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.

a. Three polyphonic parts are distinguished, in instrumental music, as Upper, Inner, and Lower.

In writing for three solo instruments (string or wood-wind), the compass and register of the parts depend upon the instruments chosen. If a keyboard instrument is employed (Pianoforte, Harmonium, Organ), the compass is practically unlimited, though it is most consistent with the spirit of polyphonic music to confine the movements of the parts to the three and one-half octaves in the center of the keyboard and, while each of the three parts is entitled to nearly or quite this entire range, and while adjacent parts may occasionally cross, good balance must be preserved, (1) by avoiding too wide divergence of the outer parts from each other, and (2) by conducting the Inner part, as a rule, closer to the Upper than to the Lower part.

If vocal parts are chosen, they should be adjacent voices (Soprano, Alto, and Tenor, or Alto, Tenor, and Bass), and the compass and register will be defined accordingly. Further, the treatment of vocal parts constantly calls for more limitation (in every respect), and more careful consideration, than that of instrumental parts. This species of writing is, however, not to be chosen at present.

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:

Example ex116

Example ex116-2

Example ex116-3

Example ex116-4

*1) Auxiliary part.

*2) From this point on, a very distinct intention of omitting the first tone of the original M. is exhibited; these two versions of the Motive — with and without the initial accented tone — actually participate in the development, throughout the entire composition (Well-temp. Clavichord, Vol. II, Prelude 19).

*3) The lower part does not appear with its Imitation of the M. until the upper and inner parts have announced it four times. The upper part has the M. at the same time, in parallel thirds; such double announcements are not uncommon (see measure 6).

*4) The derivation of this episodic passage is somewhat indirect, but manifestly consistent.

*5) Here the M. appears to be divided between the inner and upper parts. Such interaction of the parts is, naturally, very exceptional, though not without occasional justification. See Bach, 3-voice Invention No. 1, second measure from the end; M. in Contrary motion, announced by the upper part, but, after one beat, taken up without interruption, and concluded, by the inner part.

EXERCISE 19.

A. Analyze the following Expositions:

B. Elaborate each of the following four Motives into a First Section, or Exposition; imitating the character and extent of those analyzed at A.

The pupil may choose any technical style, but he is advised to write for a keyboard instrument, — unless he may chance to be entirely familiar with the trio of strings, or some other ensemble. The choice of vocal parts must be deferred for a time.

Begin each example on a separate sheet, and leave ample space for its completion in the next lesson.

First review pars. 21; [par.] 28; [par.] 41 (thoroughly); [par.] 60; [par.] 61 entire (especially [61]d, [61]e); [par.] 62; [par.] 63; [par.] 64; and [par.] 65 (thoroughly):

Exercise 1901

Exercise 1902

Exercise 1903

Exercise 1904

* 1) Poco andante, — with gentle, but quite palpable, motion. The tempo must always be taken into consideration, as it affects, very directly, the question of euphony, — the number, extent, and quality of dissonant combinations; see par. 65b. The more rapidly these pass by, the less objectionable they are; and conversely. See also par. 14.

*2) The final tone is optional, both as to pitch and duration.

*3) This M. is to begin in the inner part, with auxiliary Bass. It may also be manipulated an 8ve higher, beginning in the upper part.

*4) Beginning in the inner part, with or without auxiliary Bass. Also a 5th higher (in a minor), as upper part.

*5) The prevailing rhythm should be quarter-notes.

*6) As lower part, — without auxiliary tones above.

*7) As upper part. Also a 5th lower (in b minor), as inner part.

C. Write two Expositions, one in minor and one in major, upon original Motives; or upon Motives chosen at option from the list given in Exercise 7A.

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 —

Bach, Well-temp. Clavichord, Vol. I, Prelude 18; Motive in the upper part with full auxiliary accompaniment; imitated in lower, in the 8ve; Section 1 closes in measure 5; the last Section (measures 18–27) is largely episodic, but derived strictly from the Motive; the last 3 measures are a Codetta.

