Quite frequently the Contrary motion of the M. is adopted as thematic basis for the Second Part. It should be derived from the original M. in the manner defined in par. 29a (Exs. 72 and [ex.] 73), and must then be shifted (transposed) to the key or harmony with which Part II is to begin, — possibly with such modifications as may facilitate its adjustment. Comp. Ex. 74, Note *4), entire. When this is done it is likely, though by no means certain, that the Contrary motion will be held in abeyance during the First Part.

The new form of the M. may either extend to the very end of Part II, or it may be exchanged for the original motion in the later course of the Part; or the two forms of the M. may alternate, more or less regularly, throughout.

This device is a characteristic feature of the so-called Gigue-form (par. 51), in connection with which it will be more fully illustrated.

See Bach, Well-temp. Clavichord, Vol. II, Prelude 10. the M. of Part I (already analyzed) appears at the outset of the Second Part, but in Contrary motion, and extended by sequence to four measures (double its original length). In this new form it appears twice in the First Section (ending in measure 24 of the Second Part), and again twice at the beginning of the Second Section; the last announcement is followed by a recurrence of a long passage from Part I (measures 33–55, corresponding closely to measures 23–48 of the First Part, with inverted voices for a short distance); during this parallel passage the original motion of the M. naturally reasserts itself. The cadence falls in measure 55, but is evaded (by a VI, — par. 43d), and a Codetta is then added.

Bach, English Suite No. 5, "Allemande"; M. of one measure in upper part, lower part auxiliary; the original motion of M. recurs near the end.

c. In somewhat rare instances a new Motive is adopted for the Second Part. Though thus quite independent, it should be intimately related in general character to the first Motive. As before, the new thematic form may be retained throughout the Second Part; but it is much more likely that the first Motive will reappear, near the end,—possibly in alternation with the new one; more rarely in conjunction with it, when, be it by accident or design, they harmonize. For illustration: The First Section partially shown in Ex. 90, after being continued in a very similar manner up to its cadence (E♭ major), in the 15th measure, runs on as follows:

EXERCISE 14.

The Invention in Three-Part Song-form.

49. In all Three-Part forms there is, in addition to the above two Parts, a more or less distinctly marked return to the beginning, and consequent recurrence of the essential thematic contents of the First Part or Section; it is the fulfilment of this structural condition which devolves upon the Third Part.* This affects, primarily, the cadence of the Second Part, which should be made upon the Dominant of the original key, and may therefore influence the later modulatory and thematic design of the Part.

The Primary Grade.

a. The primary grade of the Three-Part Song-form, when applied to the Invention, will resemble the Three-section design, explained in par. 40–[par.] 43, with the significant exceptions, however, that the Third Section is not to be, as there, merely the continuation of its predecessors, but must represent the Return of the original key, and must reproduce a portion of the early contents of Section I (perhaps no more than one or two measures); and that, consequently, the Second Section must be so conducted, near its end, as to lead to this result. (Compare par. 43b.) For example:

* Homophonic Forms, par. 81.

Furthermore, Ex. 96 is completed as follows:

The Genuine Three-Part Form.

50. In the genuine (broader and more clearly defined) Three-Part Song-form, the details of Part I correspond to those given in par. 47, which review; and the conduct of Part II corresponds to all the details of par. 48a, [48]b, and [48]c, — excepting such as concern its cadence, which, in the Three-Part design, must be made on the Dominant, or, at all events, upon such harmonies, and in such a manner, as to prepare for and lead decisively into the recurrence of the first measures (as beginning of Part III).

a. As before, the thematic basis of the Second Part may be:

(1) The same Motive (usually with new, and more or less characteristic, counter-motives),—par. 48a, first and second clauses;

(2) The Contrary motion of the original Motive, as in the "Gigue" form (see par. 51); or

(3) A new Motive, — par. 48c.

b. The object of the Third Part is, as usual, to re-establish the principal key, and to re-announce the original Motive and its Imitation as they appeared at the outset, in a sufficiently accurate manner and through a sufficient number of measures to identify itself as the corroboration of the First Part. In some cases, where the design is broad, the parallelism extends through a large portion of the Third Part (perhaps with inverted voices, and occasional modifications), or even to the end, — excepting, of course, the necessary change of modulation and cadence. But more commonly it is limited to the first two or three measures, and the remainder of the Part is then elaborated independently, and, as climax of the form, as ingeniously and effectively as possible. Review par. 43a, which has peculiarly direct bearing upon "Part III."

When the Second Part has used the Contrary motion of the Motive, the original motion is resumed at the beginning of Part III, and is then either retained to the end, or, far more effectively, the two forms of the M. subsequently appear in more or less regular alternation, or even in conjunction (as Stretto). And precisely the same principles apply when Part II is based upon a new motive (as in Exs. 90, [ex] 96, [ex] 98).

See Bach, 2-voice Invention No. 3; Part I (already analyzed) closes in measure 12; Part II contains two well-defined sections, closing in measures 24 and 38; between the last cadence and the beginning of Part III (end of measure 42) a brief passage intervenes, which, though largely thematic, serves the purpose of a Re-transition,* or returning passage; Part III corroborates the first 4 measures of the First Part exactly, transposes and inverts the following four, then resumes the original line (transposed), but cadences on the VI (par. 43d); a Codetta follows. Throughout the Second Part the M., as already seen, is reconstructed by the addition of three preliminary tones; this form recurs once, in the Codetta.

Bach, French Suite No. 2, "Air"; the M. (one-half measure) is announced in the upper part in a somewhat imperfect form, and imitated in slightly altered Contrary motion; Part II begins with Contrary motion, but otherwise maintains the original motion; it has two well-defined sections, of 4 measures each; Part III (the last 4 measures) is vague in effect, though the structural purpose is clear; during the first 2 measures the lower voice agrees almost exactly with the upper voice at the beginning of Part I.

Bach, French Suite No. 4, "Air"; Part I largely episodic; the Contrary motion of the M. prevails in the Second Part, which contains two sections; Part III corresponds very closely to the First, — transposed after one and one-half measure, without other changes.

EXERCISE 15.

The "Gigue."

51. The adoption of the Contrary motion of the Motive as thematic basis for the Second Part (already touched upon, in par. 48 and par. 50a), is so common in the "Gigue" as to constitute a partly, though not definitely, distinctive trait of that old Dance-form; and the term "Gigue-form" is therefore often applied to a polyphonic Invention thus designed, irrespective of its character. On the other hand, many examples of the old-fashioned Gigue may be found in which the Second Part uses the original Motive, or a new one, as in ordinary forms.

* Homophonic Forms, par. 90c

The design of the whole is usually the Two-Part (more rarely Three-Part) Song-form, with repeated Parts. The most common measure is . Review par. 48b. For illustration, see —

The Invention with Two (or more) Motives in Alternation.

52. A second (new) Motive may appear not only at the beginning of the Second Part, as specific basis of the latter (par. 48), but may be introduced and developed in closer connection and alternation with the first, or principal, Motive.

a. Such an additional thematic germ may be so unimportant in character and extent as to subserve, chiefly or entirely, the episodic purposes, in which case it is to be called an Auxiliary Motive (or Figure), rather than "2nd Motive."

An example of this kind has already been seen in Bach, French Suite No. 6, "Gigue"; and others will be cited later.

b. When the new M. is more nearly or completely co-ordinate with the principal (first) one, it may appear at the beginning of the second (possibly a later) section, and become its thematic basis. Or it may enter into the polyphonic texture still earlier,—during the First Section, or Part, — and be utilized thereafter throughout the Invention, in more or less constant close alternation (not simultaneous conjunction) with the principal Motive.

As already stated (par. 48c), the new M. must, while asserting a certain measure of distinct individuality, still be conceived in intimate consistency of character with the first Motive.

For illustration, see Bach, 2-voice Invention No. 13:

The first (principal) M. is used during 2 measures; the 2nd M. during the rest of Part I (up to measure 6); the same arrangement prevails, very nearly, during the First Section of Part II (measures 6–13); in the remainder of Part II (up to measure 18) the 2nd M. appears alone, somewhat modified; in Part III (measure 18 to the end) the two Motives are employed, in closer alternation.

Bach, Well-temp. Clavichord, Vol. II, Prelude 23:

The 1st M. appears only at the beginning of Part I, with one Imitation, partly in Contrary motion; the 2nd M., which, but for its domination, would be regarded merely as an auxiliary figure, supplies the basis of development up to measure 8, after which fragments of M. 1 lead to the cadence (measure 12); Part II extends to measure 37; its First Section, ending in measure 17, is episodic, but derived from M. 1; an independent episode follows, suggesting a third M. (compare par. 52c); in measure 23 the second M. again asserts itself, and continues some time, though fragmentary, measures 29–32 closely resemble the episode of the foregoing section; Part III (measure 37 to end) is much like the First Part, but the 2nd M. is absent. There are several evidences of 3-voice texture, but scarcely enough to be conclusive.

The whole example belongs, more accurately, to the Prelude-class (Chap. IX). And the same is true of Bach, Well-temp. Clavichord, Vol. II, Prelude 13, in which the following contrasting thematic members are discoverable:

Of these, Motive 2 appears to be the more essential and important. The design is 3-Part Song-form; Part II contains three well-defined sections; in the first one the two Motives are announced in conjunction (simultaneously); Part III resembles Part I very closely, but is abbreviated. A coda of 8 measures is appended.

Händel, Clavichord Suite No. 7, "Andante," employs the following Motives:

The design is 3-Part Song-form, Part III somewhat vague and abbreviated.

Händel, Clavichord Suite No. 16, "Allemande," is a very clear exposition of the following, in almost constant close alternation:

The design is 2-Part Song-form, each Part containing two sections, and repeated. The thematic development is unusually regular and perspicuous.

c. More rarely, three Motives participate in the development of an Invention; either (1) as the respective thematic basis of three successive sections, or (2) in closer and more constant alternation with the first (principal) M., or with each other, in any order.

The Lyric Invention, with a Long Theme.

53. The 2-voice Invention may, exceptionally, be based upon a thematic sentence of greater length than the ordinary Motives, seen in the above examples. Such a lengthy theme is very likely to represent the regular 4-measure Phrase, or even 4- to 8-measure Period-form, with a correspondingly definite melodic design, usually distinctly lyric in character, and with a well-marked semi-cadence (upon either a Tonic or Dominant chord).

Obviously, so extended a Motive cannot be announced (imitated) effectively very often in the course of an ordinary Invention, at least not at its full length; and therefore the development, while none the less strictly polyphonic, will necessarily be more largely episodic than usual; and in general the structural idea and considerations of "form" will prevail almost constantly over the thematic purposes (compare par. 45, last clause). The episodic interludes will probably be derived from some figure or figures of the large Motive, though they may be independent. (Compare par. 38d and par. 41b; see also par. 42c.)

The Student’s Attitude Toward the Prescribed Tasks.

54. In working out the required Exercises in these grades of 2-voice Polyphony, the student need harbor no fear that he may imitate the given authoritative examples of Bach too closely, and thus perhaps unconsciously acquire the unwelcome habit of conceiving and writing in the somewhat antiquated manner of these old-fashioned compositions. The propagation of this particular style — the multiplication of pieces for which our modern ears have but little sympathy — is not the aim of the student’s present labors; it is simply the exercise of contrapuntal discipline within the dominion of these forms, as a means to an end, — an end which may be as modern and original as the student (or the listener) could desire.

There is but little likelihood that the pupil will wholly escape the influence of modern musical thought, especially if he be observant (as successful students invariably are), alert to recognize and to appropriate the acquisitions of recent times, whether in the polyphonic or in the homophonic domain of musical creation.

Polyphony is merely a product, resulting from the employment of the contrapuntal method; and this method may be applied in dealing with any phase of musical style, romantic, classic, dramatic, or archaic. The distinction rests mainly, perhaps, upon the choice of harmonic basis, out of which all Polyphony must emerge, just as well as Homophony (par. 11); for this harmonic element it is which has grown "modern," leaving former simpler customs of harmonic progression behind. The distinctive contrapuntal "method" adopted for the presentation of the harmony is, however, not thus subject to the changes of time; Polyphony is the embodiment of the same principle in the twentieth century as in the fifteenth; but its character and complexion will differ, as the harmonic material becomes richer and more pliable.

There can be no excuse for writing an unattractive Invention in our day, on the ground that it must be produced by contrapuntal methods. Nothing is devoid of interest in which the operation of a quick imagination is discernible; and nothing discloses, from the proper point of view, a more powerful and constant stimulus to the imaginative faculty, than the contrapuntal methods of tone-association.

EXERCISE 16.

The Natural Species of Double-Counterpoint.

55. Double-counterpoint is a process; but the term is generally-applied to the product resulting from it. The counterpoint is said to be "double" when the added voice (i.e., the contrapuntal associate) presents perfect agreement with the given voice or Motive, in two different relations to the latter. These two relations always imply, in Double-counterpoint, the distinction of register, and refer to the agreement of the added part both above and below the given part; or, in a word, the counterpoint is "double" when the parts admit of inversion.

a. The inversion of the parts is effected by transferring either part toward and beyond the other (shifting it up or down, as the case may be); thus, the upper part may be shifted down, past the lower; or the lower part shifted up; or each may be shifted so that they exchange registers. See Exs. 105, 106, 107.

b. When one of the parts is shifted just an octave (or possibly two octaves), while the other part remains where it was, it is obvious that no essential change in their harmonic relationship takes place, because each retains its original series of letters (or tones), and the association or union of the melodies is actually the same as before; the only difference being that their respective registers have been exchanged. Each contrapuntal interval is simply inverted, and the octave-inversion of an interval, as has been amply tested, is practically identical with the original interval. For illustration:

*1) At b the two parts are inverted, the original upper part becoming the lower, and the lower the upper. The original upper part remains where it was, and the lower is shifted upward one octave, beyond the other. That no essential change takes place in the harmonic relations of the parts, is easily verified by comparing the contrapuntal intervals.

The result would be precisely the same if the lower part were to remain, and the upper part shifted down an octave:

Or if each part were shifted one octave (possibly two octaves) towards and beyond the other:

*1) Here the original lower part is shifted up one octave, and the upper is shifted down two octaves.

c. Further, the same result is obtained (without essential change) when the Inversion of the original counterpoint is transposed. In this case each voice is shifted toward (and past) the other in such a manner that the sum of the two shifts equals an octave; for instance, if the upper voice is shifted down a 5th, the lower must be moved up a 4th; or one a 3rd and the other a 6th; or one a 2nd and the other a 7th. For example:

*1) The upper part is shifted down a 7th, the lower up a 2nd (or 9th, which is the same thing); the original counterpoint is thus transposed bodily, as Inversion, from C major to d minor. That no other change than simple "inversion" has taken place, is shown by the first contrapuntal interval (a 3rd, becoming a 6th in the Inversion). See Ex. 86, Note *6).

*2) The inverted form does not need to be enchained with the original counterpoint, as chances to be the case in Ex. 107; it may occur and recur at any later moment in the form.

56. Such Inversions as these, in the octave or in intervals equalling an octave (or two or more octaves), are so common, so nearly inevitable in contrapuntal writing, and the product is, as has been shown, so likely to be exactly equivalent to the original, that this — the Inversion in the Octave — is called the Natural species of Double-counterpoint. Its feasibility is almost a foregone conclusion, and therefore all good contrapuntal association is, in a sense, naturally double-counterpoint.

57. No specific rules can be given for natural Double-counterpoint. The best method is to write the counterpoint as usual, and then simply test the effect of inverting the parts; any lurking discrepancies can thus easily be detected and removed. The following general points may, however, be borne in mind:

(1) The Original counterpoint should be as perfect and free from irregularities as possible.

(2) Some caution should be exercised in the use of the chord-5th, for certain irregularities that are permitted with it in the upper part become objectionable in the lower; this refers particularly to skips to or from the chord-5th, during a change of harmony. Compare par. 17d, last clause; (Ex. 50B, No. 2, the last measure, would be much worse in inverted form). See also par. 62.

A curious instance of characteristic disregard of this rule is seen in the following. Its undeniable peculiarity is palliated by broad considerations, that will become obvious to the more advanced student:

*1) The c♯ in the lower part is the 5th of the chord (I of f♯ minor). In the Inversion, the chord-5th f♯, also, is unpleasantly prominent in the upper part.

(3) If the two parts are kept within an octave (from each other), the shifting of either part a single octave suffices to effect Inversion. If the parts diverge more than an octave at any point, however, it will be necessary to shift each voice an octave (or either voice two octaves) in order to obtain Inversion throughout; and so on.

58. Frequent unconscious use has already been made of natural Double-counterpoint in the preceding exercises. Systematic application of it may hereafter be made, in the Invention, in many ways that will suggest themselves to the student. For instance:

In the sectional form, any later section may correspond exactly (or nearly) to some foregoing section, but with inverted voices, and, of course, in a different key.

Or, in the 2-Part Song-form, a portion, or the whole, of the Second Part may be an inverted reproduction of the First, in the proper key. This is strikingly illustrated in Bach, Well-temp. Clavichord, Vol. I, Fugue 10, to which brief reference may be made; the entire Second Part (measures 20–38) is an Inversion of Part I (measures 1–19) in a different key; the necessary modulation is made in measure 29, first beat (compare with measure 10).

Or, in the 3-Part Song-form, Part III may corroborate Part I in the same manner.

See Beethoven, Pianoforte Sonata, Op. 10, No. 2, Finale, measure 87 (ff) to 106.

Beethoven, Violin Son., Op. 30, No. 1, Finale, Var. V; meas. 1–8, inverted in meas. 9–16; meas. 17–24, inv. in meas. 25–32.

EXERCISE 17.

Write a number of 2-voice Inventions, applying the principle of natural Double-counterpoint, according to the suggestions in par. 58.

CHAPTER VI.
 The Contrapuntal Association of Three Melodic Parts (Voices).

59. Review the definition of Polyphony given in the Introductory Statement (page 1).

The "harmonious" association of three co-ordinate melodies must necessarily be controlled by the conditions of chord-structure to a far greater and more manifest extent than that of only two voices, — for which latter a schedule of euphonious intervals was found to suffice.

For this reason 3-voice Polyphony exhibits a much more evident harmonic character than the 2-voice; and the chief difficulty in its successful manipulation consists in respecting and enforcing the control of the Chord-forms, without fettering the individual parts and interfering with that independence and melodic smoothness which is, in true Polyphony, as significant a requisite as that of unanimous action.

Details of Three-Voice Polyphony.

61. a. This imparts a corresponding degree of importance to the harmonic idea, and greatly emphasizes the rules of chord-succession given in pars. 18 and [par.] 19, which must be carefully reviewed.

b. Of the three parts, two will very likely co-operate temporarily according to the rules of 2-voice polyphony given in Chapter II; and the remaining (third) part aims to secure some essential tone which, with the essential tones already present, completes some legitimate chord-structure.

This rule is merely stated for the convenience of the student, who, as beginner, can scarcely expect to conduct three independent parts successfully, all at once, but will need some such division of the labor as the rule indicates. He must observe that no attempt can be made to intimate which two of the three parts will be chosen thus to form the temporary basis of the contrapuntal fabric, or how far the choice each time extends; for that depends upon conditions that are either self-evident, or follow as a matter of course out of later details, — especially par. 64. And in any case the rule does not refer to a certain pair of voices throughout, but implies a temporary choice, liable at any moment to be exchanged for another pair. The ultimate consideration is, after all, that the three parts together must represent, in their simultaneous essential tones, some legitimate chord-form.

Hence, in the preliminary draught of the three-fold melodic association, the intervals of the 3rd, 6th (8ve, etc.), will govern the choice of simultaneous essential tones, as shown in pars. 14 and [par.] 15. For illustration:

Further:

c. As stated in par. 60, second clause, the harmonic points thus definitely fixed as basis for the conduct of the additional (3rd) part, should be so modified or disguised by means of auxiliary tones, unessential neighboring and passing-notes (inharmonic tones, in a word), as to counteract the impression of simple chord-succession. This device is omitted in Ex. 110, but plainly seen in Ex. 111, No. 2; and may be verified in the other given illustrations, also.

But this is not all; the insertion of passing-notes must not be adopted as a device to this end alone, or the texture will, after all, amount to no more than "embellished harmony." A higher purpose — that of independent melodic progressions — must dictate the employment of such inharmonic tones; and while the progressions must necessarily be governed by the chord-contents, their independence must be ensured by sufficient evidence of thematic purpose. Review, in this connection, par. 17b, (pars. 13i, [par.] 21b); also par. 7.

d. Of the purely mechanical means of obtaining voice-independence, none is more efficient and indispensable than the Tie, which advances in importance in proportion to the number of polyphonic parts associated. Review thoroughly par. 22d, and par. 9, entire. For example:

*1) Some of the ties in this sentence result in positive dissonance, by producing Suspensions; at other places, on the contrary, the tie simply modifies the rhythm of its part, without influencing the consonant effect. See also Ex. 57, No. 6 (ties in lower part); Exs. 58, [ex.] 59, [ex.] 60; Ex. 111, Nos. 1 and [ex 111]-2; Ex. 113.

e. The greater the number of parts employed in a polyphonic complex, the greater the likelihood and necessity of indirect coincidence between a certain pair of them, — to counteract the danger of excessive dissonance from the independent movements of so many individual parts. This is probably most frequently exhibited in the prevalence of parallel movement in 3rds or 6ths, between two of the three (or more) voices, — a trait which is strikingly common in the best examples of Polyphony, and affords the surest guaranty of smooth and euphonious effect. The limit of such a parallel series of 3rds or 6ths can be defined only by a perfect understanding of the momentous principle stated in par. 60, and of the "spirit of Polyphony" in general. Sometimes (as if to redeem the independence of the parts, or perhaps for thematic reasons) the line of parallel 3rds or 6ths is disguised by some means; for instance, in Ex. 112 the inner part is obviously defined in parallel 3rds with the upper, from measure 4 to 8; but by embellishment, first in one part and then in the other, their indirect coincidence is completely veiled. See further:

*1) Measure 1, beat 2,— 6ths between outer parts (up to first pulse of next beat); beat 3, — 6ths between inner and lower parts (again up to first pulse of next beat); measure 2, beats 1 and 2, — 3rds between outer parts, disguised by the omission of alternate 16ths in upper part (again the parallels extend into the following beat, modified by transferring the last tone to the higher octave); beat 3, — 3rds between inner and lower parts. See also Ex. 57, No. 6; Ex. 111, No. 2.

Of similar (though far inferior) efficiency is that variety of indirect coincidence in which two of the parts reciprocate in the embellishment of chord-tones that lie a 3rd apart,— both using the same tones, but in contrary direction. Thus:

Bach uses this device so rarely, as compared with his employment of parallel 3rds and 6ths, that it may justly be regarded with suspicion, as a polyphonic factor. See Beethoven, Pianoforte Sonata, op. 106, first movement, measures 55–61.

f. All general rules of contrapuntal association (as those of par. 17d and [17]e; pars. 18, [par.] 19, [par.] 20) apply alike to every variety of polyphonic texture, regardless of the number of parts employed. The rule in par. 17f, with reference to conducting the parts in contrary (opposite) directions, applies to polyphony for three and more parts also, but with certain modifications. It is evident that all three (or four) parts cannot move at the same time in different directions; but it is possible (1) to hold one part level, while the other two are respectively ascending and descending (or even moving in parallel direction); (2) to carry one part, at least, in contrary motion with the other two, so that one descends while two are ascending, or vice versa. It is wise to conduct the two outer parts in opposite directions, as a rule, and to avoid parallel movement in all three parts at once.

Of peculiar value in 3-voice polyphony is the device of modulatory Substitution expounded in par. 19c, which is to be thoroughly reviewed.

62. The conduct of the lowermost part is of increased importance in 3-voice polyphony, because of the more pronounced harmonic character of this species of writing (par. 59), and the consideration due to those forms (Inversions) of harmony in which the chord-fifth lies lowermost (i.e., the 6-4 chords).

It is, of course, impossible (and needless) to shun this chord-form altogether; but vigilance must be exercised in the treatment of all obvious 6-4 chords. Former rules apply strictly; see par. 18h. To recapitulate:

a. Avoid leaping to, or from, a bass tone which is manifestly the 5th of the momentary chord, — excepting in chord-repetitions.

b. Avoid a succession of chord-fifths in the lowermost part (i.e., 6-4 chords) when both represent Consonant forms of harmony; if either of them is an imperfect 5th, or the inverted form of any Dissonant harmony, the succession is good. This grave error is most easily checked by avoiding parallel perfect 4ths with the Bass, in the conduct of any upper part, when the 4ths are both essential intervals (par. 14).

c. Avoid any very conspicuous 6-4 effect, excepting when the harmony is Tonic. Avoid, hence, beginning or ending a Section upon a 6-4 chord. As a rule, the lowermost part should not be announced (or re-announced after a rest) upon the 5th of the momentary chord; nor should it discontinue (pass into a rest) after a tone which is evidently the chord-fifth.

d. These rules may be said to apply to all 6-4 chords excepting that of the Tonic; the latter is largely, if not entirely, exempt.

For example:

63. The rhythmic conditions of 3-voice Polyphony are identical in principle with those of the 2-voice, as detailed in par. 22, which review.

a. The chief rule is stated in par. 22a: the three voices participate, with a certain regularity of alternation, in sustaining the adopted rhythmic movement (of [8th] notes, [16th]-notes, — or whatever the prevailing uniform rhythm may be). Rhythmic diversity between the parts being, as repeatedly emphasized, the principal means of instituting voice-independence, it is evident that its importance, and the necessity of its careful treatment, increase in proportion to the number of parts engaged. Review, very thoroughly, par. 22a and [22]d.

Quite frequently the same rhythm will be given to two of the parts simultaneously; but this similarity must never be carried very far (best not more than 2, 3, or 4 beats), before being transferred to another pair, or abandoned temporarily in favor of one part alone. See Ex. 114, No. 2, [Ex. 114, ] No. 3; Ex. 113; Ex. 111, No. 1.

One of the three parts may run on in uniform rhythm almost indefinitely, if sufficient provision for diversity is made in the remaining two parts. See Ex. 110 (Soprano); Ex. 113 (Bass); Ex. 114, No. 2, [Ex. 114, ] No. 3.

As a general rule, the most definite and constant aim is, to assign to each of the three parts, temporarily, a different rhythmic movement, i.e., different tone-values; not obstinately, but as an ever-conscious preference. This, and the maintenance of a smooth, uniform, collective rhythmic effect, satisfy, together, all the rhythmic demands of polyphonic texture.

See Ex. 110, — different values in each of the three parts; Ex. 111, No. 2,—during almost every beat the three parts have different values; Ex. 112, the same; Ex. 113, measure 2. This may best be verified by careful analysis of the given references.

Finally, the exchange of one rate of rhythmic movement for another (faster or slower) may, of course, be effected within the same Invention without confusion, if care be taken to preserve good balance of total effect (by regularity of recurrence, — on the principle of par. 22e), and a perfectly clear impression of the fundamental metric design. See Bach, 3-voice Inventions, No. 15 (alternating [16th] and [32nd]-movements); No. 2; and Ex. 117, with context (par. 70).

b. The Rest enters into the rhythmic design of Polyphony more significantly when three or more parts are used than when there are but two. Review par. 10, and par. 22d, last clause.

In general, short rests, interspersed promiscuously through the polyphonic texture, are of inferior value, and often rather injure than improve the effect. It is far more judicious to interrupt the conduct of one of the three parts by a longer rest, for a whole measure or more, so that a decided and noticeable change of volume results.

A part may be thus definitely discontinued (1) at any cadence; or (2) at any point in the course of a Section where the part reaches a tone that has no special obligation or tendency to fulfil, — especially when it is any interval of the Tonic harmony; and, as a rule, only at an accented beat or the accented fraction of a beat; rarely, if ever, after any dissonant tone that demands resolution.

In 3-voice Polyphony, generally no more than one part should rest at a time (unless it be very briefly); hence, another part must not be discontinued until the absent part has fairly recommenced; in other words, the extremities of a discontinuing and recommencing part should overlap noticeably.

After a protracted pause, the part may recommence with an announcement of the Motive. This is the most appropriate and effective method, but is by no means essential.

c. Further, the part should recommence, after a rest, on an unaccented beat; or, still better, on a fraction of the beat, as a very general rule.

For illustration of all these points, see Ex. 112, inner part; Ex. 113, lower part; Ex. 114, Nos. 2 and [114]-3; Bach, 3-voice Inventions, No. 1, measure 13 (Bass), 15 (inner part), 16 (lower part pauses directly after inner part recommences, overlapping one beat), 17 (brief rest in upper part). 3-voice Invention No. 2, — in measures 5 and 6, the outer parts pause together during the last beats; this is unusual, but the reason is obvious; the irregular acceleration of the rhythm in the inner part (contrary to the fundamental principle, par. 63a), is fully justified by its recurrence, or sequence, in the following measure, and again, at intervals, throughout the Invention. Compare pars. 22e and [par.] 21f. In this same Invention, measure 4 from the end, the lower part discontinues precisely as the upper part recommences, i.e., without overlapping; this is least confusing when, as here, the parts in question are so distant from each other that their extremities cannot be confounded. In nearly or quite all of these cases, the rule of par. 63c is illustrated conclusively.

Leading Parts.

64. It is extremely difficult—for the beginner, almost out of the question — to lead three polyphonic parts abreast, and preserve the individuality of each part as if it were alone. Before this supreme command of simultaneous part-leading shall have been acquired, the student must adopt some method of systematic division of the labor, by centering his attention upon first one and then another single part for a time. This is entirely feasible and justifiable, because it is consistent with the processes of polyphonic texture, that a certain one of the three (or more) parts temporarily takes the lead, — the other parts meanwhile deferring to the "Leader," as simple contrapuntal associates, until some other part, in its turn, assumes the lead.

The choice of temporary "Leader" may be made arbitrarily; but it is far more likely to determine itself, as a matter of course, out of the natural conditions and exigencies of the progressive development. For example, that one of the three parts which has charge of the Motive invariably assumes the leadership for the time being; and, during episodes, that part takes the lead which pursues the most obvious and important thematic purpose, — as, for instance, the projection of a line of Sequences, the pursuit of some significant imitatory process, or any other definite and far-reaching melodic or structural aim.

Further, it is precisely the same with the question "how long" a part may assert the leadership, before abandoning it to some other part; it depends upon the conditions which determine the choice in the first place; it may be a measure or several measures, or possibly only a single beat.

In any case, the leading part should be written down alone, as far as it is to extend; it is then comparatively easy to return and "fill out" the remaining parts.

This idea is closely allied to that expounded in par. 61b, which review.

See Bach, 3-voice Invention No. 1; during measure 1 the upper part "leads"; during measure 2, the inner part; measures 3, 4, and 5, the lower part; measure 6, the inner; measures 7 to 9 (beat 3) the lower part "leads," first with its Sequences and then with the Motive; measures 9 (beat 3) to 10 (beat 3), the inner part; measures 10 (beat 3) to 11 (beat 3), the upper; meanwhile, during the first half of measure 11, the lower part claims the lead, and maintains it to the end of the measure; and so forth. The student is to continue the analysis to the end of the Invention, with reference to the "leading parts."

Summary.

65. a. The simultaneous essential tones should constitute some chord-structure; and the chords should succeed each other according to the fundamental conditions of chord-progression.

b. The problem of good Polyphony for more than two parts is, to preserve an equipoise between the Consonance of the chord-forms and the Dissonance involved by independent part-conduct.

c. Ties are invaluable in effective Polyphony.

d. Parallel movement in 3rds or 6ths is the most legitimate and reliable guaranty of smooth and euphonious voice-association. At the same time, a certain degree of Contrary motion should be maintained.

e. The lowermost part must be so conducted as to avoid conspicuous or faulty 6-4 chord effects.

f. The rhythmic requirements are, to diversify the tone-values of the several parts, but to maintain a generally, uniform collective rhythmic effect.

g. Rests — especially of palpable extent—are invaluable in effective Polyphony for more than two parts. After a rest, the part should re-enter upon an unaccented fraction or beat.

h. In the execution of a multi-voice polyphonic texture, it is necessary to concentrate the attention upon a certain single part, as temporary "leader" — the choice and extent depending upon thematic conditions.

EXERCISE 18.

CHAPTER VII.
 The Three-voice Invention.

66. The structural conditions of the 3-voice Invention coincide exactly with those of the 2-voice Invention. Review pars. 37, [par.] 38, [par.] 39.

b. The "Sectional" form is, here again, the most fitting. Its details correspond to those given in Chapter V; but there are a few additional considerations, naturally involved by the additional voice, which call for special explanation.

The First Section, or Exposition.

67. Review par. 40.

a. The Motive — which is likely to be a trifle less ample in compass, and less lively in rhythmic character, than the foregoing ones — may be announced in either one of the three parts, most commonly in the inner or upper part.

b. Unless occupied with the M., the lower part, at the beginning (seldom any other voice), is generally utilized as an auxiliary accompaniment, of quiet, unpretentious character, and of optional length,— though usually discontinued several beats before it (as legitimate third voice) is to announce its Imitation of the Motive.

See Bach, 3-voice Inventions, Nos. 4, 10, 12, 13, 2,—first few measures of each. The more exceptional method of passing immediately out of the auxiliary melody into the Imitation of the Motive is seen in Bach, 3-voice Invention No. 1, measure 3; the abrupt change of rhythm, and the leap of an octave into the first tone of the Motive, serve, however, to identify the latter. See, also, 3-voice Inventions, Nos. 6, 7, 8, 11, 14.

c. The first Imitation of the M. may follow in any voice,—generally in the next higher or lower one (i.e., the neighbor of the first voice). The interval of this first Imitation is optional; but very positive preference is given to that in the 5th. The necessity of accurate and natural adjustment, expounded in par. 35b (which review, thoroughly), is here again to be respected, especially when any other Imitation than the 8ve is chosen. Any unessential modifications (pars. 28b, [par.] 30a and [par.] 30b) which serve this important end, are permissible.

Bach, 3-voice Inventions, No. 1, first Imitation in the 4th; No. 2, in the 8ve; Nos. 4, 6, 7, 8, 10, 11, 12, 13, 14, first Imitation in the 5th.

d. The second Imitation (third announcement) of the M. is most likely to be made in the remaining part; though in many instances the latter does not begin its imitatory function until the first two parts have announced the M. several times (Ex. 116); or, as is the best and most common procedure, until they have interpolated one or more episodic measures, — not only for variety, but as a means of achieving some necessary or desirable modulatory purpose.

The interval of Imitation is here again optional, but nearly always the 8ve of the first announcement is chosen. See, again, par. 35b.

Bach, 3-voice Inventions, No. 1; first the upper, then the inner, then the lower part takes the M., in regular succession; the same in No. 2 and No. 12. — In No. 6, the order is inner, upper, and lower part, in regular succession; the same in No. 8. — In No. 4, the M. appears first in the upper part, then in the inner; then an episode of one measure intervenes, before the last part takes up the Motive; the same in No. 11 and No. 14; No. 13 similar. — In No. 7, the upper part has an additional (3rd) announcement of the M. before the absent (lower) part follows with its legitimate Imitation; the same in No. 10.

e. As concerns the rest of the Section, — the episodic passages, the modulatory design, and the cadence,— review par. 40d, [40]e, [40]g, and [40]h.

For general illustration:

EXERCISE 19.

The Remaining Sections.

68. The details of the further development and conclusion of the sectional form correspond exactly to those given in pars. 42, [par.] 43, and [par.] 44, which review thoroughly.

a. Contrary motion of the M. is a peculiarly valuable resource, and should be freely used in these remaining sections, Stretto-announcements (for two, or for all three, parts) are most desirable in the later Sections. Perhaps an Imitation in Augmentation (or Diminution) may be successfully introduced in the 3-voice Invention, though these unusual forms of Imitation are most likely to be applied to a portion only of the Motive. Compare [par.] 41d.

b. The student should conceive this present Exercise chiefly as an effort to discover and apply as many of the latent resources of his Motive as possible. Therefore, he should employ the Motive (entire or in part) almost constantly, testing every form of presentation which the chapter upon "Imitations" (Chapter IV) designates, or which his own imagination may suggest, and introducing comparatively few and brief episodic passages. In pursuing this interesting and profitable course of thematic experiment to a satisfactory conclusion, the number of Sections may be increased to any reasonable extent (see par. 68c); and each Section, in turn, may be devoted more or less exclusively to testing some certain (untried) resource of thematic presentation (compare par. 39b); this will tend to individualize the several Sections, while, on the other hand, the necessary unity and consistency of form may easily be restored by establishing points of similarity and corroboration between the Sections (par. 42c). See —

c. Sometimes the design of an Invention is extended to embrace an unusually large number of Sections, or even Parts. The result is either a Large Group-form *; or, less frequently, the middle Sections are approximately equivalent to a "Trio," followed by a broad Da capo of all the anterior ones (quasi Song-form with Trio **). In such long lines of development it is almost indispensable to introduce complete episodic Sections, often of quite distinctly homophonic character, based more upon harmonic figuration (in the prevailing rhythm) than upon thematic recurrences. Compare par. 45, last clause; and par. 84.

EXERCISE 20.

Other Structural Designs.

69. a. The primary Two-Part Song-form. Review pars. 45 and [par.] 46; and analyze the following examples very thoroughly: —

* Homophonic Forms, par. 115.

** Ibid., par. 117.

Bach, 3-voice Invention No. 14; Part (or Section) I, already analyzed, closes in measure 12, with a very distinct Dominant cadence; Part II (to the end) is characterized by abundant stretti. — Bach, Well-temp. Clavichord, Vol. I, Prelude 23; Part (or Section) I terminates in measure 6, Part II in measure 15 (somewhat indefinitely); a Codetta, with evidences of four-voice texture, follows. — Bach, Partita No. 1, "Praeludium"; M. of one and one-half measures,—possibly two measures; Part I ends in measure 14. — Bach, 3-voice Invention No. 15; two Motives in close alternation, in different rhythms; the Counter-motive is retained throughout, in Natural Double-counterpoint (compare par. 58); Part I ends in measure 14.

b. The genuine Two-Part Song-form. Review pars. 47 and [par.] 48; and see —

c. The conventional Gigue-form, with Contrary motion of the M. as basis of Part II. Review par. 51, and see —

d. The primary Three-Part Song-form. Review pars. 49 and [par.] 49a; and see —

e. The genuine Three-Part Song-form. Review par. 50, and see —

In the following examples of the 3-part Song-form, the Third Part is a more or less accurately transposed recurrence of the main contents of Part I: *

70. A very effective variety of the 3-Part Song-form is obtained, on the basis of the idea expressed in par. 48a (second clause), by introducing in Part II a Counter-motive in more animated rhythm.

a. This implies that the original Motive should be of a rhythmically quiet or stately form, with correspondingly quiet counterpoint during Part I.

* Homophonic Forms, par. 110.

The characteristic Counter-motive of Part II may be nothing more than an ordinary contrapuntal associate, in shorter note-values. But it is not unlikely that its figures may be generated, by Diminution, out of parts of the Motive itself and, in either case, it should be treated to a certain extent as an "Auxiliary motive," i.e., recurring, entire or in part, from time to time (freely modified, if necessary), in order to avoid the impression of desultory rambling. For example (Bach, 3-voice Invention No. 7):

b. If the characteristic Counter-motive in quicker rhythm is to distinguish Part II especially, it will be abandoned at the beginning of Part III, and the latter will resume the original fundamental rhythm, — possibly only for a few measures, however; for the animated rhythm is quite likely to assert itself again, either in the later course of Part III, or in the Coda or Codetta, which, in such definite structural designs as these, is almost indispensable. The first of these alternatives is illustrated in the continuation of the above example (Bach, 3-voice Invention No. 7), thus:

The Song-form with Trio.

71. As intimated in par. 68c, an extension of the sectional line of development to an abnormal length is not unlikely to resolve itself into that broad homophonic design of three Divisions, the third of which is a more or less exact "Da capo" (recurrence of the first), thus isolating the second Division somewhat, — like the "Trio" of certain dance-forms.

EXERCISE 21.

Distinctions of "Style" in the Invention.

72. Distinctions of Style are necessarily less definite in polyphonic than in homophonic composition; not only because Polyphony is, in itself, so characteristic a "style" as to counteract the assumption of other specific style-distinctions, to a large degree; but also because the peculiar restrictions of polyphonic writing render it difficult to realize all the essential details of certain (especially the conventional) styles.

But the broader distinctions of style may, nevertheless, be exhibited definitely enough in an Invention (or any other polyphonic form for at least three voices), as far as these distinctions rest upon the choice of tempo, mode, rhythmic character, and similar general qualities; or upon the melodic character of the Motive; and it is therefore entirely feasible, as it is desirable, to distinguish at least three broad divisions of polyphonic style, namely:

a. The Light or Spirited style (with its kindred qualifications, sprightly, joyous, vigorous, brilliant, capricious, flowing, etc.). The chief characteristics of these species are a comparatively brief Motive, of lively, flowing, gay, or rhythmically capricious (distinctly individualized) character; fairly rapid tempo; probably (though by no means certainly) the major mode; and general brightness and vivacity of expression.

For example: Bach, 3-voice Inventions, Nos. 8, 6, 1, 10, 14, 15; Well-temp. Clavichord, Vol. II, Prelude 5.

b. The Serious style (with its kindred qualifications, grave, somber, stately, pathetic, etc.), characterized mainly by a Motive of stately or even heavy character, generally brief; quiet or moderately slow tempo; generally the minor, though not infrequently the major, mode; and subdued, dignified expression.

For example: Bach, 3-voice Inventions, Nos. 4, 9, 13; Well-temp. Clavichord, Vol. I, Prelude 18; Vol. II, Preludes 9 and 17.

c. The Lyric (melodious) style; characterized by a M. of distinctly melodious nature, and generally of considerable length, — often in regular (4-measure) Phrase-form; graceful, flowing tempo; major or minor mode indifferently; and unusual definiteness of structural design.

For illustration: Bach, 3-voice Inventions, Nos. 7, 12, 3, 2 (the last-named is to be thoroughly analyzed; it is largely episodic); Well-temp. Clavichord, Vol. II, Prelude 4.

d. Another, scarcely less genuine, variety of the Lyric class, is distinguished by a brief Motive, or simple thematic Figure, out of which (1) the broader lyric sentences are sometimes constructed, by sequential combination; or which (2) enters still more incidentally into the lyric texture, apparently as a mere figural accompaniment (or auxiliary Figure) derived from the successive harmonies that underlie the principal melodic lines.

Exceptional Species of the Invention.

73. a. The Invention in Contrary motion ("per moto contrario"). In this species the Motive appears throughout in nearly, or quite, regularly alternating original motion and Contrary motion.

See Bach, Prelude of the "Preludio con fughetta" for Clavichord, in e minor (Peters ed. 200, No. 7). The thematic texture is exclusively two-voice, but an auxiliary third part is frequently introduced. — Bach, Organ Comp. (Peters ed.), Vol. VII, No. 58, measures 1–7, 11–18, 22–28; in measures 32–40 a similar association of the original M. with its Diminution and Contrary motion is effected.

b. The Invention with an Independent Lower part. The thematic manipulation is restricted, largely or wholly, to the inner and upper parts; and the Bass accompanies these, chiefly as an auxiliary contrapuntal associate. The latter may (1) be based upon some more or less characteristic figure, usually reiterated regularly, as in harmonic figuration; or (2) it may be a Running part, in a uniform rhythm of two (or more) notes to each beat.

The first species is most common in Organ music; the peculiar difficulties and limitations of Pedal-technique render it often expedient to assign certain adapted figures to the Pedal-part, either quite independent of the Motive, or as a modified (simplified) form of the latter.

In either case it is absolutely necessary to preserve a certain (if not constant) uniformity of melodic delineation in the independent Bass; especially when it is a running part, which must be prevented from deteriorating into a "rambling" part by consistency of formation,— i.e., by frequent recurrences, sequential or otherwise, of the leading figures. Review par. 17c. For example:

EXERCISE 22.

CHAPTER VIII. 
The Invention for More than Three Voices.

74. As the number of polyphonic voices or parts is increased, the texture assumes a proportionately pronounced harmonic character; and the difficulty of preserving proper balance between the dissonances of friction, inevitable in the "independent conduct" of the parts, and the consonances indispensable to their "harmonious union," becomes more and more real and severe. Review par. 59, and par. 60.

Details of Four-Voice Polyphony.

75. a. As before, the sum of 4 parts may be successively accumulated by adding contrapuntally first a second voice, then a third, and finally the fourth voice, to the leading part, — in such order as appears most convenient, and generally in brief stages of about five or six beats at a time. Review, thoroughly, par. 61b.

b. Or, probably better and easier, the three other voices may be led more nearly, or exactly, abreast of the leading part, and of each other; their movements will then be controlled directly by the successive harmonic structures, or chords (i.e., the vertical clusters of essential tones, which are to represent the successive rhythmic pulses); and the vital condition of voice-independence must be satisfied at the same time by judiciously disguising these harmonic clusters. Review, thoroughly, par. 61c.

The choice between these two processes will probably be determined by individual disposition; some students will find the "cumulative" process easier, while others will prefer the "harmonic" one.

c. The importance of the Tie, and of parallel movement in 3rds or 6ths between two of the parts, is as great, here again, as in three-voice texture, and must not for an instant be lost sight of. Review, thoroughly, pars. 61d and [par.] 61e; also par. 61f.

d. The rules relative to the conduct of the lowermost part, to the rhythmic conditions of the polyphonic texture, and to the adoption of a temporary leading part, apply without modification also to the association of four contrapuntal parts. Review, thoroughly, pars. 62, [par.] 63, and [par.] 64; also the summary, par. 65. Especial care should be taken to avoid too great density of texture. To this end, it is wise to sustain the rhythm of at least one of the voices as much as possible,— as shown in Ex. 122 (Note *4); and, at all events, to avoid conducting all the parts together in (simultaneous) rapid rhythmic movement, or in any fashion that produces a "jumbled" rhythmic effect.

e. The condition which probably increases most in significance, in this fuller species of polyphonic writing, is that of the Rest; not only because the temporary cessation of one (or more) of the voices conduces to greater variety of volume, and to greater clearness of texture; but also because it facilitates, very materially, the manipulation of the whole. On the other hand, the indispensable discipline of strictly 4-voice Polyphony obliges the student (for a time, at least) to abstain from such frequent use of Rests, — especially protracted omission of one or another of the four parts, — as would reduce the present task to that of the 3-voice texture. Review, particularly, pars. 63b and [par.] 63c.

For illustration of the domination of the harmonic principle, and the methods of preserving voice-independence, etc.:

Analyze the following specimens of 4-part Polyphony; very minutely, but only with reference to the voice-conduct, — not thematically:

Bach, Well-temp. Clav., Vol. I, Fugue 1, last 7 measures; Vol. I, Fugue 12, last 6 measures; Vol. I, Fugue 14, last 9 measures; Vol. I, Fugue 17, last 8 measures; Vol. I, Fugue 18, last 10 measures.

Bach, Well-temp. Clav., Vol. II, Fugue 5, measures 1–16; Vol. II, Fugue 9, measures 1–9; Vol. II, Fugue 23, measures 14–27.

The Four-Voice Invention.

76. Review par. 37. — When four polyphonic parts are used, they are always named Soprano, Alto, Tenor, and Bass, in analogy with the vocal quartet. Review par. 66a.

The structural designs are somewhat more limited, — in keeping with the other specific limitations of 4-voice Polyphony; hence, while any of the forms already enumerated may be adopted for the 4-voice Invention, the Sectional form is probably the most appropriate and effective.

The First Section, or Exposition.

77. a. The Motive must, as a rule, be brief, comparatively narrow in compass, and of quiet (or at least not too lively) rhythmic character. The following Motives are used by Bach for 4-part development:

See also Ex. 120, Nos. 1 and 120-2; and Ex. 122.

b. The first announcement of the M. may occur in any one of the four parts; and, as usual, one or two, or possibly all, of the other parts may supply auxiliary lines (either contrapuntal, or simply harmonic) until their turn comes to imitate the M. legitimately. Review par. 67a, [par.] 67b, and [par.] 67c.

c. The order of Imitations at the beginning of a 4-voice Invention may be regular; i.e., each successive Imitation may appear in the part nearest (adjacent) to the preceding imitating voice; thus, after Soprano, in the Alto; after Bass, the Tenor; after Alto, either Soprano or Tenor; after Tenor, either Bass or Alto.

But this regularity of voice-succession is by no means necessary in the Invention, and the utmost freedom is exercised in the choice, both of the interval of Imitation, and of the voice in which the Motive is next to appear, — not only at the beginning, but through the entire Exposition. Compare par. 67d; and see also par. 67e.

For illustration:

78. The remaining Sections of the 4-voice Invention are conducted in the usual manner. Review par. 68; and analyze the following Inventions, in sectional form, very diligently:

EXERCISE 23.

A. Write a 4-voice Invention, in brief sectional form, in minor; with an original Motive, patterned after those shown in Ex. 121. Especial reference must be made to par. 64 (Leading part); Ex. 122, Note *4) (sustained parts); par. 61d (Ties); par. 63b, [par.] 63c (Rests). The Imitation in Augmentation, and also in Diminution (par. 31a, [par.] 31b), are both available in 4-voice texture, and must not be neglected.

B. A 4-voice Invention, sectional form, in major.

Other Structural Designs.

79. Besides those in sectional form, occasional examples of the 4-voice Invention are found in the 2-Part or 3-Part Song-form. For example, see —

80. The fullness and weight of 4-voice Polyphony leave less opportunity for distinctions of style than were definable in 3-voice texture, and therefore the Serious or Stately style is almost the only consistent variety (par. 72b).

a. But it is possible, by such use of protracted rests as will virtually reduce the texture to three voices, for a time at least, to realize the lyric, and even the moderately spirited styles. This is ingeniously illustrated in Bach, Clavichord Sonata (Peters ed. No. 213), No. I. "Gigue."

b. Another device, very common in the 4-voice Invention, and especially effective in the lyric style, is the adoption of a brief thematic Figure, which is carried through the several voices more as an incidental than as an essential motive, and merely enlivens what is actually a definite harmonic stratum. Compare par. 72d. This was seen in Bach, Well-temp. Clavichord, Vol. I, Prelude 12, cited above.

In organ music the association of three thematic parts with an independent Bass (pedal-part), as explained in par. 73b, is effective and not uncommon, — especially in connection with the elaboration of a chorale melody (to be considered later on).

See Bach, Organ Compositions (Peters compl. ed.), Vol. V, Nos. 1, 14, 16, 38, 56, and others.

The Five-Voice Invention.

81. An Invention for 5 parts is naturally rare. When so elaborate a polyphonic apparatus is employed, it is mostly in the service of the higher grades of Polyphony. It is, however, easily possible to expand the 4-voice to an ostensible 5-voice texture, by the occasional addition of a 5th part, with entire freedom as regards register, though usually in thematic form. The M. should be brief, narrow in compass, and of quiet, if not heavy, rhythmic formation; the style will probably be lyric, or stately.

See Bach, Well-temp. Clavichord, Vol. II, Prelude 11; M. of 4 notes, Soprano, reproduced twice in same voice, in Contrary motion, before the regular Imitations begin. The design is genuine 3-Part Song-form; Part I ends in measure 16, an is followed by a complete sequential reproduction, before Part II appears (in measure 33). Texture largely 4-voice. Analyze minutely.

Bach, Organ Comp. (Peters compl. ed.), Vol. IV, No. 12. — Same Vol., No. 11, second Division (Grave); M. 2 measures, Soprano; observe, also, the frequent ascending scale-passage, in whole measures.

EXERCISE 24.

CHAPTER IX. 
Free Polyphonic Forms. — The Invention as Prelude. — The Fantasia, Toccata, Etc.

82. In a genuine Invention the principle of thematic Imitation prevails with little or no interruption; for though it represents the lower grade of polyphonic writing (par. 37), it is nevertheless Polyphony; the thematic development is of primary, the structural design of secondary, importance. In Homophony this relation of qualities is reversed,— the material subserves the Form.

But it is not always possible, or desirable, to separate these two domains of musical thought absolutely, and many intermediate varieties exist, in which a mixture (or the alternation) of the two ruling purposes is exhibited. Thus, the Invention may very gradually deteriorate from its original polyphonic rank, — as the thematic treatment becomes more and more loose and free, and the episodic passages more extended and independent, in the pursuit of some more and more marked structural purpose, — until it becomes partly (at times totally) homophonic in character and effect. And, on the other hand, a genuine homophonic form may, by the interlineation of more or less assertive and extensive imitatory passages, assume a partially (at times distinctly) polyphonic character.

Examples of such intermediate grades have been quite frequently cited in the preceding pages, and in some instances their classification among the "Inventions" has been doubtful, — in exact proportion to the increasing importance attached to all essentially structural (formal) conditions. See, especially, pars. 45, [par.] 51, [par.] 53, [par.] 72, [par.] 80b.

It appears, therefore, that this primary division of the polyphonic forms, for which the collective term "Invention" has been adopted, embraces a number of subordinate varieties, inclining more or less positively toward the homophonic domain, and distinguished by certain peculiarities of design or treatment.

The Prelude.

83. As its name indicates, the Prelude was not, originally, a separate and independent composition, but always an adjunct of some legitimate form (or of a collective set of pieces), in the inferior capacity of a preliminary or introductory movement.

The inferiority of rank thus involved is exhibited in many and various ways: either in looseness of form, or in freedom of technical detail, or both; in frequency, extent, and homophonic quality of episodes; in indifference to the number of parts,—the frequent employment of purely auxiliary tones or melodic fragments, and free interchange of 2, 3, 4 (or more)-part texture; or in a certain general superficiality and sketchiness of character, suggestive, in extreme cases, of a mere improvisation.

Such a form, consisting mainly in a free exposition of the principal harmonies of the key, perhaps with thematic allusions, may very appropriately precede, and prepare the hearer for, the more definite design and thoughtful contents of the principal movement to follow.

The degree of inferiority depends mainly upon the function assigned to the Prelude; and likewise, while the species of texture (homophonic or polyphonic), and the general style (lyric, dramatic, brilliant, etc.), are almost entirely optional, they may be partly definable according to the character and quality of the principal movement with which the Prelude is connected.

a. The treatment of the Prelude is, as a rule, most serious when it precedes the Fugue. In this connection it is likely to be a genuine Invention, entirely (or largely) polyphonic. Generally it bears no other relation to its Fugue than that of key; — time, tempo, Motive, and character may be independent of the latter, though occasionally the M. of the Prelude is derived from the Subject of the Fugue.

The latter (thematic) coincidence does not appear in any of the 48 numbers of the Well-temp. Clavichord, excepting, perhaps, in Vol. I, No. 23 (B major), where a faint, probably accidental, resemblance between the first 4 notes of the Prelude and of the Fugue, may be traced. In the 6 numbers of Mendelssohn’s op. 35, also, there is no thematic connection between Prelude and Fugue, save a brief coincidence in No. 4 (A♭). On the other hand, see Rubinstein, op. 53, where thematic connection is obvious between Prelude and Fugue in Nos. 1 and 6; and, more incidentally, in Nos. 3 and 4.

Generally the Prelude to a Fugue ends with a complete cadence on the Tonic, becoming thus a separate piece, virtually independent of its Fugue. In rare instances, however, especially when the Prelude is brief, and of a looser, more extemporaneous character, it closes with a Dominant semi-cadence, leading, as Introduction, into the Fugue.

b. The Lyric Invention, with a long, melodious Motive (pars. 53, [par.] 72c), belongs properly to the Prelude variety; and when the lyric purpose so overshadows the polyphonic that evidences of thematic imitation are faint, and incidental in effect, it becomes ultimately a Prelude as Aria, with, at most, occasional imitatory traits in the accompanying parts.

See Bach, Well-temp. Clavichord, Vol. II, Prelude 24, 14; Vol. I, Prelude 13, 8. The extreme limit of this design is touched in the following—almost distinctly homophonic—Preludes of the Well-temp. Clavichord: Vol. II, No. 12; Vol. I, No. 10 (with long Coda, as Toccata, — par. 84), No. 1 (simple chord-figuration); Vol. II, No. 3, first division (the same).

c. The Chorale-Prelude is an organ composition, designed to precede the congregational intonation of the opening chorale in the Lutheran and other Reformed church-services, chiefly in Germany. Hence its M. is derived recognizably from the first line of the chorale, and the treatment is usually distinctly, sometimes severely, imitatory, as in the Invention; though evidences of the freedom of design and treatment characteristic of the Prelude-species are seldom wanting, and sometimes so pronounced as to lower the Prelude to the rank of a mere Chorale-Fantasia, — especially in practical expositions, which are quite commonly actual polyphonic improvisations, i.e., made extempore.

Examples of this form will be cited in Chapter XI.

d. The Prelude as opening number of a Suite is more independent than any of the foregoing, and may be isolated, as well as any other number of the Suite. In this respect it resembles, and probably was the incentive to, the variety treated at [par.] 83e below.

It relates to the succeeding numbers of the Suite solely in point of key; and its texture may be selected, at option, from the whole range of Polyphony; very rarely, indeed, however, is it any more severe than the genuine Invention (Bach, English Suite No. I); most commonly it is of the looser fabric of the "Prelude"-species (as in Bach, English Suite No. VI, first 37 measures; Bach, Prelude to Suite, Peters ed. 214, pages 32, 33, — first 15 measures introductory); sometimes of a general imitatory character, without manifest thematic development (as in Händel, Suites Nos. V, VI, VIII; Bach, Sonata, Peters ed. 213, pages 4, 5; same volume, pages 20, 21); possibly still more nearly, or absolutely, homophonic (as in Händel, Suites Nos. I, III; Bach, Prelude to Suite, Peters ed. 214, pages 18, 19).

The Prelude as "Fantasia" is touched upon in par. 85.

e. The modern Prelude, as isolated piece. The propriety of the title Prelude is apparently cancelled by isolation, for its relation as "Prelude" to a subsequent movement is uncertain, if not utterly chimerical. But it is nevertheless possible to institute close analogy with the legitimate Prelude-form, by preserving such traits as distinguish the latter, or, at least, imply its origin in that early era of musical history which gave rise to the conventional Prelude. The modern isolated Prelude will therefore usually be found to exhibit some traces of this origin, in remnants of the polyphonic bearing of earlier centuries; in the presence of certain scholastic details which suggest (if they do not constitute) "imitation," "contrapuntal treatment," or other distinctive traits of the traditional Prelude; particularly in the absence of that dominating romantic expression, significant of the modern conception of music. For example:

Further, the title "Preludes" has been assigned by several modern writers to a series of 24 pieces in each of the 24 major and minor keys, partly in analogy with the design of Bach’s Well-temp. Clavichord; and also partly because this device supplies the pianist with a piece (presumably brief, and either extemporaneous and sketchy in character, or of the traditional "prelude" consistency) in every key, and therefore actually available, if desired, as preliminary sentence to any number upon a concert-program, — as far as the relation of key is concerned.

The Toccata.

84. This is one of the earliest forms of instrumental music, and derived its name from the primitive mechanical act of manipulating the keyboard (toccare, to touch). Originating thus, long before instrumental music had assumed any of its present definite structural designs, the early Toccata was a formless succession of figures and runs, sometimes purely harmonic, again imitatory and contrapuntal, often incoherent and indefinable. It was the legitimate forerunner of the Fantasia, but has retained its own title to the present day, and has gradually developed into a somewhat more definite and characteristic style, the basis of which is the manipulation of a small Motive, or mere brief Figure, usually of but two or three notes, — possibly strictly polyphonic, as in the genuine Invention, — much more commonly, however, only partly polyphonic, or even purely homophonic; generally in lively, vigorous tempo.

a. The Toccata as single movement:

b. The Toccata sometimes appears as collective form, of three, four, and even more distinct divisions, or movements. In this broader and more elaborate design it usually comprises as many distinctions of style as there are divisions, and is therefore a composite of Invention, Prelude, Toccata, Fantasia, — very frequently including also the higher Fugue-species, — in apparently optional succession.

The Fantasia.

85. This is of still less definite and definable form and consistence than the Toccata, though in many respects closely connected with the latter in origin and character. It is, as its name indicates, a fanciful combination of tone-effects. Irregularity of design, freedom of melodic and rhythmic treatment, and generally incoherent character, are therefore almost essential conditions of the species; at the same time, the domination of a central tonality, occasional concurrences of style (corroboration of former sections), and the evidences of at least a broadly consistent progressive design, cannot be wholly dispensed with.

The texture of the Fantasia, as a whole, is more likely to be homophonic than polyphonic, though the latter style is frequently adopted for certain sections, — probably in unconscious imitation of the technical conditions under which, centuries ago, the Fantasia came into existence.

Mixed Forms, of a General Imitatory Character.

86. Finally, there is a very numerous class of musical forms which are neither definitely homophonic nor polyphonic, but a mixture of both; partaking of the characteristics of the Invention, the Prelude, and the Fantasia, though not strictly to be classified as any of these.

Such mixed forms rest upon a homophonic basis, and therefore exhibit distinct harmonic and melodic traits, and, generally, well-defined form. The polyphonic elements are exhibited, side by side with these, and more or less sparingly, in incidental imitations, or a general imitatory bearing, quite different from that continuous thematic development of which Imitation is an essential factor,—the essential condition of the genuine Invention, as has been seen, and, in a higher degree, of the Fugue and Canon, as remains to be seen.

Homophonic Forms with Polyphonic Episodes.

87. A mixture of the polyphonic and homophonic styles, of still another kind, is obtained by introducing brief thematic imitations, or complete thematic sections, into a composition of distinctly homophonic character and otherwise unalloyed homophonic texture.

Such incidental polyphonic episodes may occur in the course of a homophonic design (as, for instance, during the Second Part of the Three-Part Song-form); or the form may begin, like an Invention, with genuine thematic imitations, which extend for a few measures and then gradually (or even abruptly) relax and yield to pronounced homophonic treatment; or, more rarely, the polyphonic texture may be adopted near the end, as a means of promoting interest or creating a climax, — or as basis of the Codetta. For illustration:

Additional Miscellaneous Examples.

EXERCISE 25.

---

DIVISION THREE. CHORALE-FIGURATION. 
Introductory.

89. Chorale-elaborations are divided, according to their magnitude, and certain distinctions of treatment, into two classes known as the Small Species and Large Species.

CHAPTER X. 
The Small Species of Chorale-Figuration.

90. In the small species the adopted chorale melody (called the cantus firmus) is placed in the uppermost part, as regular Soprano, and in its original metric condition, without extensions or interruptions. The exercises are to be written for the Organ, and therefore the lowermost part is for the Pedal keyboard, while the upper three parts are placed on two staves for the Manual keyboard (generally one, possibly two).

The student who is unfamiliar with the technique of the Organ must first obtain at least a general insight into the treatment of the Manuals and Pedals, before undertaking the present tasks. The only information that can be given here is, that the compass of the pedals is, generally, as follows:

and that the tones of two adjacent manual-parts should always be well within reach of one hand.

Elaborate Harmonization.

91. As the basis of this species of polyphonic texture is again mainly harmonic (see par. 75b), the student had best begin with experiments of a specifically harmonic nature, and make a number of chorale harmonizations, as ingeniously as possible and elaborately as desired, in ordinary 4-part writing (with or without Pedal-bass), after the manner of the following:

Bach, Organ Comp. (Peters compl. ed.), Vol. V, No. 36 (analyze thoroughly); end of No. 53; page 60, I; page 68, I; page 76; page 105. — Further, Vol. V, No. 27.— Vol. VI, No. 26 (5-voice). — Vol. VII, No. 53 (chorale melody extended by rests before and between the lines; imitatory, but not thematic).

Thematic Accompaniment.

92. The number of parts ordinarily employed is four: the cantus firmus, two inner parts, and the Pedal bass.

a. The three lower (accompanying) parts — including the Pedal — are to be thematic; that is, a Motive (or brief Figure of one or two beats) is adopted, and imitated in the usual manner, as contrapuntal harmonization, or Figuration, of the given chorale. The cantus may be written in [quarter]-notes, with a thematic figure (below) in [16th]-notes; or in [half]-notes, with figure in [8th] or [16th]-notes. Or, these values dotted ( or time).

For illustration (beginning of a chorale):

b. The usual harmonic process must be pursued, more or less insistently, in defining the chord-basis of each beat or tone of the cantus firmus; but the effect of the accompanying (figural) voices must be thoroughly polyphonic.

Much liberty may be taken with the adopted Motive; as a rule, it should be present constantly, in some part, in some shape or other, — Ex. 124, Note *3); though it may, briefly, be replaced by episodic fragments, either derived from the M., or independent.

It is not necessary to have a separate chord for each tone of the c.f. The same chord may be held through two successive tones, or more; or the harmony may change within one c.f. tone. Modulations, both diatonic and chromatic, must be freely made, and may be as swift as is compatible with perfect smoothness.

The Pedal-part should be kept somewhat more quiet (sustained) than the inner parts. See also Ex. 124, Note *4).

The end of each "Line" of the chorale is designated by a [fermata]; this, however, merely serves to mark the lines, and is not to be respected, in the Small species, — no check of the rhythmic movement is to occur, anywhere. At the same time, these final tones ([fermata]) should produce a certain cadential impression, and therefore they should, as a rule, be harmonized with some triad, in fundamental form.

At the end, the thematic rhythm runs on, a beat or so (usually in one or both of the inner voices), past the final c.f. tone. Or, better, the final tone may be expanded to a whole measure, or more, while the lower parts effect a plagal ending.

The following illustrations are to be analyzed very thoroughly and minutely:

Bach, Organ Comp., Vol. V, No. 22 (M. in Alto, one beat); No. 48 (M. in Tenor, one beat); No. 33; No. 32 (M. in Pedal, two beats); No. 5; No. 2 (M. in Pedal, two beats); No. 4, verse II (M. in Tenor, four beats); No. 47 (manuals only); No. 31 (M. in Pedal, four beats, divided into two definite figures; inner parts largely episodic).

Table of German Chorales, for Use During This Entire Third Division.

N. B. It is not obligatory to use the keys here given. The chorales may, sometimes must, be transposed to other, higher or lower, keys.

Same as 17, but in (-measure:

A similar transformation of any (-measure chorale into measure may occasionally be made.

EXERCISE 26.

Independent Pedal-Part.

93. Partly for the sake of effective variety, and partly on account of the limitations of pedal-technique, it is quite common to conduct the Pedal-bass independent of the inner thematic voices. This is done (1) either by so modifying (simplifying) the Motive as to adapt it better to the character and technique of the pedals; or (2) by adopting an independent (auxiliary) figure for the bass, in more sustained rhythm. See par. 73b; Ex. 119; and the following:

Bach, Organ Comp., Vol. V, No. 1; No. 13 (inner parts thematic, but largely episodic); No. 14; No. 16 (running Pedal-bass); No. 28 (entire Pedal-motive 3 measures long); No. 38 (very characteristic Pedal); No. 40; No. 46; No. 50 (Augm. of Motive, in Pedal; observe rhythmic form of c.f.); No. 54; No. 55 (Pedal-motive, a simplified form of figural motive); No. 56 (M. in Pedal related, but longer); No. 4, Verse 3.

Brahms, "Choral-Vorspiel" (and Fugue) in a minor.

Embellished Cantus Firmus.

94. Although it is characteristic of the present task to restrict the c.f. to the exact form of the original chorale, it is, nevertheless, both natural and desirable (especially in actual practice) to modify certain tones of the given melody by means of unessential passing- or neighboring-notes.

a. Such embellishment of the c.f. may be limited to strictly unessential auxiliary tones, introduced here and there in order to facilitate the thematic development, but not altering or obscuring the original chorale tones. Or it may consist in occasional slight changes of the original even rhythm, by means of dots. For example:

Bach, Organ Comp., Vol. V, No. 22 (already cited); No. 25 (Pedal indep.); No. 49 (ditto); No. 41 (c.f. embellished thematically, i.e., according to figural Motive; Pedal, simplified form of M.); No. 53 (compare with above Table of Chorales, No. 22; the modification of the c.f. oversteps, somewhat, the present limit. Compare, also, with reference to the c.f. only, the preceding and following numbers of Vol. V — Nos. 52 and 54).

b. Or the modification may extend to a systematic ornamentation of the chorale melody, involving all (or nearly all) of the original tones, and resulting often in a richly embellished form of the c.f., to which the lower parts, though usually thematic, appear to constitute a subordinate accompaniment. This variety of elaboration will be considered in detail further on (par. 107).

Motive Derived from Chorale.

95. The motive of the thematic accompaniment may be, and very frequently is, derived from the first line of the c.f.; usually by simple Diminution of the first group of (three or four) tones; or by unessential figuration of them. Thus:

More elaborate forms are shown in Ex. 128

See Bach, Vol. V, No. 21 (contrapuntal associate retained throughout); No. 12 (ditto).

96. Finally, each of the three accompanying (figural) parts may have its own, separate, motive. Each should be sufficiently characteristic, especially in its rhythmic form, that of the Pedal-bass being naturally the most sustained; and they are likely to differ in length. Each part announces its motive independently, and without necessary regard to regular association with the others.

In Bach, Vol. V, No. 9, the following 3 Motives are manipulated, more or less independently of each other:

Analyze the whole number thoroughly, and see also Bach, Vol. V, No. 11 (less thematic than "figural"; Alto and Tenor appear to coöperate in announcing a composite motive, or figure, of one or two beats; the Pedal is independent, and not obviously thematic). — No. 17 (somewhat similar; inner parts coöperate; Pedal plainly thematic).

EXERCISE 27.

A. Write a 4-voice example, with Independent Pedal-part, according to par. 93. Select chorale from the table given in Exercise 26.

B. An example with slightly embellished c.f., as in par. 94a.

C. An example with a Motive one measure long, derived from the c.f.; par. 95.

D. An example with separate M. for each part; par. 96.

Three-Voice Elaboration.

97. When two parts only are added to the c.f., they are most likely to be an inner and lower part for the manual keyboard; though a Pedal-bass is of course possible.

The following specimens are all somewhat peculiar, especially those in which the c.f. is placed in a lower part, instead of in the Soprano. Analyze carefully:

Bach, Vol. V, No. 30 (c.f. in Soprano, slightly embellished; running inner part; Pedal independent). Vol. V, page 81 (Var. VI) — cantus firmus in Pedal-bass. Vol. V, page 86 (Var. IX) — cantus firmus in Pedal, as inner voice; two motives-

Five-Voice Elaboration.

98. For this an Alto, two Tenors, and Pedal-bass are added to the c.f. The motive is apt to be brief, and rests may be freely used. See par. 81.

EXERCISE 28.

One or two examples each of the 3-voice and 5-voice chorale elaborations.

---

CHAPTER XI. 
The Large Species of Chorale-Figuration.

First Variety: Invention With Chorale.

99. In this larger and more elaborate species, the thematic or figural voices are the chief, essential factors, while the chorale melody is (at least apparently) an incidental factor. The first Line of the c.f. is preceded by an introductory exposition of the Motive; similar thematic Interludes occur between the Lines of the chorale; and a more or less lengthy Postlude follows the final Line. Hence the chorale melody has the appearance of entering incidentally, when convenient, into the thematic texture, while the lower parts pursue the imitatory development of the adopted Motive (precisely as in the Invention), as aim and burden of the entire composition.

Of the Large Species there are several varieties, the first and simplest of which is called "Invention with Chorale."

Cantus-Firmus in Soprano.

100. This — as in the Small Species — is the most natural, and probably most common, location for the chorale melody (c.f.).

a. The Motive is usually at least a measure long, often much longer. It may be invented "free," i.e., independent of the c.f., and in that case it is wise to select some melodic progression (of two or three tones) that occurs frequently in the course of the chorale (as, for instance, the tone-repetitions in chorale No. 24 of the above table), and invent the Motive as characteristic counterpoint to that figure; this ensures its availability at these points, at least.

b. But it is somewhat more likely that the Motive will be derived from the first Line of the c.f., — possibly, though rarely, from the last line, or even some other (striking) line of the chorale. The derivation may be simple, as shown in Ex. 126 (which see). Or it may be elaborate; for example, all the following motives (and many more) are derived by Bach from the first line of the same chorale [Table, No. 18]:

c. Not infrequently, two or even three Motives are used (par. 52).

d. The introductory measures, or "Prelude," are a regular Exposition of the Motive, as in the Invention, and subject to the same rules (par. 40); but a cadence is not made, as a rule, until the c.f. (the first line of the chorale) has entered and has been conducted to its end.

The first tone of each line of the c.f. must be some chord-interval, but may be either consonance or dissonance (7th, 9th, etc.). The final tone of each line may be Root, 3rd or 5th of the chosen triad, but the latter must be fundamental (Root in Bass).

The c.f. should not be modified, excepting by an occasional, strictly unessential, passing-note; or by some other equally harmless change.

Care must be taken not to proceed into a new chord or key so soon after the final tone of each c.f. line, as to leave the latter (after its cessation) an implied dissonance; that is, the final tone should, for at least a full beat after its conclusion, appear (in the hearer’s recollection) to harmonize with the thematic voices, and fade away in their subsequent conduct.

e. The end of each "Line" is, practically, the termination of a Section of the Invention, — though a definite cadence is not obligatory. Each succeeding Section begins with an "Interlude," devoted to continued thematic development in the figural voices while the c.f. voice pauses; very similar in character and conduct to the "Prelude," but more free. The length of these Interludes is optional; usually a measure or two, often more, — the c.f. reëntering, each time, when convenient. Review par. 99.

f. The very last tone of the c.f. (the final tone of the last line) should be a Root, if possible. The voice which has the c.f. — the Soprano, in this instance — may, after prolonging the final tone a few beats, join in the thematic elaboration, usually beginning its participation with an announcement of the Motive. This extension, the "Postlude," may be of any reasonable length.

101. In executing the task, the thematic (or figural) parts and the c.f. (when the latter is present) may be carried along abreast of each other, with constant regard to the announcements of the Motive; or the M. alone may be inserted, beforehand, in one part and then another, where it promises to agree well with the c.f. — somewhat after the manner of leading parts (par. 64, which review).

At all events, the Motive should appear very frequently, if not incessantly, in some part or other; and therefore great freedom may (must) be exercised in rendering the M. adjustable, by altering the quantity of its interval-progressions (rarely, however, by changing its rhythm, excepting for possible Augmentations, complete or partial).

Contrary motion, shifted rhythm, and stretto Imitations are to be freely employed.

The Pedal-bass should be conducted, in general, more quietly than the manual parts. It may, occasionally, be independent (par. 93). Progressions in alternate opposite direction, with or without skips, are peculiarly adapted to pedal-technique:

For general illustration of the process (No. 16 of the above Table of Chorales; Motive in large notes):

EXERCISE 29.

Cantus Firmus in Bass.

102. When used as lowermost part, the c.f. is written for the Pedals, of course. The final tone of each line must be a chord-root. Especial care must be taken to avoid implied dissonance for a beat or more after the cessation of each final tone (review par. 100d, last clause). All other details correspond precisely to those given above (pars. 100, [par.] 101).

For general illustration (chorale 22 of the Table):

Cantus Firmus in Tenor.

103. The general details agree exactly with those given for the Soprano.

a. The c.f. may be written in the Tenor part in the usual manner; but it is desirable, and customary, so to arrange the parts that the chorale melody may be made prominent by being played upon a separate (louder) manual of the organ. In this case it stands alone on the middle staff, and, during its presence, the two thematic voices above it (Soprano and Alto) must be so written that they are playable together with one hand (i.e., within the compass of an octave). During the Prelude and the Interludes, this restraint is, of course, removed.

b. Or, the c.f. may be assigned to the Pedals (written in Bass register), and played with a 4-foot stop, so as to sound an octave higher, — i.e., in Tenor register. The middle staff then belongs to the Bass proper, and care must be taken to keep it below the c.f. (Tenor), as a rule; and, being played with the hand, it may be more free and lively than an ordinary Pedal-bass.

Cantus Firmus in Alto.

104. This is rare, especially in 4-voice counterpoint. Rules the same as for Soprano.

Cantus Firmus in Alternate Voices.

105. Successive Lines of the chorale may be assigned to different voices; or, if definite 2- or 3-Part Form, different voices may assume the successive Parts. Or, at any point where it appears desirable or convenient, a change of voice may be made, — never, however, during a Line of the chorale.

On the termination of its share of the c.f., the voice in question may (as at the end, during the Postlude — see par. 100f) immediately join the contrapuntal parts, usually, here again, with an announcement of the Motive.

The voice to which the c.f. is next to be given must rest during the whole (or a good portion) of that Interlude.

The choice of voice for the c.f. is wholly optional; but some attention is due to technical considerations; and the voices should be so written that, if possible, the c.f. may be played upon a separate manual, — when not in the Pedal-bass (comp. par. 103a).

EXERCISE 30.

Second Variety: Chorale as Invention-Group.

106. This variety differs from the preceding only in that a new Motive is devised and used for each Line of the chorale in succession. Consequently, each Line appears to constitute a complete brief Invention by itself, usually with a fairly decided cadence; and the whole is a group of Inventions.

As a rule (though not necessarily), the Motives are each time derived from the corresponding (following) Line of the chorale. They will, therefore, be independent; but they should all agree with each other pretty closely in character, especially as concerns their rhythmic formation. The first Motive may be reverted to, incidentally, at any moment. All rules as before.

EXERCISE 31.

Two or three examples (minor and major) of the above variety.

Third Variety: Chorale as Aria.

107. This species of manipulation differs considerably from the specifically polyphonic elaborations of the chorale-accompaniment, inasmuch as it affects, chiefly, the chorale-melody itself, while the accompanying voices may be simply of a general imitatory character, or nearly (or quite) homophonic. Review, thoroughly, par. 94, especially [par.] 94b.

The main object is, so to embellish the c.f. tones with auxiliary notes (passing-, neighboring-notes, etc., in florid rhythmic form) that the original stern chorale-melody is completely transformed into a graceful (though dignified and impressive) lyric melody or "Aria." This dissolution of the c.f. must be so effected, however, as to preserve the original rhythmic disposition of the tones, i.e., the distinction of accented and unaccented tones, as closely as possible, — so that the ornate product, reduced to its tonal elements (at accented points), would correspond nearly to the original chorale. Hence, while the embellishment may include many additional tones (perhaps distant from the given ones), and may tend to shift certain of the given tones past their primary place at the beginning of their respective beats, it is rarely justifiable to evade the tone altogether, or to shift it entirely beyond its beat, into the next; and it is still more rare to anticipate a given tone, by shifting it back into the preceding beat. At the same time, it will be found possible to exercise considerable freedom, totally eradicating all resemblance to the chorale, and still preserve the fundamental melodic design of the original.

The chorale-Aria is almost always placed in the Soprano; the lower accompanying parts may be purely homophonic, — slightly figurated, — or imitatory, without being thematic; or, more rarely, they may adopt and manipulate a Motive, as in the 1st Variety. The Pedal-bass is frequently independent, and of a quiet rhythmic character.

For illustration of the treatment of the chorale: [Original (Table, No. 18).]

Further:

Fourth Variety: Ritornelle with Chorale.

108. In this variety the Motive (or, more properly, Theme) is much longer than in the foregoing; generally a complete 8-measure Period, or extended Period, or even Double-period. It is frequently a sort of running voice, in nearly or quite uniform rhythm; but sometimes a lyric melody of striking, impressive character. It may be invented entirely free, or (as is more common) may be derived from a Line or two of the c.f., as an elaborate embellishment and radical modification of the latter.

This Theme appears as an introduction (or Prelude), usually with complete perfect cadence; recurs, generally at its full length, as an Interlude (once or twice, according to the length of the chorale), and again as a Postlude, — hence the term "Ritornelle." During the chorale lines it is present in fragments only.

See Bach, Organ Comp., Vol VI, No. 2; 3-voice: c.f. in Soprano; Pedal independent. Vol. VI, No. 17; 4-voice; c.f. in Bass; long Theme, in Tenor; upper two parts constantly imitatory. Vol. VI, No. 3; 2-voice, no Pedal; c.f. in Soprano; M. from c.f, treated with great freedom. Vol. VII, No. 44; 3-voice; c.f. in Pedal, as Tenor; quasi running parts, independent rhythms. — Brahms, Choral- Vorspiele, op. 122, No. 4; c.f. in Sopr.; 4-voice; Ped. indep. — No. 7; c.f. in Sopr. and Bass alternately; 3 to 6-voice. — No. 10; c.f. in Ped. as Tenor; 4-voice.

Fifth Variety: Chorale-Fantasia.

109. The c.f. may consist of a portion, or portions, of the original chorale, instead of the whole; possibly of one or two characteristic lines only; or even of certain distinctive members of the lines (naturally the very beginning, or ending, of the chorale). These may appear in optional succession and frequency, generally in different parts, and in different keys and registers.

The accompanying voices may be conducted with great freedom; they are generally imitatory, but not necessarily thematic; and are likely to contain many, more or less disguised, allusions to the chorale.

The form is optional, but is most likely to be sectional, or "group," design. A certain progressive structural idea should be embodied, as general outline, and one or more effective climaxes introduced. Review, carefully, par. 85.

EXERCISE 32.

Sixth Variety: Chorale-Invention, or Prelude.

110. See par. 83c. In this variety the chorale, as c.f., does not appear. The whole is an Invention (as chorale-Prelude) of the usual character, based upon a Motive, or Motives, derived from the first Line of the chorale (or from some other characteristic Line).

Chorale Variations.

111. A number of different elaborations of the same chorale, in the various methods shown above, may be associated as a set of Variations. The manner in which the Varieties of manipulation are chosen, and the number of variations collected, are subject to no rule; but decided contrast (especially in reference to rhythm and measure) must be obtained; and the interest should be progressively increased, by choosing the more elaborate and effective species for the final numbers.

See Bach, Organ Comp., Vol. V, pages 60–67; 68–75; 76–91. Mendelssohn, Organ Sonata, op. 65, No. 6, movements one to four (up to the Fugue). Brahms, Motet, op. 74, No. 2; chorale in first verse, with contrapuntal accomp.; the following 3 verses (II, III, and IV) are elaborations with the c.f. (more or less embel.) in different voices.

EXERCISE 33.

DIVISION FOUR. 
THE FUGUE.

Introductory.

112. The Fugue differs from the Invention chiefly in being a more strict and serious contrapuntal form. Review par. 37. While the Invention is subject only to the general conditions of contrapuntal treatment, the Fugue, on the other hand, involves certain special conditions and limitations.

These special qualities, which distinguish the Fugue, are as follows:

(1) The Subject or Theme of a Fugue is usually more extended, and has a more definite form, than the "Motive";

(2) The Subject is first announced alone, in a Fugue, unattended by auxiliary tones;

(3) During the first Section, or Exposition, the Subject is (as a rule) announced alternately in the Tonic and Dominant keys, i.e., it is imitated alternately in the 5th and 8ve; and

(4) There is, throughout, less freedom of detail, and greater seriousness of character and manipulation.

The Fugue-Subject.

113. The thematic germ of a Fugue is called "Subject" or "Theme."

The former term is used in a specific sense; the term "Theme" as a general designation of the thematic basis.

a. It is, with rare exceptions, definite in form, being either a complete Phrase or (more rarely) Period, and closing as a rule with a distinctly cadential effect. Its length is optional, — from one large measure (Bach, Well-temp. Clav., Vol. I, Fugue 17) up to 6, 8, or even more measures (Bach, Well-temp. Clav., Vol. II, Fugue 15; Organ Comp., Peters compl. ed., Vol. III, Fugues Nos. 3 and 8).

b. Generally it begins either upon the 1st, 3rd, or 5th scale-step of the key; but in any case the Tonic note should appear near (if not at) the beginning. It may begin upon an accented beat, or upon the preceding unaccented beat; but by far the best and most common practice is to begin the Subject with a brief rest, i.e., immediately after an accent (Ex. 134).

It ends, frequently, upon the 3rd scale-step, or upon the Tonic (more rarely upon the Dominant), of the principal key; or upon the Tonic or 3rd step of the Dominant key. Other cadences are possible, but very rare. The final tone falls usually upon an accented beat, and produces a decided cadential impression; but there are exceptions to this rule, and it is sometimes difficult to determine precisely where the Subject terminates (see Bach, Well-temp. Clav., Vol. I, Fugue 9,— doubtful whether the Subject ends on 3rd beat of second measure, or on 1st beat of third measure). The Subject may contain transient modulations, in its course, but can scarcely end in any other than the principal, or the Dominant, key; possibly in the Relative major, from minor.

c. As Subject of a Fugue, and as complete melodic sentence, it should be distinctly individualized. Its melodic and rhythmic contents must be serious, but characteristic, and pregnant (susceptible of manifold polyphonic manipulation); and its delineation must be distinct and moderately striking, — to the exclusion of vagueness, of a too lyric melodic form, but also of eccentricity. Sequences are seldom absent, in good Subjects; the harmonic basis is clear, natural, and forcible; and there is usually at least one salient rhythmic feature (an effective tie, syncopation, or contrasting figure). The compass of effective Subjects seldom runs beyond an octave. Review par. 38a.

EXERCISE 34.

The Construction of the “Response.”

114. As stated above, the Subject or Theme is to appear, during the first Section (the Exposition) of a Fugue, first in the principal key, then in the Dominant key, and so on, alternately in the Tonic and Dominant registers, as far as the number of voices dictates.

The first announcement (tonic) is called the Subject proper; the second announcement (dominant) is called the Response or Answer.

115. In order to place it in the Dominant key, the Subject must be imitated in the perfect 5th above (or perfect 4th below). Hence, the fundamental rule for the construction of the Response is:

To imitate each tone of the Subject in the perfect fifth.

This gives what is known as the "real" Response or Answer. For example:

*1) The adjustment is perfect, and no circumstance exists which would necessitate an exception to the fundamental rule.

116. But this strict imitation often gives rise to awkward or abrupt modulation, and a lack of adjustment at the extremes (beginning or end) of the Response. The element invariably involved in such embarrassment is the Dominant. Hence, the first general exception to the fundamental rule is:

That the Dominant element, wherever peculiarly conspicuous in the Subject, is to be imitated in the perfect fourth, instead of 5th.

a. This applies (1) to the Dominant tone at the very beginning; or (2) near the beginning (as 2d, 3rd, or 4th tone of the Subject, especially when connected with the Tonic note); (3) to all tones inseparably connected with this initial Dominant (as embellishment, repetitions, and the like); (4) to a strong Dominant chord-impression at, or very near, the beginning; (5) to the cadence in the Dominant key (at the end of the Subject); and (6) to all tones that pertain inseparably to this final Dominant. All such tones should be imitated in the perfect 4th.

This is called the "tonal" Response.

117. a. The Dominant note at the beginning. For illustration:

*1) The Dominant note at the very beginning would, if answered in the perfect 5th, transfer the Response abruptly, and bodily, into the Dominant key (c minor). Thus:

The first tone, g, would not adjust well with the cadence tone of the Subject (a♭). In a word, this initial g is the Second-dominant (Dominant of the Dominant) in the key of f minor thus far pursued; and while this comparatively remote tone, or any other, can be reached in time, it is certain to sound abrupt at the very beginning of the Response. Therefore the above Subject is imitated as follows, the first (Dominant) tone in the 4th, and the remainder, as usual, in the 5th:

By this means the Response is retained for an instant in the original key, until perfect adjustment, at the beginning, is secured. It is called the "tonal" Response because of this (at least temporary) adherence to the tonality of the Fugue; the Tonic elements being answered by the Dominant, and the Dominant elements (where salient) by the Tonic (imitation in the 4th).

*1) All large notes indicate the imitation in the 4th; the small notes that in the 5th.

b. The Dominant note near the beginning:

This always applies to the Dominant as second note of the Subject, when it follows the Tonic; and, in case the initial Tonic note is embellished, it may be the 3rd or 4th tone of the Subject. Thus:

c. Repetitions or embellishments of the Dominant, at or near the beginning:

Or, adding to this last Theme (Ex. 139-3) various embellishments of the initial Tonic (as in Ex. 138), the results would be:

d. A cluster of tones at (or very near) the beginning, that constitute a very obvious Dominant chord:

e. As declared in par. 116a (3), all tones that pertain inseparably to the Dominant at or near the beginning of the Subject, share with it in the exception to the rule. To this class belong the repetitions and embellishments illustrated in Ex. 139; also a diatonic run from the initial Tonic down to the Dominant; thus:

Possibly also the nearly continuous run from Tonic up to Dominant

This comes under the head of Ex. 140; but there is a subtle distinction between it and Ex. 140, No. 4 (which it closely resembles), that is left to the student’s analysis.

f. Finally, the Dominant key, at the end of the Subject, when introduced by a palpable modulation, is subject to the exception. Thus:

g. The puzzling questions can, in many instances, be determined only by carefully testing the effect, and preserving a good, smooth, modulatory and melodic result. The trouble consists, as stated, simply in deciding which tones are inseparably connected with the Dominant; and this may depend upon the melodic structure, the modulation, rhythm, or other circumstances bearing upon the characteristic formation of the Subject as a whole. Therefore, the ultimate decision is, here and elsewhere, very often indeed a matter of common-sense judgment, or individual taste.

118. Partly in keeping with this last idea, and partly for general reasons, a third rule must be observed, which constitutes in a sense an exception to the rule of tonal imitation (par. 116), and therefore reverts partially to the fundamental rule, namely:

Under no circumstances shall any characteristic feature of the Theme be violated.

Consequently, neither the real nor the tonal imitation can be insisted upon at any point where they threaten any tone or figure of the Subject that is significant or characteristic. For illustration:

119. The single Dominant note at the end of a Subject is not to be imitated in the 4th (tonal), unless it is strongly suggestive of the Dominant key, or Dominant chord:

120. a. When the Theme begins with the Dominant note, and also ends in the Dominant key, it may be possible, and necessary, to imitate the initial Dominant in the 5th. Thus:

*1) As the Dominant key has already been reached, there is no danger of imperfect adjustment, and therefore the "real" imitation is entirely feasible.

b. Further, when the Dominant effect prevails decidedly through the whole or a great part of the Theme, it may be necessary to imitate it in the 4th throughout. Thus:

In both of these cases all that is not actually Dominant appears to be inseparable from the prevailing Dominant effect.

Miscellaneous.

[ed. note: The A♭ on beat 4 of measure 3 in example 149-3b is almost certainly a typesetting mistake, meant to be A♮. I have used A♮ in the audio example.]

EXERCISE 35.

CHAPTER XII. 
The Four-Voice Fugue. — The Exposition.

121. The Exposition or first Section of a Fugue contains as many announcements of the Theme (Subject and Response alternately — par. 114) as there are parts employed. In the 4-voice Fugue the order is, therefore (when regular), Subject, Response, Subject, Response.

a. The first Response may begin simultaneously with the final tone of the Subject (Bach, Well-temp. Clav., Vol. I, Fugue 8). Or immediately after the Subject ends (Vol. I, Fugue 6). Or still a little later, so that one or more tones must be added to the Subject, as intervening figure (Vol. I, Fugue 1, one intervening tone; Vol. I, Fugue 2, ditto; Vol. I, Fugue 12, two intermediate tones; Fugue 11, three tones; Fugue 3, four tones; Fugue 7, seven tones, — more than this number could scarcely be justified). Or, more rarely, the Response may enter before the cadence tone of the Subject, as brief stretto (Vol. I, Fugue 9; the Response overlaps the Subject one beat, possibly three, — the length of Subject is somewhat uncertain).

b. In the third of these possible cases, where intermediate tones are used, the latter must be carefully chosen, in keeping with the conduct of the Subject, and with a view to their subsequent employment as thematic basis of the episodic passages (as in Vol. I, Fugue 7).

122. The first counterpoint — that which follows the Subject in the same part, as contrapuntal associate of the Response — is sometimes called the "Counter-subject"; as this term is misleading (in the Single Fugue), it will be spoken of here simply as the "Counterpoint." Comp. par. 34.

It is a very important factor in the Fugue (or may become so), and especial pains must, therefore, be taken with its formation. It may be derived from the figures of the Subject itself:

*1) Both of these figures of the Counterpoint are derived from those of the Subject, in contrary motion. See also Bach, Well-temp. Cl., Vol. II, Fugue 5.

Or the Counterpoint may be more or less independent of the Theme, its conduct being governed by the general conditions of good contrapuntal association.

Or it may assume a characteristic rhythmic or melodic form, in intentional opposition to the current of the Response, or as a wholly individual factor of the entire Fugue. Thus:

*1) The Counterpoint is admirably individualized by the line of sequences. See further, Bach, Well-temp. Cl., Vol. I, Fugue 18, similar; Vol. I, Fugue 2— rhythmic contrast with the Theme; Vol. I, Fugue 12; Vol. II, Fugues 10, 11, 16, 20 (rhythmic), 22 (chromatic).

In any case, but especially in the last mentioned, the first Counterpoint is more than likely to reappear from time to time in connection with later announcements of the Theme, as part of the thematic material of the composition; and this possible use must be kept in mind, and must emphasize the thoughtfulness and strictness of technique with which the Counterpoint is to be devised. It is well to make several experiments, in various styles, and choose the most promising version.

EXERCISE 36.

123. These and the succeeding announcements of the Theme, during the regular Exposition, are determined by the following formula:

1. Subject, — in either one of the four parts;
2. Response, — invariably in the next higher or next lower part;
3. Subject, — in the parallel part to that in which the Subject first appeared, an octave higher or lower than the former announcement;
4. Response, — in the remaining part, i.e., the parallel to the part in which the first Response appeared, and an octave higher or lower than the latter.

In other words, the Subjects appear in parallel parts, and the Responses, likewise, in the other parallel pair of parts.

124. In some, comparatively rare, instances the Exposition is irregular, for some valid reason, and in one of the following respects:

(1) The order of the parts;

See Bach, Well-temp. Cl., Vol. I, No. 1, — the order is, Alto, Soprano, Tenor, Bass, instead of Alto, Soprano, Bass, Tenor; i.e., the 3rd announcement is not in the parallel of the first part.

(2) The alternation of Subject and Response;

See, again, Fugue 1, Vol. I; the order is Subject, Response, Response, Subject (the second announcement of the Subject is in the parallel of the first part, but occurs too late — as fourth voice). See also Vol. I, Fugue 12; Subject, Response, Subject, Subject, in Tenor, Alto, Bass, Soprano. — Vol. I, Fugue 14; Vol. II, Fugue 17.

(3) The number of announcements, which may be more (very rarely less) than the total number of parts.

The "extra" announcement is rare in the 4-voice Fugue, though common in the 3-voice. See Bach, Well-temp. Cl., Vol. II, Fugue 17; the Exposition is irregular, as already seen; and a 5th announcement ("Subject") is added in Bass, meas. 13–15. Vol. II, Fugue 23, extra announcement (Bass), in meas. 19–22. Bach, Org. Comp. (Peters compl. ed.), Vol. II, Fugue 3, extra announcement, somewhat abbreviated, in Bass, meas. 45–49. Vol. IV, Fugue 2.

125. a. After the first Response (second announcement of the Theme), an episodic interlude of one or more measures is generally inserted, partly by way of variety, but chiefly as a means of modulating back into the original key, and preparing for the next announcement of the Subject. The episode must, of course, be strictly in keeping with what precedes, and is usually derived directly from it. Review par. 41b. For illustration, Ex. 150 continues thus:

b. As a rule, there is no further episodic interlude (in the 4-voice Fugue) before the last (4th) announcement of the Theme, — the last Response. But when the latter is finished, an episode, more or less lengthy, is almost obligatory, as a means of establishing the key in which, at this juncture, the Exposition is expected to close. It is during this final episodic passage that an extra (5th) announcement of the Theme (as "Subject," probably) may occur. See par. 124 (3).

126. The Exposition ends, as a rule, with a perfect cadence in the Dominant key (from a major beginning), or in the Relative key (from a minor beginning). Other keys, especially the original key itself, are possible, however, and not infrequently chosen. The perfect cadence is often (perhaps most commonly) made fairly strong, by the emphatic succession V–I in Bass, Tonic in Soprano, on an accented beat. But sometimes it is much lighter; and occasionally it is so transient and indefinite that the actual close of the Exposition can be defined in a general way only, or not at all. In no case, however, no matter how strong the harmonic form of the cadence may be, is any decided check of the rhythmic movement permissible. Review par. 40h.

The Fughetta.

127. The Fughetta is a small Fugue, containing no more than one Section (the Exposition, possibly extended by one or two extra announcements of the Theme); or perhaps two Sections, — the Exposition and one additional Section. In the first of these cases, the Exposition must terminate with a strong perfect cadence in the original key.

EXERCISE 37.

The Sectional Form.

128. The Exposition (first Section) is an essential and characteristic factor of this form of composition, appearing in every genuine Fugue, no matter what its subsequent development (its design as a whole) may be.

That which follows the Exposition, however, is not (as a rule) subject to any further specific conditions, — excepting such as may be involved in some "special design" of the Fugue as a whole (to be considered further on). The constraint of special rules is relaxed; in the second Section, and other following ones, it does not matter how often the Theme appears, in which parts, nor on which scale-steps. The subsequent conduct of the Fugue may be as free as that of the Invention, always excepting that a certain dignity and general seriousness of style should be maintained. After the Exposition the writer is free to realize more definite structural purposes; to carry out more extensive modulatory designs; to develop the thematic resources of the subject, both as a whole, and in its component figures; and to pursue some broad (quasi dramatic) design, leading in successive stages to effective climaxes, at, or near, the end.

129. The most convenient and common design for the Fugue is the simple Sectional form; for this provides the most natural means for the simple progressive development of the resources of the Theme. Review par. 39.

The number of sections is optional (from 3 to 6 or 8). Their cadences, and the modulatory design of the whole, correspond to the directions given for the Invention.

130. a. The second Section may begin with an announcement of the Theme, in any part, and in any next-related key, preferably the one in which the Exposition closed.

See Bach, Well-temp. Cl., Vol. I, Fugue 16 (meas. 12); Fugue 18 (meas. 11).

And, as already stated, this section, and all which follow, may contain as few or as many successive announcements as appears convenient or desirable, — as a rule, however, not in the same part twice in immediate succession.

b. Or the Section may begin with a carefully planned Episode. This seems to be the best and most common practice.

c. Such an episode is likely to acquire a certain independent importance in the Fugue, and to reappear, in the same section or in later ones, — not literally, but in the same general thematic form; in different keys, naturally, and in various inversions. This is the case with the episodic passages in general.

See Bach, Well-temp. Cl., Vol. 1, Fugue 17; the episode in meas. 11 (with sequence in following measure) reappears in meas. 14, 15, and 19, 20, each time in a different key, and with inverted parts. Also Vol. I, Fugue 14; similar episodes in meas. 7, 18, and 28.

These recurrences of the episodic material not only institute well-defined variety (as opposed to the thematic announcements), but contribute to the unity and definite form of the whole. In some instances, especially in the broader organ fugues of Bach, the episodes assume an importance fully equal, if not superior, to that of the thematic portions, and lend (by their frequency, extent, and characteristic treatment) a very effective physiognomy to both form and contents.

See, for example; Bach, Org. Comp. (Peters ed.), Vol. III, Fugue 3; the episodes are constructed, throughout, in very similar fashion upon an auxiliary motive (derived from a figure of the Counterpoint); they appear in meas. 15–17, 25–28, 36–42, 50–56, 64–66 (new episode), 67–70, 78–80, 88–100, 108–114, etc., etc. Also Vol. II, Fugue 4; episodes after nearly every announcement of the Theme: meas. 7–9, 12–14, 18–21, 28, 32–36, 39–43, 47–50, 54, 57–65, 68–79 (similar to preceding one), 82–93 (ditto), 97–100 (like 47–50), 106–109 (like 32–36).

131. Each succeeding Section of the Fugue may (perhaps should) contain some new traits, — most naturally, new "Counterpoints" to the Theme. And each Section should be more interesting and effective than those which preceded. Therefore it is customary to introduce the contrary motion of the Theme, in later Sections; and, near the end, good stretto-imitations are desirable. Review, very thoroughly, par. 33 (Ex. 83).

132. As intimated above, it is quite common to retain the first Counterpoint, and to use it more or less constantly with later announcements of the Theme. This retention of the "Counterpoint" is not, however, to be too persistent in the "Single" Fugue, — such constant recurrence of a contrapuntal associate being a distinctive condition of the "Double-fugue," as will be seen.

It may be retained during the Exposition only; perhaps recurring from time to time in later sections; or it may be abandoned after the first Response, and recur later; it may be used entire, or in part; and may be modified to any extent.

It occurs in Bass (meas. 3), recurs in Tenor (meas. 4–5), and Alto (meas. 6). It reappears episodically (without the Theme) in Tenor (meas. 8). In meas. 11–12 it appears, somewhat modified, in Tenor; and immediately afterward in Soprano, curiously modified thus,

EXERCISE 38.

Additional Miscellaneous Directions.

133. Review, thoroughly, par. 41a and par. 61a. As repeatedly shown, and confirmed by the analysis of the authoritative contrapuntal works of Bach and other great polyphonic writers, the original source of all multi-voice music is the chord; and the prime impulse of all associated voice-movements is, obviously, the natural law of chord-succession (par. 18). For a certain period, the choice of tones and the melodic movements will be, and must be, dictated by the rules of chord-progression; the voices or parts cling, for a time, to the harmony for their support, as children (so to speak) are led by their older and stronger associates. But the time finally arrives when (in the growing experience and skill of the student) the "voices" outgrow this guardianship of fundamental harmonic law, and exercise greater independence in their movements; and, in fact, the exercise of independent melodic will may become so imperative as to reverse the conditions, so that the parts dictate the chord-successions. In other words, as the student’s command of melodic conduct increases until he can trace the course of three or more simultaneous melodic parts unerringly, so that each part by itself is a perfect melody, moments will arrive when these individual voice-movements will determine the succession of harmonic nodes, called "chords"; when, instead of the parts moving obediently towards the several harmonic points fixed by each succeeding chord (in the pre-defined order of natural chord-progression), the parts themselves assume the lead, and dictate what the chord-successions shall be. For if each part describes a faultless melodic line, and the parts harmonize, the result will be acceptable and legitimate, whether it conforms to the common law of chord-sequence or not.

For example, the chord-successions in the following examples cannot be satisfactorily defined in accordance with the common rules of chord-progression; and yet the result of the three or more associated melodies is good.

When this result is achieved, the product belongs to the highest grade of polyphonic thought. But it is scarcely conceivable that this lofty phase of polyphonic effort can be often reached or long sustained; even in the works of Bach and Brahms, unmistakable evidences of emancipation from natural harmonic law are rare; in those of Beethoven and other great homophonic masters, naturally still more so. And in the more modern writings of Wagner, Rich. Strauss, and others, where such evidences are again more frequent, one cannot always quite escape an uncomfortable sensation of harmonic bewilderment. The growing vigor and independence of melodic conduct may incite to occasional successful rebellion (so to speak), but the student will never wholly outgrow the necessary and wholesome habits of harmonic action contracted during early studies. The habits formed during the discipline of deriving all melodic movements from the sub-current of natural harmonic sequence, will, in polyphonic texture of greatest power and stability, never cease to assert themselves.

Hence, the present student will apply this most eminent resource of polyphonic development chiefly as a means of defining the choice between many possible chord-structures which await each coming beat; and far more rarely, with much caution, as a legitimate device for obtaining unexpected harmonic clusters, and evolving greater freedom and opulence of harmonic movement. Review, further, pars. 59 and [par.] 60; and, particularly, pars. 61c, [par.] 61d, and [par.] 61e. Also par. 75.

134. a. The voice-movements should be conjunct, in largely preponderant measure. Skips, of course, can not and should not be avoided altogether; but they must be made with caution, and may require careful testing. They are always good when occurring within any unchanged chord, or when the first of the two tones is common to the following chord. It is best to avoid leaping to any sharply dissonant, or inharmonic, tone.

Transient harsh effects, even extreme, cannot be precluded; they are as essential in effective polyphony as are the pure consonances; but the manner of their approach and departure must be very guarded, — abrupt dissonances are usually objectionable.

b. Review, thoroughly, par. 64. It is absolutely necessary that one of the four parts should assume the lead, for a more or less extended period, — until another of their number becomes in turn the "leader." This function devolves, naturally, upon the part which has the Theme, though not to the exclusion of some concurrent part, especially Soprano or Bass, — one of which is very likely indeed to contribute most noticeably, in this way, to the tracing of the Form.

A good illustration of this vital condition is seen in Bach, Well-temp. Cl., Vol. I, Fugue 22, meas. 6–12 in Soprano. See also Vol. II, Fugue 18, meas. 85–93 in Bass. Vol. II, Fugue 9, last 6 measures in Soprano.

Mendelssohn, Organ Fugue, op. 37, No. 1, — the "leading" character of the Soprano, especially, is obvious in many places; see meas. 18–19, 20–22, 41–45. Without such definite, and, if need be, lengthy melodic lines, a Fugue can hardly escape monotony, diffuseness, and vague, ineffective form.

c. For this very reason, sequences are of the utmost importance. Review par. 41c.

d. Review par. 63b and [par.] 63c; par. 75e. It is well to avoid long rests during the Exposition, until the four parts have all appeared with the Theme. Short rests are always good (Bach, Well-temp. Cl., Vol. I, Fugue 23, meas. 5–6); especially in the Theme itself (Vol. II, Fugue 22), or in the first Counterpoint (Vol. I, Fugue 12). And longer rests are not only permissible, but desirable, in the later course of the Fugue. It is positively unwise to keep all four parts constantly present and moving.

e. In the Exposition avoid any circumstance that tends to obscure the successive announcements of the beginning of the Theme.

Observe how effective the entrances of the parts are in Vol. II, Fugue 9 and Fugue 8. In Vol. II, Fugue 7, the last note in meas. 6 interferes somewhat with the Response in the next. Observe, further, the entrances in Mendelssohn, op. 35, Fugue 1, especially in meas. 6.

f. The character of the Subject influences its Exposition to a certain extent. A heavy Theme is somewhat likely to appear first in Bass or Tenor (i.e., low). A Theme that ends higher than it begins must appear first in a high voice, to avoid interference with its next imitation, and vice versa.

The tempo of the Subject must be taken into account also; it influences the number of parts, the number of rests, the degree of liveliness (or of stateliness) in the rhythm of the first Counterpoint, and, in fact, of the entire Fugue; and, somewhat, the number, extent, and quality of dissonances. Attention is again directed, particularly, to par. 33.

Continue the work of thorough analysis with the following sectional 4-voice Fugues:

EXERCISE 39.

Write a large number of 4-voice Fugues, in sectional form; major and minor alternately; different species of measure, different style and tempo for each example.

The Song—Forms.

135. The Two-Part Song-form. The chief difference between this and the sectional design is the distinctly marked cadence (usually perfect) in or near the middle of the Fugue.

The First Part is likely to consist of the Exposition, and one additional section; the latter may be brief and largely episodic, or it may be longer and more independent; but in either case it leads into a well-prepared and fairly emphatic cadence in the Dominant key (possibly the Relative major, in a minor Fugue, or some other next-related key).

Part II is often individualized to some extent; most commonly by adopting the contrary motion of the Theme (for a time), or by means of a new and characteristic Counterpoint. At the same time, Part II may (perhaps should) exhibit more or less distinct parallelism with its First Part, — especially in its episodes; and, as usual, the last few measures may corroborate the ending of Part I. A Codetta or Coda may be added. Review par. 45.

136. The Three-Part Song-form. Part I the same as in the 2-Part Song-form. Part II is here again generally characterized in some manner; and is led into a more or less distinct semicadence upon the Dominant of the original key, usually confirmed by an emphatic (sometimes quite extended) organ-point.

Part III must be, as usual, a well-marked "Return to the beginning"; but it does not need to contain any more than the first few measures (two or three) of Part I, — enough to establish key and formal design; its subsequent contents are likely to be entirely independent, and should be more elaborate and interesting than any preceding Section; hence, stretto-imitations are peculiarly appropriate, and more brilliant (even partly homophonic) episodes are legitimate and desirable. A Coda or Codetta is frequently added. Review pars. 49, [par.] 50; also [par.] 33.

EXERCISE 40.

A number of 4-voice Fugues in the 2-Part and 3-Part Song-forms.

The Fugue with Special Design.

137. No good Fugue is barren of some structural design, as the foregoing paragraphs show. But it is possible to pursue some special plan in the manipulation of this polyphonic form, evolved more particularly out of the resources of its Theme, and therefore peculiarly identified with the processes of Thematic Development.

The formal plan is usually that of the sectional Fugue; and the "special design" consists in assigning to each Section in succession some specific method of thematic treatment, resulting in a systematic presentation of such possibilities of manipulation and combination as are latent within the Theme (e.g., effective stretti, contrary motion, etc.). These possibilities, or resources, are usually determined beforehand by most thorough examination and experiment with the Theme; and it is more than likely that these resources may be systematically multiplied by judicious revision and alteration of the Subject, — possibly created outright in draughting the Theme.

Review Chap. IV; especially pars. 29, [par.] 33, [par.] 36.

Analyze, most thoroughly, the following:

EXERCISE 41.

Two or more Fugues with Special Design.

---

CHAPTER XIII. 
The Fugue with Less or More Than Four Parts. — The Three-Voice Fugue.

138. The Exposition. The three parts are called lower, inner, and upper, without reference to voice-compass, though they are likely to represent adjacent registers. The regular Exposition contains Subject, Response, and Subject (comp. par. 123), the last Subject always either an octave higher or lower than the first Subject.

The enlargement of the Exposition to four announcements is, however, quite common in the 3-voice Fugue; the last announcement is again "Response," usually an 8ve lower or higher than the first Response.

See Bach, Well-temp. Cl., Vol. I, Fugue 19; the 4th announcement is made noticeable by the peculiar leap in Bass (meas. 5–6).

Vol. I, Fugue 8 (meas. 12). Vol. II, Fugue 11 (meas. 21). Vol. II, Fugue 19 (meas. 7).

139. The Theme of a 3-voice Fugue is likely to be of a more spirited rhythmic character, and possibly wider compass, than that of the 4-voice Fugue; otherwise there is no essential difference. The structural designs and all details of treatment are the same.

140. Sectional form. Review pars. 128 to [par.] 132, and analyze the following, most thoroughly:

141. Two-Part Song-form. Review par. 135, and analyze the following:

142. Among the many devices adopted for the characterization of the Second Part (the most common being the contrary motion of the Theme, pars. 48b, [par.] 51), there is one that is peculiarly effective in the Fugue, namely, the introduction of a new and striking Counterpoint, retained more or less constantly throughout the Part, as new thematic member. This process was touched upon in Ex. 156, which see. For illustration see —

143. The Three-Part Song-form. Review par. 136, and see —

144. The Special Design. Review par. 137, and see —

Bach, Well-temp. Cl., Vol. I, Fugue 8; the Exposition ends in meas. 19; Sec. II contains stretti, and a curious partial Augmentation (Alto, meas. 24–27); Sec. III meas. 30, is an Exposition of the contrary motion; Sec. IV, meas. 44, closely resembles Sec. II (in contrary motion); Sec. V, meas. 52–61, contains triple stretti in regular and contrary motion, and one regular (single) announcement of the Theme; Sec. VI, meas. 61–83, is an Exposition of the Augmentation (Bass, Alto, Soprano); the rest is an extremely beautiful Codetta. Vol. I, Fugue 15; Sec. I, Exposition, to meas. 20; followed by an Exposition of the contrary motion; and later, various stretti; analyze thoroughly. The episodic sections in this Fugue are very distinct, and corroborative of each other.

The 2-Voice Fugue.

145. The Fugue with two parts only is naturally rare, because such slender means are inadequate to the dignity and richness that distinguish this polyphonic form.

The Theme must be of a lively rhythmic character, and ample compass. Episodes are frequent and somewhat free (brilliant); and the occasional addition of an auxiliary part, or parts, is permissible, — almost necessary. See —

The 5-Voice Fugue.

146. The extra, 5th, part is either a second Soprano, second Tenor, or second Bass (rarely an additional Alto); and the compass as a whole is somewhat expanded, either by adding to the height of the usual Soprano, or the depth of the Bass, or both.

Review par. 123. The Exposition consists of Subject, Response, Subject, Response, Subject. The "Subjects" must be an octave apart; the "Responses" likewise. Parallel parts (those which are to announce the "Subject"), be it recalled, are separated by one (or three) parts.

Five-voice Fugues are seldom effective for the pianoforte, but entirely so for organ. In any case, however, it is desirable to use rests frequently; especially protracted rests which reduce the texture occasionally to 4-voice, or even 3-voice. Review, carefully, par. 134d and par. 75e.

The Subject is usually brief, stately, and narrow in range.

The very positive difficulties attending the addition of a 5th part may be minimized: (1) by preserving a perfectly distinct consciousness of the chord-basis, and the harmonic progressions in general; (2) by sustaining at least one of the parts upon some lengthy tone, important in the chord (as root), or in the key (Tonic, Dominant), — that is, by refraining from leading all the parts abreast, in active rhythm; (3) by using many parallel 3rds and 6ths and reciprocal figures, illustrated in Exs. 113 and [ex.] 114 (which see); and (4) by judicious use of brief rests.

For general illustration:

Analyze, very minutely, the harmony, thematic texture, and form of the following:

Fugue with Six and More Parts.

147. It is very uncommon to employ more than five parts in the Fugue, or any other strictly polyphonic form, not only because of the technical difficulty, but chiefly that of rendering the form intelligible. As the parts are multiplied, the style becomes more and more harmonic, and all voice-individuality is lost. The most effective device consists in so using protracted rests that, for the most part, no more than 5 of the voices appear at one time together. In any case, the extent will rarely exceed that of a Fughetta.

EXERCISE 42.

CHAPTER XIV. 
Miscellaneous Varieties of the Fugue-form. — The Concert-Fugue.

148. It is entirely feasible, and permissible, so to elaborate the Fugue-form that, without violating any of its essential conditions or materially modifying the dignity of its character, it may exhibit those qualities of brilliancy, passion, and freedom which better adapt it for public concert use, or, in a word, enhance its effectiveness and external beauty. Such a version bears about the same relation to the more genuine, serious Fugue that the Prelude bears to the Invention. Review par. 83.

The consequent relaxation of fugue law, and general freedom of treatment, will affect: (1) The Theme itself, which may be more characteristic; (2) the tempo, which is usually more lively; (3) the number of parts, — very frequently limited to three fundamental parts, but freely augmented by the occasional addition of auxiliary lines or whole "bunches" of auxiliary tones (incidental chords); (4) the episodes, which are both more frequent and more extensive, and often nearly or quite homophonic and "figural" in character; (5) the form, which is perhaps most likely to be definite 2- or 3-Part Song-form, with firm cadences, — often embracing purely homophonic (or at most "imitatory") transitional passages, or complete contrasting sections; (6) the dramatic design, embracing more pronounced dynamic and rhythmic contrasts, and the steadily progressive development of one or more brilliant climaxes.

The strictest fidelity to the Theme is, however, indispensable; not necessarily to the whole Theme, nor constantly, but to its pregnant or salient figures. This (the original Theme, entire, and in fragments), the contrary motion, possibly Augmentation, stretti, and an effective variety of "Counterpoints," constitute the thematic material of the Concert-fugue; to which are to be added striking episodes (as usual, largely corroborative of each other), and all the factors which contribute to an impressive dramatic design, as a whole, and brilliancy of detail.

149. The Concert-fugue seldom, if ever, appears as an isolated composition, but either as a movement of a larger work, or at least in company with an Introduction or Prelude.

The latter, as stated in par. 83a, may be connected thematically with the Fugue, or may be a totally separate piece, independent of the Fugue in every respect, excepting in key, which should be the same. Review par. 83a, thoroughly; and examine, again, the Preludes of Bach, Mendelssohn (op. 35, 37), and Rubinstein (op. 53).

EXERCISE 43.

The Fugue for Other Instruments.

150. For String-quartet. The four instruments used are first and second Violin, Viola, and Violoncello. Their notation and average compass are as follows:

The Viola is written in a C-clef (the so-called Alto C-clef), and the student, if not yet familiar with it, should embrace this opportunity of learning it thoroughly. In performing this task, the student should adopt the following system: The C-clef should be learned by itself, and not by comparison with, or reference to, the G- or F-clefs. That is, the name of each line or space must be independently mastered. The clef-sign ( ) indicates the letter c 1 (the "middle" c of the pianoforte). Thus:

After learning this perfectly, write familiar melodies or Themes in the new clef. Then read or play the Viola part alone of the String-quartets of Haydn, Mozart, and Beethoven. Then play, at the pianoforte, the String-trios of Beethoven, and afterwards the above-named quartets, slowly, and with less reference to the rhythm than to melody and general harmony. This being accomplished, the student may write a few fairly simple 4-part harmonizations of the chorales given in Exercise 26, upon the four staves of the String-quartet.

There is no essential difference between the Fugue for string-quartet and that for pianoforte, as regards the form and structural treatment. But the technique differs materially, because of the superior freedom and independence of the string-parts; hence, the parts may diverge, or cross, more freely. In a word, the constraint of keyboard technique is wholly removed.

151. The Fugue for Pianoforte and one or more Solo instruments (Violin, ’Cello, etc.) will derive its character and treatment from the technical nature of the instruments employed; but will be, in any case, more free and more effective than the pianoforte Fugue.

The Vocal Fugue.

152. The constraint of technical treatment is most imperative in the Fugue for vocal parts. The compass of each voice must be respected, constantly and rigorously; awkward intervals, rhythms, or any other circumstances which impair the melodiousness and "singable-ness" of the several parts, must be scrupulously avoided; and good balance of effect (excluding wide spaces, though not an occasional crossing of the parts) must be preserved.

The form should be fairly definite (strict) and intelligible. Episodes are necessary, but they must be of a more sober character than in the instrumental Fugue, and must be held well within the general thematic atmosphere of the Subject. Particular attention should be directed to the uppermost voice, which is mainly responsible for the clear and effective melodic form of the whole.

The Theme should always be a striking setting of some brief, pregnant text-sentence, — melodious, but rhythmically characteristic, — and it accompanies the same words throughout. The voices not occupied with the Theme, however, are generally written without regard to the text, — the latter being subsequently adjusted to the finished tones, with strict regard to grammatical sense and order, and to the correct prosodic disposition of accented and unaccented syllables and words.

Rests are indispensable; short ones for breathing, and occasional protracted silence (especially before an announcement of the Theme) for variety and contrast.

153. If, as is almost invariably the case, the Vocal fugue is to be accompanied, the instrument chosen (pianoforte or organ) may either be limited (1) to an exact duplication of the parts, unisono; or (2) may double either outer part, especially the Bass, in octaves, perhaps adding an occasional full chord to support the vocal parts where their effect is somewhat meagre; or (3) the accompaniment may add materially to the bulk, or to the rhythmic movement (or both), of the vocal parts,—even to the extent of introducing independent imitations and announcements of the Theme. Further, the accompaniment may provide a brief instrumental Introduction, occasional Interludes, and a Postlude, if necessary or desirable.

EXERCISE 44.

Fugue in Connection with Chorale.

154. Fugue with Chorale. This form corresponds in design exactly to the Invention with Chorale, but differs from the latter in that greater degree of seriousness and strictness which distinguishes the Fugue in general from the Invention. All the specific directions are given in paragraphs 99 to [par.] 105, which must be thoroughly reviewed.

The introductory measures (par. 100d) are usually a regular Exposition (par. 121, etc.), during the later course of which the chorale melody appears, in the part left vacant for the purpose. Thereafter the form is that of the ordinary sectional Fugue, into the texture of which the chorale Lines are successively interwoven, apparently as incidental addition, — though naturally they influence (or even dictate) the progressive development.

The Subject is almost invariably evolved out of the first Line of the chorale, with more or less freedom.

155. Chorale as Fugue-group. This is the parallel form of the chorale as Invention-group, explained in par. 106, which review thoroughly.

Out of each successive Line of the chorale a Subject is evolved; each Subject in turn is carried strictly through the parts, as Exposition, in which the chorale finally participates, as usual. Thus the whole constitutes a group or chain of Fugues (or Fugue-Expositions, — Fughettas), corresponding to the number of Lines in the chorale.

See Bach, Organ Comp., Vol. VI, No. 21; 4-voice; c.f. in Soprano, each time as last announcement of the Theme. — Vol. VI, No. 28; 4-voice; c.f. in Soprano, as Augmentation of Theme.—Vol. VII, No. 37; 4-voice; c.f. in Soprano, somewhat embellished, and each time as last announcement of the Theme; a new (10th) Motive for the Coda, in animated rhythm. — Vol. VII, No. 50; 4-voice; the last announcement of Theme each time in Bass, as Cantus firmus. — Vol. VII, No. 55; 4-voice; the Pedal is added as duplication of the Bass at end of each Exposition, to emphasize the c.f. — Vol. VI, No. 13; 6-voice; c.f. in 1st Bass, as Augmentation of the Theme; several thematic Counterpoints. — Brahms, Chorale-Vorspiele, op. 122, No. 1.— Brahms, Motet, op. 29, No. 1; 5-voice; c.f. in 1st Bass.

156. The Chorale-Fugue. Somewhat allied to the Chorale-Invention, par. 110, which review. The Subject, or Subjects, are derived from the first, or later, Lines of the chorale, and manipulated in the usual manner. But the chorale-melody, as such, is absent.

See Bach, Org. Comp., Vol. VI, No. 33; 4-voice; many stretti; two auxiliary, or episodic, Motives. — Vol. VI, No. 1 1; 3-voice; thematic Counterpoint in later Sections. — Vol. VI, No. 20; 4-voice; special design. — Vol. VII, No. 41; 4- to 5-voice; secondary Motive, derived from Counterpoint. — Vol. VII, No. 60; 4-voice; basso ostinato in Pedal (transposed recurrences); thematic Counterpoints.

A smaller variety, the Chorale-Fughetta, is illustrated in the following:

Bach, Org. Comp., Vol. V, No. 20; 3-voice. — Vol. V, No. 43, 3-voice. — Vol. VII, No. 61; 3-voice. — Vol. VII, No. 40c; 4-voice; Exposition in stretto. — Vol. VII, No. 54; 3-voice; the Subject, and two secondary Motives, are derived from three Lines of the chorale; Line 4 is intimated by the descending scale, constantly present in the Counterpoints.

The Group- (or Motet-) Fugue.

157. The Fugue-group is similar to the form described in par. 155) but is usually broader in design, and by no means necessarily identified with the chorale. Different Subjects — usually, though not necessarily, of similar character (and perhaps related in contents) — are successively, sometimes alternately, manipulated as separate complete Fugues (or Fughettas), more or less extensively and independently.

EXERCISE 45.

Irregular Fugue-Species

158. The Fugue in Contrary motion (per moto contrario). In this species the first and third Imitations of the Theme are made in Contrary motion, so that the 4-voice Exposition consists of the alternate "regular" and "contrary" motion (the latter standing each time for the usual "Response"). This arrangement may extend through the entire Fugue; or it may be confined wholly (or nearly) to the Exposition; and, further, the alternation may be more or less irregular (for instance, in the Exposition, or later, the regular motion twice, followed by the contrary motion twice; etc.).

The relation of the contrary motion to the original form of the Theme is generally that defined in par. 29a, particularly Ex. 72, which review. See also Exs. 73 and [ex.] 74. The Theme in contrary motion may be announced in the original key, or, as usual, in the Dominant key (by simple transposition to the upper 5th or lower 4th).

Analyze, thoroughly, Bach, "The Art of Fugue," Fugue No. 5. The Exposition runs as follows:

159. The Fugue in Augmentation, or in Diminution. In this species, which is very similar to the above, the Augmentation, or Diminution, of the Subject is substituted for the contrary motion; or, in rare instances, is combined with the latter.

See Bach, "Art of Fugue," Fugue No. 6; this is a 4-voice Fugue in "Diminution and Contrary motion"; probably 3 Sections and Coda; the Exposition begins thus:

160. The Fantasia-fugue. This somewhat contradictory term maybe justified in the case of those Fugues which begin seriously, and contain a more or less legitimate Exposition, but thereafter degenerate into a free, fantastic series of sections or sentences (passages), based upon fragments only of the Theme, possibly in distorted forms.

A beautiful and entirely defensible illustration occurs in Bach, Well-temp. Cl., Vol. II, Fugue 3; it is 3-voice, sectional form; the Exposition is in stretto, and Contrary motion (Subject in Bass, 1½ measure), ending in meas. 7; in Sec II (meas. 7–11) the 2nd half of the Theme is reconstructed; Sec. III (meas. 11–14) is episodic; Sec. IV (meas. 14–17) reverts to the original form of the Theme; the last Section (meas. 17 to the end) does not contain the original Theme entire, but is one long episode, or Fantasia (18 measures), in which intimations of the Diminution, Augmentation, and a unique mixture of other thematic fragments occur. — See also Bach, Clav. Comp., Peters ed. 216, No. 6, "Capriccio"; the purpose is evidently that of a Fugue, but the extensive episodic passages (quasi homophonic figuration), and the general treatment, make the title "capriccio" more appropriate.

Kindred forms are (1) the Recitative-fugue:

See Mendelssohn, Pfte. Sonata, op. 6, Adagio movement; no definite measure; 4- to 5-voice; large 2-Part form, with a homophonic (lyric) section as Interlude, and Postlude, in time.

and (2) the Harmonic fugue, i.e., a fugal thematic design, but of marked harmonic character, or with distinctly harmonic auxiliary parts.

See Schumann, op. 32, No. 4, "Fughetta." — Bach, Clav. Comp., Peters ed. 211, No. 3.

EXERCISE 46.

One example each of the Fugue in Contrary motion (par. 158), and the Fugue in Augmentation, — or in Diminution, at option, — (par. 159).

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CHAPTER XV. 
The Double-Fugue.

161. The Double-fugue is one in which two Subjects appear, and are manipulated, simultaneously.

It is not to be confounded with the forms cited in par. 52, par. 106, par. 155, and par. 157, in which two (or more) Themes are treated successively, each by itself for the time being; but takes its name from the fact that its thematic basis is a Double-theme — thematic duet.

It is not necessary that the two Subjects should always be together, for, as will be seen, either (or each) may be announced alone, or even have a separate Exposition; but, in order to achieve the idea and purpose of the Double-fugue, the Themes must appear in conjunction, distinctly, and during a reasonably extended section of the whole.

162. The Double-fugue has its inception in that variety of the single Fugue in which, as shown in par. 132, the first Counterpoint is retained, more or less persistently, throughout a part, or the whole, of the Fugue; for such companionship between the Subject and its Counterpoint approaches the effect of an intentional double thematic basis. Review par. 132, and context, thoroughly. But there still remains a characteristic difference between such examples of retained Counterpoints and the genuine Double-fugue.

163. An important intermediate grade, sufficiently independent to merit separate treatment, is

The Fugue with Thematic Counterpoint.

An ordinary contrapuntal associate of the Theme, such as is found in the majority of simple Fugues, could not be called "thematic," even if "retained" and introduced occasionally in subsequent announcements, for the reason that it provides no especial thematic feature, does not enrich the thematic resources, and takes no active part in the development of the design.

In order to be thematic, the Counterpoint must be to a certain extent characteristic, must contain rhythmic and melodic features which distinguish it somewhat from the Theme; must recur often enough and emphatically enough to become a recognizable (though not obtrusive) line in the physiognomy of the Fugue; must influence the development, and enter actively (though not vitally, or perhaps even essentially) into the thematic texture as a whole. All this the "Counterpoint" may be, without becoming a genuine Secondary Theme, or subject to any special conditions with regard to time, place, frequency, or accuracy of recurrence.

164. During the Exposition the Thematic Counterpoint appears, at each succeeding announcement of the Theme, in the part which last contained the latter; i.e., the Counterpoint follows the Theme, each time, in the same part (whether interrupted by episodes or not). After the Exposition, however, the location of the Counterpoint, like that of the Theme, is optional; and it may be occasionally omitted, or more or less modified.

EXERCISE 47.

One or two examples of the Fugue (3- or 4-voice) with Thematic Counterpoint.

The Genuine Double-Fugue.

165. In the authentic Double-fugue, the two Subjects are strictly coördinate. The secondary Theme (sometimes so called merely by way of distinction), or Counter-theme, is not a "thematic counterpoint," but an essential part of the thematic material, subject to precisely the same specific limitations as the principal Theme.

Rule 1. Each Subject must be a perfectly good melody, in and by itself. Hence, each must be tested alone, in order to verify its individual validity as thematic sentence.

Rule 2. Each Subject must be well individualized; must differ from its fellow (chiefly as regards its rhythmic formation) sufficiently to contrast perceptibly in character, though not obtrusively. They should not begin exactly together, nor need they end upon the same beat.

Rule 3. The two Subjects must constitute peculiarly faultless counterpoint, — not by any means to the exclusion of characteristic dissonances, but without any awkward irregularities. They should not cross each other; and, as a rule, should not run much beyond an octave or tenth apart, in their original associated form, when designed for a Fugue with 4 or more parts.

Compare these rules with the primary definition of polyphony on page 1, of which they are simply a singularly severe and just exposition.

Rule 4. After the Double-subject has been completed, it must be tested in inverted form, i.e., the parts so exchanged that the upper becomes the lower. Also, though less urgently, in their joint Contrary motion.

This is necessary, not only because it is impossible to avoid Inversion, in the development of the Double-subject, but because the art of the Double-fugue consists in a great measure in these, and many similar, changes in the relations of the two Themes to each other. Review pars. 55 to [par.] 58, especially par. 57; and refer, briefly, to Artificial Double-counterpoint, par. 169, etc.

Examples of Double-subjects:

166. Double-fugues are divided into three classes or Species, according to the degree of importance assumed by Theme B.

The First Species of Double-Fugue.

167. In this Species, the two Subjects are announced together at the beginning of the Fugue.

a. They may appear in any two of the parts to be employed, but are almost certain to be in neighboring parts (either the upper, inner, or lower pair). During the Exposition, for instance in 4 parts, the rules of par. 123 (which review) apply to each Theme independently of the other; i.e., each one takes its way through the four voices in the usual order. For instance (assuming them to start in the inner pair of voices):

If announced in parallel parts, a collision is possible, but always easily to be avoided. Thus:

These principles can also be readily applied to the Fugue for 3 or 5 voices.

b. After the Exposition these regulations are relaxed, as usual; the two Themes may appear in any pair of parts, in optional frequency; and, possibly, one or the other of the Themes may occasionally appear alone, though this should occur very rarely, as it militates against the specific conditions of this species of the Double-fugue. Review par. 128. Either Subject may, as usual, be slightly modified or abbreviated, as occasion or necessity arises, but not to the extent permitted with a mere "Thematic Counterpoint."

The formal designs, and all other structural details, correspond exactly to those given in Chapters XII, XIII, and XIV.

Analyze, very minutely, the following examples of the First Species:

EXERCISE 48.

The Second Species of Double—Fugue.

168. In the Second Species, Theme B enters as first contrapuntal associate, in connection with the second announcement of Theme A (i.e., with the first "Response"). It therefore corresponds, in this respect, to the Fugue with Thematic Counterpoint; but all the conditions detailed in par. 165 must be strictly observed.

The order of voices during the Exposition is simpler than in the First Species, because Theme B naturally (and almost invariably) follows Theme A in the same voice,— precisely as shown in Exs. 164, [ex.] 165, excepting that the contrapuntal associate is a genuine Counter-theme, and not merely a thematic counterpoint. But, as Theme A thus appears once alone, the Exposition is generally extended by one extra announcement, in order that Theme B may appear in every part; i.e., in the 4-voice Fugue the Exposition usually embraces five announcements of Theme A, the 5th time in the voice which began the Fugue.

See Bach, Well-temp. Clav., Vol. I, Fugue 12; Theme A is announced in Tenor, then in Alto (meas. 4), Bass (meas. 7 — this is irregular — par. 124), Soprano (meas. 13), and again in Tenor (meas. 19); Theme B follows, each time, in the same voice; the Exposition closes in meas. 22. Exactly the same in Vol. II, Fugue 16, in every particular, excepting that the order of parts is regular; the Exposition closes in meas. 24. — In Vol. II of the Org. Comp., Fugue 9, the Exposition is not thus extended.

The distinction between the 1st and 2nd Species is limited, thus, to the Exposition alone. The subsequent development is identical. Analyze, very carefully, the following; observe, here again, the degree and quality of freedom of detail exercised, and endeavor to recognize the factors that must be regarded as vital and inviolable:

EXERCISE 49.

A number of Double-fugues, 2nd Species; 3-, 4-, or 5-voice; different character and tempo; instrumental or vocal. Some of the Double-subjects of Exercise 48A may be utilized.

Artificial Double-Counterpoint.

169. The term "artificial" is adopted (in its most serious sense) in distinction to "natural," with reference to those varieties of Double-counterpoint in which the harmonious result is not a matter of course, but must be assured by calculation. Review par. 55.

As stated in pars. 55 and [par.] 56, when the Double-counterpoint is obtained by inversion in the 8ve, no change of interval-relations takes place, and an equally harmonious agreement results, naturally. But no such natural guarantee exists when any other interval of inversion is used. Therefore, Double-counterpoint in the 8ve, without any other modification, is the only Natural kind, while Double-counterpoint in any other interval, or with any other modification of either part, belongs to the Artificial kind, and is to be determined only by calculation or experiment.

170. Double-counterpoint in the Twelfth. Double-counterpoint is obtained by transferring one part towards and past the other; and the species is defined by the interval of inversion involved. For example, if the lower part remains, and the upper part is shifted downward a 12th (an 8ve and a 5th, or perhaps two 8ves and a 5th) the result is Double-counterpoint in the 12th. For illustration:

(a) The Original Counterpoint.

(b) Inversion in the 12th (affecting Th. A).

An apparently new result is obtained by moving the other Theme down, past its fellow, a 12th. But this, or any other movement of both parts together, equivalent to the 12th, represents simply a transposition of the Inverted form. Thus:

(a) Inversion in 12th (affecting Th. B).

(b) Inversion in the 12th (affecting both Themes).

171. The invention of a Double-subject (or any two-voice-sentence) which may thus submit to Inversion in the 12th — or any other interval excepting the 8ve — is so largely a matter of incessant experiment, tone for tone, that scarcely any valid rules can be given. At the same time there is a certain device for each separate species of Double-counterpoint, which systematizes and simplifies the formation to some extent.

The device for Double-counterpoint in the 12th consists in the frequent use of the interval of a 3rd (or 10th) in the Original form; for this interval, when inverted in the 12th, results again in a 3rd; for example:

This point, and others, are illustrated in the following:

172. Double-counterpoint in the 11th. Frequent use of the interval of a 6th will, as a rule, yield a good Inversion in the 11th (the 6th becoming again a 6th). For example:

This species, Double-counterpoint in the 11th, is the companion (the counterpart) of that in the 12th; and, because of the harmonic similarity between the 6th and the 3rd, is scarcely distinguishable from it. One is, technically speaking, simply the 8ve-inversion of the other. For illustration: invert the parts in Ex. 167a (in the octave), and also invert Ex. 167b in the same manner; upon comparing the two results with each other they will be found to constitute Double-counterpoint in the 11th.

173. a. Double-counterpoint in the 10th. The best device for Double-counterpoint in the 10th consists in doubling one of the Themes in the 3rd, and counterpointing the other Theme against this double line. In order to yield counterpoint in the 10th, the duplication must fall between the principal lines as a so-called inner 3rd; i.e., it must be the lower third of the upper voice, or the upper third of the lower. Thus:

*1) The large notes constitute the Original counterpoint; the inner part (small notes) is a duplication of the upper Theme in the lower or inner 3rd, in order to provide for Double-counterpoint in the 10th by inverting the parts, thus:

b. Although Double-counterpoint always implies Inversion of the parts (as stated in par. 55), it must be understood that the principle is the same whether the Inversion actually takes place or not; and therefore Ex. 172 is as certainly Double-counterpoint, with its duplication of one part in the 3rd, as Ex. 173, or any other of the inverted forms.

c. Such a duplication in the 3rd is less difficult and hazardous than might be suspected, and will quite frequently be found practicable with little or no change, in any ordinary counterpoint. The only necessary condition or limitation is, that the parts shall move in contrary directions (at those points where both are moving). This may be verified in Ex. 172. It is applied, with precisely equal certainty, to the other part (Theme B) of the above example, by Bach himself. Thus:

N.B. Each lower part alone must be valid with the upper.

d. Further, exactly the same result is obtained by duplicating either part in the outer 6th (instead of inner 3rd, as in Exs. 172 and [ex.] 174). Thus:

N. B. Play each duplicated part alone with the other. And write out the Inverted forms of each example, complete, as in Ex. 173.

174. Double-cpt. in the 13th (or 6th). This is the companion-species of that in the 10th, and is obtained by duplicating either Theme in the outer 3rd (comp, par. 173a), or inner 6th (par. 173d). For example:

N. B. Play each upper part alone with the other. Write out the example also with duplication of the lower part in the outer (i.e., lower) 3rd. Write out each example in its Inverted form, complete.

175. It is sometimes possible to apply the device of duplication in the 3rd (or 6th) to both parts at once. Thus:

*1) Slightly changed from the Original (Bach, Well-temp. Clav., Vol. II, Fugue 16, meas. 59–63). Comp. with meas. 9–13; and see, also, meas. 45–49; 51–55; 69–73.

The complication of Double-cpt. "Species" involved in such twofold duplications can be defined only by reference to the Original form (here shown in large notes): it is exceedingly confusing, — and no doubt wholly unnecessary.

A long and instructive example of Double-counterpoint in the 10th may be found in Bach, "Art of Fugue," Canon III; meas. 5–39 are inverted in the 10th in meas. 44–78; the lower part one 8ve higher, and the upper a 10th lower, than before.

Bach, 3-voice Inv. No. 8, meas. 17–18; upper, part duplicated in the inner 6th.— Well-temp. Cl., Vol. II, Fugue 22, meas. 6–3 from the end (double duplications, partly in 6ths, and partly in 3rds). — Bach, Org. Comp., Vol. VI, No. 18, meas. 22–23; Theme A in Bass, Theme B doubled in 3rds, slightly embellished, in upper parts.

176. Double-cpt. in the 9th, and its companion, in the 7th. For these extremely difficult and rare species there is no other guide than the rigid application of the two general principles, of (1) stepwise progression and (2) contrary direction. For example:

A double-subject, devised thus strictly in contrary directions, and with exclusive stepwise progressions, will generally prove available for every species of Double-cpt. That is the case with Ex. 178, as the student may (and should) verify.

Other Varieties of Artificial Double-Counterpoint.

177. These are purely experimental, and cannot be obtained by any method of calculation. They consist in multiplying the relations of the two Themes to each other by applying the ordinary modifications (Contrary motion, Shifted rhythm, Augmentation, or Diminution) to either Theme alone, while the other retains its original form. For illustration, Ex. 167 chances to admit of transformation as follows:

And Ex. 170, No. 2, reappears later thus:

*1) See Ex. 178, Note *2).

See further, Bach, 2-voice Invention No. 11; Original cpt. in meas. 1–2, Theme A in upper, Theme B in lower part; inverted in meas. 3–5, Theme A as before, but in lower part, Theme B in upper part in Contrary motion and Shifted rhythm. — Bach, Well-temp. Cl., Vol. II, Fugue 23; comp. meas. 60–63 with meas. 27–30 (Theme B in Shifted rhythm).

EXERCISE 50.

The Third Species of Double-Fugue.

178. In this species, which may be regarded as the most genuine and distinctive of the Double-fugue, the entire Exposition (first section) is devoted to Theme A alone. And, in the broader Song-forms, this Exposition may be extended a section or more, so as to complete the measure of a full First Part.

The following sections or Parts may then be designed in either of two ways:

(1) Theme B may simply join Theme A, so that they appear in conjunction the rest of the way; or (2) Theme B may also be first manipulated alone, for one section or Part, and the conjunction of the two Subjects follow in the final Sections, or Third Part.

In the latter case, where each Subject is manipulated alone before they appear together, care must be taken to avoid contrapuntal associates that resemble the other Theme too closely, especially with regard to their rhythmic formation; otherwise the subsequent conjunction of the Themes will not be striking enough, and the product may be monotonous.

An incipient type of the first class is shown in par. 142, which review.

The first class is illustrated in the following (to be thoroughly analyzed):

Bach, "The Art of Fugue," Fugue 9; 4-voice; 3 Sections, cadences vague; Theme A alone to meas. 34; A and B together from meas. 35 to the end. Contains Double-cpt. in the 12th. — Same work, Fugue 14; 4-voice; Theme A alone to meas. 21; A and B together from meas. 22 to the end; in Section III (meas. 34) there is a regular Exposition of an auxiliary Motive, derived from the first Counterpoint (meas. 6–7); in Sec. V (meas. 67) another brief auxiliary Figure appears. Contains Double-cpt. in the 10th and 12th.

The second class is illustrated in the following:

Analyze, further, the following miscellaneous examples (irrespective of class):

Irregular (4th) Species of Double-Fugue.

179. An irregular variety of the Double-fugue, which might be designated as the 4th Species, consists of one principal Theme, with two or more contrasting thematic Counterpoints, one or the other (or all) of which may assume the importance of a genuine secondary Theme.

The thematic Counterpoints (or Counter-themes) are likely to appear in successive sections, or Parts, of the usual forms.

EXERCISE 51.

CHAPTER XVI. 
The Triple-Fugue.

180. The Triple-fugue is based upon three different coördinate Themes, which appear together, as a threefold Subject, during some portion of the composition.

All the rules of par. 165 apply strictly, and must be reviewed. The chief difficulty in devising a Triple-subject is, so to individualize each one of the three Themes that it constitutes by itself a wholly independent and characteristic melody, especially in its rhythmic formation; and that, furthermore, each one may serve equally well as Soprano, Bass, or inner part. Compare par. 57.

Probably the best plan is to follow the principle of par. 61b (which review), i.e., to invent the Themes successively; first, Theme A, in stately rhythm (preponderantly [whole] and [half] - notes); then to add Theme B to this in more animated rhythm ([quarter] - notes), and then Theme C to these, in still another form of more active rhythm. This is, however, by no means imperative.

Illustrations of the Triple-subject:

181. The Inversion of a Triple-counterpoint yields a fivefold result (or 6 forms in all), thus:

a. As in Double-cpt., it is generally a foregone conclusion that the 8ve-inversions will all be possible (par. 56), though some embarrassment, with regard to register, may be encountered; and it may be necessary at times both to cross the parts and to allow them to diverge widely.

b. On account of the multiplied complications, only the Natural species (8ve-inversion) need claim attention. The Artificial species are exceedingly difficult to obtain, though sometimes one or another of the devices shown in par. 173 and par. 177 may be ferreted out by patient and exhaustive experiment.

182. The Triple-fugue, like the Double, may also be divided into three Species.

In the First Species, all 3 Subjects are announced together at the outset, and the order of voices during the Exposition is to be defined strictly according to par. 167a; that is, each Theme passes from part to part in the established order (par. 123), independently of the others — common sense being employed to avoid collisions. For example (4-voice):

*1) Theme C in Soprano following C in Bass. This is not passing to the "next higher or lower voice," it is true; but it is equivalent, because these are not parallel voices.

Irregular Expositions are not uncommon. See also par. 167b,

Analyze, thoroughly, Bach, Well-temp. Cl., Vol. I, Prelude 19; 3-voice; the first tone in Bass is auxiliary; the Triple-subject is 2½ measures long; the design is 3-Part Song-form; Part I is a regular Exposition, to meas. 12; Part II (meas. 12–17) begins with the original counterpoint; Part III (end of meas. 17) contains two announcements.

Beethoven, String-quartet, op. 18, No. 4, second movement, measures 64 to 81 from the Double-bar; original counterpoint given in Ex. 180, No. 2; a complete Exposition, 4 announcements.

183. In the Second Species, Themes A and B begin together, and Theme C follows immediately (usually in one of the same voices).

184. In the Third Species, Theme A is manipulated alone during the whole Exposition, or Part I; thereafter, several different designs are possible and equally legitimate. For example, — among many possible arrangements, in successive Sections (or Parts):

Theme A alone.

B alone, or A and B together.

C alone, or A and C together, or B and C together.

A, B, and C together.

Analyze diligently Bach, Well-temp. Cl., Vol. I, Fugue 4; 5-voice, Two-Part form; Theme A alone in Part I (to meas. 35); Theme B begins with Part II, in Soprano, as counterpoint to Theme A in Tenor; after one other announcement of A and B (meas. 44), Theme C joins them, in meas. 49, Tenor; the 3 Themes are then developed pretty steadily together to meas. 81–84, whereupon Theme B gradually withdraws entirely, leaving the rest of the Fugue to A and C; these, in meas. 94, begin a series of extremely powerful stretto-announcements together, extending nearly to the end. — Vol. II, Fugue 14; 3-voice, Two-Part form; Theme A alone in Part I (to meas. 20); Theme B then follows, in Bass, slightly modified at its end, and is manipulated alone, in somewhat abbreviated stretti, to meas. 28; at the end of meas. 28 Theme A appears (inner voice), Theme B following in Bass two measures later; in meas. 36 Theme C enters (inner voice, 16th-notes), and is developed alone to meas. 51; after one announcement of A alone (meas. 52–54, inner voice), the 3 Themes are combined (A at end of meas. 54 with disguised beginning, upper voice, — C in next measure, Bass, — B in meas. 56, inner voice), and remain together to the end.

Bach, "The Art of Fugue," Fugue 8; 3-voice, sectional; design as follows (Themes named A, B, and C, in the order of their appearance — C being the principal Subject): Sections I and II, Theme A alone; Sec. III (meas. 39) and IV, Themes A and B; Sec. V (meas. 94), Theme C; Sec. VI, (meas. 125), Themes A and B; Sec. VII (meas. 147), Themes A, B, and C. Compare carefully with same work, Fugue 11. The latter uses the same Themes as No. 8, but begins with the principal Theme; further, the Themes are all in the Contrary motion of the former. It is much longer and more elaborate, introducing a characteristic chromatic counterpoint (to one of the secondary Themes) which is retained and much used,— almost as 4th Theme (meas. 28–29), though all four do not appear anywhere together, thus escaping the design of a Quadruple-Fugue (par. 185). The design is as follows (Themes named as in No. 8): Sec. I, Theme C; Sec. II (meas. 27), Theme A, with thematic counterpoint "D"; Sec. III (meas. 71), Theme C in Contrary motion; Secs. IV (meas. 89) and V, Themes A and B (also two isolated announcements of C); Sec. VI (meas. 146), Themes A, B, and C to the end. — Same work, Fugue 15; the 3 Themes are strikingly contrasted in rhythm and character (the third one based upon the notes "b-a-c-h"). This Fugue was interrupted by the master’s death, after the Exposition of the 3rd Theme, and before all three Subjects were united. — Bach, Org. Comp., Vol. VI, No. 31; chorale as Fugue-group (par. 155); 4-voice; cantus firmus in Bass; new Theme for each Line; Double-cpt. during first Line; Triple-cpt. in all following Lines. — Thiele, Fugue (with chromatic Fantasia) for organ; 4-voice; Theme A alone, then A and B together, and then all three. — Brahms, Fugue in a♭ minor for the organ; 4-voice; sectional; Thematic Counterpoint in first Sections; stretti, augmentation, diminution, and shifted rhythm in final section; all per moto contrario. A superb masterpiece, worthy of most diligent analysis.

Quadruple and Quintuple Counterpoint.

185. The invention and employment of a complex of more than three Subjects, for the Fugue-form, is so difficult and of so little practical effectiveness as to be naturally very rare; and even for technical discipline it is of but limited value.

Brief examples of good 4- or 5-voice counterpoint with well-contrasted, independent parts, may be introduced episodically in the course of a Fugue, and reproduced in inverted forms (in 8ve-cpt. only) with good results.

A brilliant specimen of Quintuple-cpt. may be found in Mozart, Symphony in C major (sometimes called the "Jupiter" symphony), Finale. The complex of 5 Subjects, which first appears in meas. 40 from the end, is as follows (in the orchestral String-quintet):

This is followed by a complete Exposition, 5 announcements in all, up to meas. 22 from the end. But this is not all; the entire Finale is, in fact, a Quintuple-Fugue of the 3rd Species, molded in the form of the "Sonata-Allegro," and so designed that nearly all of the Subjects appear successively, and are manipulated, alone or together, in stretti, contrary motion, diminution, and even retrograde imitation, before their ultimate conjunction in the final Coda. Analyze thoroughly, from the orchestral score.

In conclusion, the student is recommended to analyze the 48 Fugues of A. A. Klengel ("Canons and Fugues in all the keys"; 2 vols., Breitkopf & Härtel ed.). This distinguished and interesting work, to which frequent reference will be made in the next Division, has been intentionally omitted in the preceding pages, in order to provide opportunity for an extended course of independent analysis. The Fugues are almost exclusively "Single"; Contrary motion, Stretti, Augmentation, and Diminution abound, and even Retrograde Imitation occurs in one instance (in the unique 2-voice Fugue, Vol. I, No. 16).

EXERCISE 52.

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DIVISION V. 
THE CANON.

186. The Canon-forms differ from the foregoing classes of polyphonic composition in two respects: (1) The Imitation is entirely, or nearly, strict (par. 26); and (2) it is continuous; that is, not limited, as in the Fugue, to the Subject alone, but extended to include all that follows in the same voice, to the end of the Section, or Part, or entire composition.

187. a. The part which begins, or leads the canonic progression, is called the Leader (proposta); the following or imitating part is called the Follower, or responding part (risposta).

b. The principal distinction between canonic species (among many) is defined, precisely like the stretto, according to the distance of the Follower from the Leader in time, and in melodic interval; for instance, "Canon in the 8ve (or 2nd, 3rd, etc.) after one measure (or two, or more)."

c. Another important distinction is made between the Unaccompanied (or Independent) and Accompanied Canon; and further, between the Round and the Progressive Canon. Other traditional distinctions will either be defined in the following pages, or will be intentionally omitted because of their doubtful utility; for the latter the curious student may consult Dr. Baker’s "Dictionary of Musical Terms," or Grove’s "Dictionary."

CHAPTER XVII. 
The Round, or Round-Canon.

188. The simplest and most venerable application of the principle of Continuous Imitation is made in the so-called Round-canon. This is usually written for at least three, sometimes four, but seldom more, vocal parts, and is nearly always a Canon in unison (or 8ve) Imitation.

The Leader begins with a distinctly lyric (melodious) Phrase, commonly 4 measures long, with a fairly definite semi-cadence; more rarely it is a 2-measure member, or a Period (8-measure, or irregular) with the usual two cadences. Thereupon the first Follower reproduces (or imitates) this leading phrase, while the Leader continues with a counterpoint, similar in character but melodically well contrasted (see par. 35a, and par. 165, Rules 1, 2, 3), if possible with a modulation, to avoid monotony. After the leading phrase is thus again finished, the second Follower enters and announces it, while the first Follower continues with the preceding "counterpoint," and the Leader adds a new contrapuntal phrase to these, again well-contrasted. At this juncture the original counterpoint (in a 3-voice Round) is complete, and represents a Triple-subject, exactly as in par. 180, but with less rhythmic diversity, and so contrived that the 3 parts (A, B, and C) constitute a continuous melody in phrase-group form, and returning to the beginning (whence the designation "Round").

What follows, as the voices continue their rotatory Imitation, or following, of the Leader, is simply Inversion of the voices, and presents nothing new, — in the unison-canon not even the effect of Inversion; therefore the Imitation is generally extended only until the last Follower has finished the entire phrase-group, whereupon a free cadence, of any length, is added, to terminate the Canon.

If a low voice (Alto or Tenor) is used in company with two high ones, or if, in any way, the Triple-subject is so devised as to embrace different registers, the 8ve-Imitation may also be employed; and in that case the effect of Inversion will be secured, subject to the usual tests (par. 181a).

For a 4-voice Round the process is the same, but the desirability of 8ve-Imitation, in company with the unison, is greater; hence, parallel voices are likely to be chosen (2 Sopranos and 2 Tenors, or Altos and Basses). The text must be so chosen as to cover either the leading phrase only, or exactly the entire group of 3 (or 4) phrases. For illustration (3-voice Round-canon):

189. Closely allied to the Round, but inclining toward the structure of the Progressive Canon, is a form of very pronounced Lyric character, in which (as a rule) there is no return to the beginning, and consequently no such rotation of parts as in the Round. The leading sentence is often of considerable length — 8, 12, or even 16 measures, in very definite Period, or Double-period, form; the number of voices is usually 3 (sometimes 4); and the form generally extends no farther than through the announcement of the leading sentence by the last Follower. A simple harmonic accompaniment is added (par. 201d).

EXERCISE 53.

CHAPTER XVIII. 
The Progressive Canon.

190. In the Progressive Canon the same principle of strict continuous imitation prevails; but any other interval (or species) of imitation may be used quite as well as the octave; and the time-interval is generally much shorter, — i.e., the risposta follows the proposta, or Leader, earlier than in the Round; and, finally, there is less distinctness or regularity of form, and no such characteristic recurrence of the leading sentence, — excepting the distinctive return to the beginning necessary when the 3-Part Song-form is chosen, or when Part I is to be repeated.

The Two-Voice Canon, Unaccompanied.

191. In the 8ve. Either part may be chosen as Leader. A simple melodic motive is devised, very similar in contents and character to the Motive of an Invention or a short Fugue-subject, but without cadence. Its length depends upon the time-interval between Leader and Follower. This is most commonly one measure, sometimes two measures, or one-half measure in any compound rhythm; more rarely one beat, or any other uneven fraction of a measure, for it is desirable that the prosodic effect of Leader and Follower (disposition of accents) should agree.

This leading motive is then imitated in the other voice, either an 8ve higher or lower, while the Leader proceeds with a contrapuntal associate devised in strict conformity to the rules in par. 35a, which review. The Follower imitates this Counterpoint, while the Leader again proceeds with a new one, — and so on, to the end of the Canon. If, for instance, the time-interval is one measure, the contents of every (or any) measure in the Leader will be literally reproduced in each following measure in the Follower; — though a duet, the contents of one voice alone will represent the entire melodic material of the composition. For illustration:

192. There are two characteristic difficulties persistently present in the constructive process of an unaccompanied Canon in the 8ve, namely:

a. The difficulty of avoiding monotony.

The 1st counterpoint is, presumably, a peculiarly fitting associate of the leading Motive. When it reappears in the Follower (3rd measure of the above example) it is necessary to devise an equally good, but new, associate, as 2nd counterpoint, whereby the natural temptation to fall back upon the leading M. must be resisted. In other words, constant care must be taken to use new contrapuntal intervals in successive measures; also intervals occasionally foreign to the key, in order to effect necessary modulations. But no liberties are to be taken with the Follower; in the 8ve-canon the imitation is absolutely strict. It is also necessary to avoid monotony of rhythm and monotony of register. All of these considerations are skilfully observed in the following:

b. The difficulty of obtaining intelligible form.

c. The time-interval is a significant factor in the Canon, as it affects both the difficulty of structure and the recognizability of the imitation. The shorter the time-interval, the greater and more insistent is the canonic constraint. The imitatory effect can scarcely be brought out clearly when the time-interval is very brief, nor, on the contrary, can the connection between Leader and Follower be easily traced when more than two ordinary measures intervene. Long time-intervals may, however, conduce to regularity of design; for instance, a 4-measure interval is likely to resolve the Canon into a perfectly regular Phrase-group form.

The following is a unique example of short time-interval:

d. The canonic imitation may extend to the very end, — in which case the Leader may pause, or may be a free counterpoint, during the final time-interval. Or it may be discontinued one, or several, measures before the final perfect cadence; the final measures will then assume the character of a free codetta or coda.

e. The Canon in Unison is very rare without accompaniment.

193. In the 2nd. The Follower imitates the Leader, at the chosen time-interval, either in the 2nd above or the 7th below. The latter distinction is wholly unnecessary (though customary), for, as explained in Ex. 67, Note *2) — which see, — the imitation of any letter in the 2nd will be the next higher letter, whether placed above or below the leading part.

Each canonic Interval has its peculiarities, and it is left largely to the student to discover and learn to master them.

a. Probably the most characteristic difficulty of any other than the 8ve-canon, is that of preserving the natural harmonic relations of the tonality; it is the direct opposite of that shown in par. 192a, for these varieties of the Canon are apt to be too restless, and to contain too much variety. The constant uniform shifting of the parts tends to an unvaried sequential structure which must be prevented from destroying the unity of key, and must be mitigated by the best possible collective formal arrangement. See par. 192b.

b. Good modulatory results are impossible without free use of the changes in interval-quality, defined in par. 28a, — which review, in connection with the Notes to Ex. 69. Therefore, it is entirely legitimate to substitute the major 2nd for the minor 2nd, or vice versa, at any point; or even the augmented 2nd for either. But the letter must not be changed; i.e., the interval-quantity must be respected.

c. All the formal conditions correspond to those of the 8ve-canon. For illustration:

194. In the 7th. This is the counterpart of the Canon in the 2nd, and exhibits precisely the same peculiarities, merely reversed. For example:

195. In the 3rd. This interval is somewhat easier to manage than the 2nd, though the same difficulties exist, and similar remedies are necessary (par. 193a and [par.] 193b).

The same applies to its counterpart, the Canon in the 6th. For illustration:

196. In the 5th, and its counterpart, in the 4th. For illustration:

EXERCISE 54.

Other Species.

197. The Canon in Contrary motion. Here the choice of "corresponding tones" is of great importance. Review par. 29a thoroughly. As there demonstrated, the best results are obtained either by answering Tonic by Mediant, or Tonic by Dominant.

All other conditions correspond to those of the above species. See, particularly, pars. 192b and [par.] 193a.

For illustration:

198. Canon in Augmentation. The two parts generally begin together or nearly so, usually in the 8ve; and the Augmentation constantly widens the distance between Leader and Follower, so that it is of course impossible to imitate the entire Leader. Usually, therefore, the second half of the leading voice is a free counterpoint to the portion of the Follower still due; but many devices, such as exchanging the parts, or substituting Diminution after a while, may be resorted to. For example:

Bach, "Art of Fugue," Canon I; Augmentation and Contrary motion.

199. In Diminution. Here the distance between the parts is constantly decreased, so that the Follower overtakes the Leader after the first time-interval has been exactly doubled. Thereafter the calculation is reversed, and the imitation becomes "Augmentation." For example:

*1) The parallel octaves at the confluence of the parts are of course inevitable. From here on, the upper part is, practically, the Leader.

EXERCISE 55.

A. Two examples (major and minor) of the 2-voice Canon in Contrary motion.

B. One example, each, of the Canon in Augmentation and Canon in Diminution, (the latter beginning with time-interval of 4, 6, or 8 measures).

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CHAPTER XIX. 
The Two-voice Canon, Accompanied. Instrumental.

200. This is by far the most practicable and valuable form of the Canon, because the added part (parte libera), or parts, disguise the constraint of the canonic imitation, and may contribute very significantly to the beauty and effectiveness of the whole. Any of the above canonic species may be thus treated, but the most common is that in the 8ve, parallel, — more rarely contrary.

201. The auxiliary (accompanying) part may be placed above, below, or between the canonic voices, at option; but much depends upon the degree of importance it assumes.

a. It may be distinctly subordinate (unessential), serving no other purpose than that of emphasizing the rhythm; or of supplementing the harmony where needed. For example:

*1) Vol. II, Canon 16; 8ve, after one beat. Analyze to end.

Schumann, Studies for Pedal-piano, op. 56, No. 1; 8ve, after ½ measure; auxiliary Bass.

b. Or the auxiliary part may be coördinate with the canonic parts. In this case it may be a carefully conducted running voice (comp. par. 73b); or it may borrow its melodic and rhythmic figures from the Canon itself. For example:

Sometimes two such coördinate parts accompany the 2-voice Canon. This is rare, however, excepting in the free harmonic manner shown in [par. 201]d below.

See Klengel, Vol. II, Canon 8; in 8ve, after one measure, two inner auxiliary parts. — Chadwick, Canonic Studies for Organ, op. 12, Canon 2; in 8ve, after 2 measures; two upper parts auxiliary.

c. Or the auxiliary part may be so conducted as to appear, as far as external effect is concerned, to constitute the essential element, which the canonic parts merely serve to sustain. Here the danger of incoherent or unintelligible form is greatly reduced. For example:

*1) Vol. I, Canon 7; analyze to end, and see also —

Vol. I, Canon 10; in 5th, after ½ measure; auxiliary upper part. — Vol. II, Canon 7; in 2nd, after two beats in 3-4 time; auxiliary Bass, beginning two measures before canonic parts.

d. Finally, the accompaniment may assume a distinctly harmonic character, imparting a more or less preponderantly homophonic effect to the whole.

It may be limited, as before, wholly (or largely) to one single auxiliary part, which exhibits the underlying harmony in broken-chord form (i.e., as harmonic figuration, in flowing rhythm). One of the canonic parts is almost certain to be given to the Soprano, the other to the inner voice, more rarely Bass. Thus:

*1) Pfte. Variations, op. 9, Var. 14; Canon in the 2nd, after 2 measures. See also Var. 15; in 3rd, after one measure; auxiliary inner part. In both of these examples occasional, very slight, licences occur. — See further, Klengel, Vol. II, Canon 19; unison, after ½ measure; auxiliary Bass. —Vol. I, Canon 3; in the 4th, after 2 long measures; auxiliary Bass. — Vol. I, Canon 5; in the 7th, after one brief measure; auxiliary Bass, partly coördinate.

Or, the auxiliary homophonic accompaniment may consist in concrete harmonic bulk, with little (or no) regard to the number or continuity of parts (i.e., variable volume). Here, again, one of the canonic parts is assigned to the Soprano, almost without exception; the other may be placed in any lower part, but (unless in Bass) is frequently so confounded with the harmonic accompaniment as to be unrecognizable as a "canon." See par. 202. For example:

202. In order to appreciate the significance of the Canon-form, it should be contemplated in the abstract, aside from its uninviting mathematical aspect. As has been observed, each successive time-interval (one measure, or whatever section it may be) of the Leader is a counterpoint to the preceding section; that is, each such member is a product of the preceding one, through the strictest and most obvious process of logical derivation, or cumulation. The fact that the leading voice may thus accompany itself, may fit into itself, member by member, indicates a degree of cohesion and consistency of evolution which vindicates the rank of the Canon among those art-forms whose merit is founded upon close logic. This being the case, it is evident that the essential properties of the form are all present in the Leader alone, whether actually accompanied by the Follower or not; and though it might be injudicious ever to advocate the complete omission of the Follower,^[*] it is interesting to question to what extent the presence of the Follower should be emphasized, — in other words, to what degree the canonic imitation should be made clearly recognizable. It is generally acknowledged that the merit of a Canon increases as the evidences of canonic labor decrease; that the more freely and naturally the leading voice runs, the more perfect the Canon; the less it betrays of its contrapuntal origin, the dry mathematical fact that one part is obstinately dogging the other, the better. Hence, the doctrine may be defensible, that a Canon need not be recognizable as such; but with one limitation, namely, not incessantly recognizable. The beauty and attractiveness of the act of Imitation, the calling of voice to voice, is so real, and so greatly appreciated by even the untutored musical listener, that it should not be banished from an art-form which, at its best, does not exhibit an excess of external beauty and grace. The proper balance between unimpassioned logic of structure on the one hand and romantic charm on the other, is most nearly achieved in the 8ve-Canon, with harmonic accompaniment, in which provision is made for clear formal arrangement, and for fairly frequent evidences of the canonic imitation. Review par. 192b.

203. When the last of the above varieties (par. 201d) is chosen, it is possible to mould the Canon in any of the Conventional styles of musical composition, as, for instance, the March, Minuet, Romanza, Étude, etc., etc. This is very desirable, as it lends definiteness of character and purpose to the Canon, and invites a certain legitimate freedom of treatment without violating any distinctive canonic condition (par. 186). For example:

Additional miscellaneous illustrations:

EXERCISE 56.

The Two-voice Canon, Accompanied: Vocal.

204. Among the conventional styles, frequently chosen for the outer vestment of the Canon, none is more effective than the vocal duet, with instrumental accompaniment.

The interval most commonly employed is the unison (when the voices are of similar register), or the octave (when parallel voices are used). But any interval is possible, and even Contrary motion is sometimes encountered. The time-interval is apt to be brief, as in the instrumental Canons.

The text is generally the same in both voices. The accompaniment is almost necessarily devoted, also, to an independent Prelude, occasional Interludes, and a Postlude; and, in general, it may assume considerable importance and independence of character. Sometimes the canonic Imitation extends to the end, but it is more common to add a free ending (par. 192d). For illustrations see —

EXERCISE 57.

A number of examples of the 2-voice Canon as vocal duet, with instrumental accompaniment.

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CHAPTER XX. 
The Canon for More Than Two Parts.

205. The 3-voice Canon. This consists of a Leader and two Followers (similar to the 3-voice Round). In order to decrease the very great difficulties of this contrapuntal form, it is necessary, or at least customary, that the same melodic interval and time-interval should prevail between the first and second Follower, as preceded, between Leader and first Follower; in other words, that the contrapuntal relations between successive voices shall exactly correspond, thus ensuring at least this degree of continuous agreement. For instance, if the first Follower is in the 8ve, after one measure, the second Follower will also be in the 8ve, after one additional measure (or two measures from the beginning); or, if the first Follower is in the 5th, the second Follower will be in the next 5th, or in the 2nd from the Leader; if in the 4th, the second Follower will be in the 7th, and so on. Thus:

For general illustration:

[ex. 203-2  ]

[ex. 203-3  ]

206. Contrary motion is employed as follows: The first Follower is the Contrary motion of the Leader, in any of the usual methods of correspondence (Tonic = Dominant being probably the best); the second Follower, being the Contrary motion of the first one, returns to the original direction, and the corresponding series of interval-relations is obtained by giving to the 2nd Follower, in every case, the exact tones of the Leader (i.e., 8ve-imitation of the latter). Thus:

*1) The 2nd Follower imitates the Leader in parallel direction, in the double 8ve. The successive intervals described by Leader and 1st Follower (beginning with the 8ve, as indicated) are exactly reproduced between 1st and 2nd Followers, but, naturally, in inverted forms. This will be the invariable result, no matter what the location of the 1st Follower is, if the 2nd Follower corresponds thus to the Leader.

207. The 4-voice Canon. The principles of par. 205 apply here also, simply extended to include the 4th voice. For example (8ve–8ve–8ve, after one measure):

[Ed. note: m. 5, beat 3, tenor part, I changed the C to C♯ to conform with the other voices, suspecting this was a typographical error in the book.]

EXERCISE 58.

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CHAPTER XXI. 
The Double-Canon, Etc.

208. Like the Double-fugue, the Double-canon has two Leaders, or a "Double-leader," imitated by two Followers. The number of canonic parts is therefore four; to these an auxiliary part may be added, but it is rarely done.

The two Leaders may begin together, but it is more common to introduce the subordinate Leader (so-called) a beat or more, possibly a measure or more, later than its fellow. The rules of par. 165 apply, to a certain extent, and may be reviewed.

The interval of Imitation is optional, the 8ve being here again possibly the most convenient. The time-interval is apt to be a little longer than in the single Canon, but must be adhered to by both Followers; i.e., the second pair of parts must agree with the first pair in time-relation. Any two of the four parts may be chosen for the two Leaders. For example:

209. The Triple-canon is far less frequent than the preceding. It consists in 3 Leaders, imitated by 3 Followers, and therefore involves six canonic parts.

See Brahms, op. 112, No. 4, Div. II (meas. 51–91); Leaders (simultaneous) on upper staff, Followers on lower, after one beat; unaccompanied.

The Quadruple-canon is still more rare; it involves eight canonic parts, and is practicable only in Double-chorus or orchestral writing.

An extraordinary example of the Quadruple-canon is found in Mozart (Serie 7), No. 49; it is written for 12 parts (as triple-chorus), and consists in a full quartet of Leaders, imitated in the unison, after 1½ measures, by a quartet of Followers, and 1½ measures later by still another quartet; it is designed as a Round, with cadence indicated.

EXERCISE 59.

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CHAPTER XXII. 
Canon as Chorale-Elaboration.

210. Chorale as Canon. In this species the chorale-melody itself appears in two voices as Canon, while the other parts provide a contrapuntal accompaniment.

The interval of canonic imitation, and the time-interval, are optional. But the relations adopted at the beginning should be, as a rule, maintained uniformly throughout the chorale; therefore it is usually necessary to experiment repeatedly with the whole, before valid relations can be determined; and it is not considered unpermissible, in case the advantage is manifest, to adopt new relations for a new Section (or even for some single line) of the chorale. It is greatly preferable, however, to overcome the necessity for such changes of canonic relation by judicious (slight) rhythmic modification, or strictly unessential melodic embellishment, of the chorale-melody, in the manner shown in Ex. 125. For example (Table, Exercise 26, Chorale 29):

First version; canon in the 5th, after one measure.

Second version; canon in the 2nd, after one (longer) measure.

211. The parts which accompany the canonic voices are in a sense their "auxiliaries," but should be strictly contrapuntal, and thematic (based upon some Motive or Motives), as described in par. 92, which review. See also pars. 99 and [par.] 93.

The number and choice of these accompanying parts, and the location of the canonic voices, are wholly optional. Either the small or large species of chorale-figuration may be employed.

For general illustration:

212. Canon with Chorale, i.e., canonic accompaniment to the single chorale-melody.

All conditions are optional. Additional auxiliary parts are sometimes employed. For example:

See Bach, Org. Comp., Vol. V, page 92; Canon in 8ve, after ¼ measure, in outer parts; c.f. in Pedal as Tenor; Large species (with Prelude, Interludes, and Postlude). — Vol. V, page 94; Canon in 4th, after ½ measure; other conditions similar to preceding.— Vol. V, page 96; Canon in 7th, Pedal-bass and Alto; c.f. in Soprano; additional lyric auxiliary part in 2nd Soprano. — Vol. V, page 98; Canon in Augmentation, Soprano and Bass, in 8ve; the Leader ends in meas. 21, the Follower in meas. 42 (end of the composition); c.f. in Pedal as Tenor; an auxil. Tenor is added.

See Bach, Org. Comp., Vol. V, page 92; Canon in 8ve, after ¼ measure, in outer parts; c.f. in Pedal as Tenor; Large species (with Prelude, Interludes, and Postlude). — Vol. V, page 94; Canon in 4th, after ½ measure; other conditions similar to preceding.— Vol. V, page 96; Canon in 7th, Pedal-bass and Alto; c.f. in Soprano; additional lyric auxiliary part in 2nd Soprano. — Vol. V, page 98; Canon in Augmentation, Soprano and Bass, in 8ve; the Leader ends in meas. 21, the Follower in meas. 42 (end of the composition); c.f. in Pedal as Tenor; an auxil. Tenor is added.

EXERCISE 60.

A. Two or more examples of the Chorale as Canon (pars. 210, [par.] 211), for Organ.

B. Two or more examples of the Canon with Chorale (par. 212).

"Canonic" Compositions.

213. When the canonic imitation falls short of the characteristic requirements of the legitimate Canon (parF. 180), either in being interrupted (periodic instead of continuous), or in containing more or less frequent licenses (instead of being strict), the product forfeits the title of "Canon," and is called simply "canonic" composition.

To this class belong also the fairly numerous examples of homophonic (or even polyphonic) forms with canonic sections, or passages.

The End.

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Endnotes

^[*] See the author’s "Homophonic Forms of Mus. Comp." par. 70, par. 72.

^[*] Idem, par. 73, par. 81a.

^[*]This actually takes place in Jadassohn, Vocal Canon, op. 38, No. 1, during Div. I.

[back to text] GUILMANT, Félix Alexandre, son of an organist of Boulogne, and born there March 12, 1837. He took to the organ at an early age, and before he was sixteen was made organist of S. Joseph, in 1857 Maître de Chapelle of S. Nicolas, and shortly after professor of solfeggio in the local École communale. In 1860 he became for some months a pupil of Lemmens, who heard him play and was struck by his ability. In 1871 he removed from Boulogne to Paris, and was appointed organist of the church of the Trinité, a post which he still fills. His playing made a great impression on the general public during the Paris Exhibition of 1878. He is one of the leading organ players of France, and has considerable extempore power. For his instrument he has published a 'Symphonie,' (with orchestra), seven sonatas and many concertos, etc., and arrangements—‘Piéces de differents styles,’ ‘L'Organiste pratique,’ and ‘Archives des Maîtres de l'Orgue’; also a scène lyrique, ‘Belsazar,’ for soli, chorus, and orchestra; a hymn, ‘Christus vincit,’ etc, various masses, motets, airs, and original pieces for the harmonium. Guilmant is no stranger to England, having played at the Crystal Palace, at Sheffield, and many other places. G. [from George F. M. J. A. Grove, A Dictionary of Music and Musicians. New York: Macmillan, 1910.]

[back to text] Henschel, (Sir) George, composer, cond., and baritone singer, b. Breslau, Feb. 18, 1850 (on father's side of Polish descent). Pupil of Wandelt and Schaeffer at Breslau, Moscheles and Wenzel (pf.), Götze (singing) and Reinecke (theory and comp.) at Leipzig Cons., 1867–70. In 1870 st. in Berlin with Kiel (comp.) and Adolf Schulze (singing); début as singer, 1868 in Leipzig. Undertook concert-tours through Europe; 1877–80, lived in London; 1881–4, cons. of the Boston Symph. Orch.: since 1885, settled in London (naturalized Engl. subject, 1890); founded the London Symphony Concerts,' which he cond. from 1885–96; he was the first cond. of the Scottish Symph. Orch. at Glasgow, whose concerts he cond. from 1891–5. 1886–8, prof. of singing at the Royal Coll. of Mus. In 1881 he married Lillian Bailey (see Henschel, Lillian); after her death in 1901 he withdrew from public appearances until 1909, devoting himself to composition. Made his final appearance as singer in 1914, and was knighted the same year. H. is equally fine as singer, conductor and pianist. He was one of the most enthusiastic champions of Brahms, with whom he was on terms of friendship.-Comps.: Operas, Friedrich der Schöne (not prod.) and Nubia (Dresden, 1899); comic operetta, A Sea Change, or Love's Castaway; an oratorio; a Requiem; a Stabat Mater, Te Deums; Zigeuner, serenade for orch.; Canon-Suite for string-orch.; a str.-quartet in E♭; incid. music to Hamlet; a mass for 8 voices a capp.: psalms, part-songs, songs, etc.—He has publ. Personal Recolletions of Johannes Brahms (Boston, 1907). Baker, Theodore, and Alfred Remy. Baker's Biographical Dictionary of Musicians. 3rd , rev. and enl. / by Alfred Remy. ed. New York: G Schirmer, 1919.

[back to text] JADASSOHN, Salomon, born at Breslau, Sept. 3, 1831. His years of study were passed partly at home under Hesse, Lüstner, and Brosig, partly at the Leipzig Conservatorium (1848), partly at Weimar under Liszt, and again, in 1853, at Leipzig under Hauptmann. From that time he resided in Leipzig, first as a teacher then as the conductor of the Enterpe concerts, and lastly in the Conservatorium as teacher of Harmony, Counterpoint, Composition, and the Pianoforte. [In 1887 he received the honorary degree of D. Phil. from the Leipzig University, and in 1893 was appointed Royal Professor.] His compositions are varied and numerous, reaching to well over 100 opus numbers. [His skill in counterpoint is shown in an orchestral serenade in canon, Op. 35; in two serenades for piano, opp. 8 and 125; in the ballet-music, op. 53 for piano duet; and in the vocal duets, opp. 9, 36, 38, and 43. Four symphonies, orchestral overtures, and serenades, two piano concertos, four trios, three quartets, three quintets, a sextet for piano and strings, two string quartets, are among his instrumental works; and of his choral works the following may be mentioned:— Psalms xliii. and c. (8-parts), ‘Vergebung,’ ‘Verheissung,‘ ‘Trostlied,’ ‘Johannistag,’ and ‘An dam Sturmwind.’ As a private teacher Jadassohn was highly esteemed, and his many theoretical works have passed through many editions, and have been translated into various languages. The chief of these are his Harmonielehre (1883), Kontrapunkt (1884), Kanon und Fuge (1884), Die Formen in den Werken der Tonkunst (1889), and Lehrbuch der Instrumentation. All have been translated into English and published by Breitkopf & Härtel, the treatises on Harmony and Counterpoint have also been translated into French and Italian. Jadassohn died at Leipzig, Feb. 1, 1902.] G.; additions from Riemann’s Lexikon. [from George F. M. J. A. Grove, A Dictionary of Music and Musicians. New York: Macmillan, 1910.]

[back to text] KLENGEL, August Alexander, born Jan. 27, 1783, at Dresden, son of a well-known portrait and landscape painter, first studied music with Milchmayer, inventor of a piano which could produce fifty different qualities of tone (see Cramer's Magazin der Musik, i. 10). In 1803 Clementi visited Dresden, and on his departure Klengel went with him as his pupil. The. two separated on Clementi's marriage in Berlin, but the young wife dying shortly after, they went together to Russia, where Klengel remained till 1811. He then spent two years studying in Paris, returned to Dresden in 1814, went London to in 1815, and in the following year was appointed Court-organist at Dresden, which remained his home till his death on Nov. 22, 1852. During a visit to Paris in 1828 he formed a close friendship with Fétis, who with other musicians was much interested in his pianoforte canons. Of these he published only ‘Les Avant-coureurs’ (Paul, Dresden, 1841). After his death Hauptmann edited the ‘Canons et Fugues’ (Breitkopf & Härtel, 1854), with a preface, in which he says, Klengel was brought up on Sebastian Bach, and knew his works thoroughly. It must not be supposed, however, that he was a mere imitator of Bach's manner; it is truer to say that he expressed his own thoughts in the way in which Bach would have done had he lived at the present day. He left several concertos, and many other works. His visit to London was commemorated by the composition of a Quintet for Piano and Strings for the Philharmonic Society, which was performed Feb. 26, 1816, he himself taking the pianoforte. There is a pleasant little sketch of him in a letter of Mendelssohn's to Eckert, Jan. 26, 1842. F. G. [from George F. M. J. A. Grove, A Dictionary of Music and Musicians. New York: Macmillan, 1910.]

[back to text] Leschetizky [lĕh-shĕ-tĭt´skē], Theodor, pianist and famous pedagogue; b. Lancut, Austr. Poland, June 22, 1830, d. Dresden, Nov. 17, 1915. Pupil of his father, an eminent teacher in Vienna; then of Czerny (pf.) and Sechter (comp.). In his fifteenth year he began teaching; also attended the Univ. as a student of philosophy until its closure in 1848 (the revolutionary year); made highly successful professional tours 1842–8, and 1852, and then went to Petrograd, becoming a teacher in the Cons., giving many private lessons, playing, composing, and acting as conductor to the Grand Duchess Helen during Rubinstein's absences. Ill health compelled him to leave Russia in 1878; he then played in London, Holland, Germany, and Vienna; there he married (1880) his former pupil, Annette Essipov, and settled as a teacher. He still made occasional concert-tours, but his interest in teaching caused him to withdraw at the height of his powers from the concert-stage in 1886, appearing for the last time in Frankfort. After the phenomenal success of his pupil Paderewski (Vienna, 1887; London and New York, 1891) L. was regarded as the worlds foremost piano-pedagogue, and pupils flocked to him from all quarters of the globe. He retained the full vigor of his mental faculties to the very end, and taught almost to last day of his life. The long list of his pupils includes the names of Gabrilowitsch, Mark Hambourg, A. Schnabel, Fanny Bloomfield Zeisler, Katherine Goodson, Ethel Leginska, etc. He was married four times, and, with the exception of his first wife (a singer, Anna Friedbourg), to his own pupils: Annette Essipov (1880–91), Dominirska Benislavska (1894–1908), Marie Rozborska (1908). These varied matrimonial ventures, except the last, ended in divorce. He wrote a successful opera, Die erste Falte (Prague, 1867), and numerous brilliant and effective compositions for pf.: Op. 2, Les deus Alouettes; op. 5, Grande Polka de Caprice, op. 10, La Cascade (concert-étude), op. 20, Perpetuum mobile, op. 22, Valse chromatique; op. 39, Souvenirs d'Italie (6 pcs.), op. 40, À la Campagna (5 pcs.); op. 41, Trois Études caractéristiques; etc.—His method was explained by Malvine Brée, Die Grundlage der Melhode L'.s (1902, also in Engl. and Fr. transl.).—Cf. Countess A. Potocka, Th. L. (New York, 1903); A. Hullah, Th. L. (London, 1906). Baker, Theodore, and Alfred Remy. Baker's Biographical Dictionary of Musicians. 3rd , rev. and enl. / by Alfred Remy. ed. New York: G Schirmer, 1919.

[back to text] Moszkowsky [mŏhsh-kŏhf´skē], Moritz, brilliant concert-pianist, teacher, and composer; b. Breslau, Aug. 23, 1854. His father, a Polish gentleman of independent means, early recognized his son's mus. talent. M. was trained at home, in the Dresden Cons., and at the Conservatories of Stern and Kullak in Berlin, in which latter he taught for several years. His first public concert, at Berlin, 1873, was highly successful, and, followed by tours to other German cities, and to Warsaw and Paris, establ. his fame as a pianist. Until 1897, M. made Berlin his headquarters; since then he has been living in Paris. In 1899 he was elected a member of the Berlin Akademie.—As a composer he is most widely known by his elegant and dainty salon-music for piano; the Spanish Dances brought his pieces into vogue, and the concert-studies, concert- waltzes, gavottes, Skizzen, a Tarantella, a Humoresque, etc., have also won favor among pianists. In larger forms he has successfully produced an opera, Boabdil, der Maurenkönig (Berlin, 1892); the music to Grabbe's Don Juan und Faust (1896); a ballet, Laurin (1896); a symphonic poem, Jeanne d'Arc, op. 19; Phantastischer Zug f. orch.; Aus allen Herren Länder f. orch., op. 23; 2 orchl. suites (F, op. 39; G m., op. 47): a violin-concerto, op. 30; a pf.-concerto in E, op. 59; Der Schäfer putzte such zum Tanz, scene from 'Faust' for soli, ch. and orch.; a Suite for 2 violins and pf., op. 71. About 75 opus-numbers have appeared. Baker, Theodore, and Alfred Remy. Baker's Biographical Dictionary of Musicians. 3rd , rev. and enl. / by Alfred Remy. ed. New York: G Schirmer, 1919.

[back to text] CANON. This is the strictest and most regular species of imitation. [See IMITATION.] It is practised in music for two, three, or more parts. The word is derived from the Greek [word for] a rule or standard. A canon, therefore, is a composition written strictly according to rule. The principle of a canon is that one voice begins a melody, which melody is imitated precisely, note for note, and (generally) interval for interval, by some other voice, either at the same or a different pitch, beginning a few beats later and thus as it were running after the leader. For this reason the parts have been sometimes respective]y called ‘Dux’ and ‘Comes,’ or ‘Antecedens' and ‘Consequens.’

The following is a simple example of a canon ‘two in one at the octave,’ i.e. for two voice an octave apart, and both singing one and the same melody. [example]

By means of a coda (or tail-piece) this canon is brought to a conclusion. But many canons lead back to the beginning, and thus become ‘circular’ or ‘infinite.’ The following is a specimen of this kind, which is ‘two in one at the fifth below,’ or ‘canon ad hypodiapente’:—

Sometimes two or more canons are simultaneously woven into one composition. The following, for instance (from Travera’s Service, 1740), would be called a canon ‘four in two.’

Byrd's ‘Diliges Dominum,’ for 8 voices, consists of four canons all sung together, each voice singing the melody of its fellow reversed.

Often in a quartet there may be a canon between two of the voices, while the other two are free; or three voices may be in canon and the fourth part free. We would quote as an example the admirable Gloria Patri to Gibbons’s ‘Nunc dimittis’ in F, in which the treble and alto are in canon while the tenor and bass are free. Again, there are canons by inversion, diminution, ang- mentation, or ‘per recte et retro,’ cancrizans, etc. [See those headings.] A modern one of great ingenuity by Weber exists to the words ‘Canons zu zwey sind nicht drey’ (Jähns, No. 90).

The old writers often indicated canons by monograms, symbols, or other devices, instead of writing them out in full. Indeed they went so far as to write their indications in the form of a cross, a hand, or other shape, with enigmatical Latin inscriptions to indicate the solution. Such pieces were called ‘enigmatical canons.’ As compositions of this nature can only be regarded in the light of ingenious puzzles, bearing the same relation to music that a clever riddle does to poetry, it will be needless to give examples here,—let it suffice to refer to those which are to be found in Fétis's admirable Traité du Contrepoint at de la Fugue, and in Marpurg’s celebrated work on the same subjects.

The great masters were fond of the relaxation of these plays on notes. They occur often in Beethoven’s letters, and the well-known Allegretto Scherzando of his Eighth Symphony originated in a canon to be sung at Maelzel’s table. Köchel's Catalogue of Mozart's works contains 23 canons ; that of Weber by Jahns, 8 ; and an interesting collection will be found in the Appendix to Spohr’s Autobiography. [The wonderfully expressive canons in Bach's ‘30 Variations’ are far more than examples of mere ingenuity. Every third variation is a canon, and each successive canon is at the distance of an interval by one degree larger than the one before it. Nearly all the canons are in two parts upon a free bass, a few in contrary motion, and they proceed from a canon at the unison (No. 3) to a canon at the ninth (No. 27).]

As popular examples of canons may be named the well-known ‘Non nobis Domine,’ which is a canon three in one, in the fourth and eighth below, and Tallis’s ‘Canon,’ a hymn-tune (usually adapted to Ken’s evening hymn) in which the treble and tenor are in canon while the alto and bass are free. The lover of cathedral music will find specimens of almost every variety of canon in the service by Purcell in B♭, which is a masterpiece of ingenuity and skill. Other good specimens will be found in the Collection of his Gloria Patris, published by V. Novello for the Purcell Club. On the tablet erected in the cloisters of Westminster Abbey to the memory of Dr. Benjamin Cooke, organist of Westminster Abbey at the close of the 18th century, there is engraved a canon, three in one, by double augmentation, which is one of the best extant specimens of that kind of composition. See AUGMENTATION. Another, by Andre, four in one, by threefold augmentation, in given in Ouseley’s Counterpoint, Canon, and Fugue, example 12.

Canons are often introduced into fugues as the closest species of ‘stretto’ [see Fugue and Stretto], and are to be found both in vocal and instrumental compositions. As specimens of the former we would refer, in addition to the references given above, to many of Handel’s choruses, especially to one in ‘Judas Maccabæus,’ ‘To our great God,’ which contains a canon by inversion; also to Sebastian Bach’s magnificent cantata on the chorale ‘Ein' feste Burg.’ As specimens of instrumental canons we would refer to the first movement of Mozart’s sonata for pianoforte and violin in E minor; or to the minuet of Haydn's symphony in the same key.

The word ‘Canon’ is also applied, somewhat incorrectly, to a species of vocal composition called a Round. And thus we have duets, trios, and quartets ‘a canone,’ especially in the works of modern Italian composers, which are not really canons, but a much freer and less scientific kind of music. Good examples may be quoted in Beethoven’s ‘Mir ist’ (Fidelio), Curschmann’s ‘Ti prego,’ Cherubini’s ‘Perfida Clori,’ and Rossini‘s ‘Mi manca la voce.’ F. A. G. 0. [from George F. M. J. A. Grove, A Dictionary of Music and Musicians. New York: Macmillan, 1910.]

[back to text] Round. 1. A species of vocal rhythmical canon at the unison, differing from the regular canon in having no coda, thus being infinite; a favorite style of composition in England, from early times (the celebrated round Sumer is i-cumen in" is supposed to date from the middle of the 13th century) down to the present day. It differs from the catch with which it was formerly identical) in eschewing the comical effects of the latter.—The round proper sometimes has an harmonic support or accompaniment called the pes.—2. A circle- dance, or round dance. from Baker, Theodore. A Dictionary of Musical Terms. 11th ed. New York: Schirmer, 1907.