Bach, Supplement (Peters ed. 1959), page 68, — called “Fuga,” but belonging to the lower range of “Invention “forms; irregular voice-texture.

Bach, Organ Comp. (Peters ed.), Vol. VI, No. 29, second division, 3/8 time; two Motives, in close alternation, — M. 1 in upper part, measures 1–3; M. 2 in upper part, measure 4.—Vol. VIII, No. 7.

Händel, Clavichord Suites, No. VII, Presto-movement of the “Ouverture”; largely episodic.

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.

For illustration of this rare design see —

Bach, English Suite No. V, “Prelude”; very broad sectional design; Section 1 extends to measure 40, and is largely thematic; Section 2 (to measure 52) is entirely episodic, and almost suggestive of a new (auxiliary) motive, — par. 52; Section 3, to measure 71, is again thematic, but largely two-voice texture; Section 4 is episodic, and closes in measure 81 with a semi-cadence; Section 5 resembles Section 2, but is longer (to measure 105), becoming strictly thematic, and, in its last six measures, corresponding to the end of Section 3; Section 6 resembles Section 4, and closes with a Dominant semi-cadence in measure 117; Section 7, from there to the end, is a literal recurrence of Section 1 (i.e., a da capo).

Bach, “Ouverture à la maniere française” (Peters ed., 208, No. 1), first number, second tempo (6/8 time), is very similar; Sections 1, 3, 5, 7 are thematic; 2, 4, 6 episodic; Section 7 is a da capo, abbreviated at the beginning. The first tempo (2/2 time) is an Introduction, balanced by a Postlude of corresponding character; they belong to a different species of polyphonic form, and are not to be analyzed here.

Bach, Partita No. IV, “Ouverture,” second tempo (9/8 time); 5 sections, the final one of which (last 26 measures) reverts to nearly every characteristic trait of the foregoing sections, and, during its last 11 measures, practically reproduces the First Section (transposed).

Bach, English Suite No. IV, “Prelude”; 14 comparatively brief sections, Nos. 13 and 14 a literal da capo of Nos. 1 and 2. The texture is largely two-voice, especially during the thematic passages; but unmistakable evidences of multi-voice counterpoint exist. — See, further, par. 71.

EXERCISE 20.

A. To each of the Expositions written as Exercise 19B add the concluding sections, — preferably not more than two or three in number. Review again pars. 19c, [par.] 61b, [61]d, [61]e, [par.] 63, [par.] 64, and [par.] 65.

B. Conclude the original work begun in Exercise 19C

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 —

Bach, 3-voice Invention No. 6; Part I embraces two Sections, closing respectively in measures 11 and 18. — Bach, Well-temp. Clavichord, Vol. II, Prelude 9; several Motives,—No. 1 in measures 1–8, No. 2 in measures 9–12, No. 3 in measures 13–15, and No. 4 in the Second Part (measures 8–10, etc.); Motive 1 recurs at the beginning of Part II; Part I closes with a long Codetta (measures 18–24), which recurs at the end of Part II (measures 19–27) with its two Phrases in reversed order, and followed by a 4-measure Coda. — Bach, French Suite No. 3, “Courante.”

Händel, Suite No. VIII, “Allemande”; largely 2-voice texture. — Händel, Suite No. IV, “Gigue”; two Motives in close alternation (upper part, measures 1 and 2, respectively); Part II begins with the second Motive, — not with Contrary motion of the principal Motive (par. 51.) — Bach, Partita No IV, “Gigue”; Part II is based upon a new Motive, which proves, after 6 measures, to be a Counter-motive to the principal Motive of Part I, in connection with which it appears once (or twice); the last 8 measures of the two Parts correspond. — Mozart, “Gigue” in G major (Cotta edition, No. 22); Part II begins with a fragment of the original Motive, answered by the same fragment in Contrary motion; the two Parts are very similar in contents; a Codetta of 5 measures is added to the whole. — Bach, English Suite No. 2, “Allemande”; the M. of Part I appears first in the upper part, curiously confounded (on the 4th beat) with one of the lower auxiliary tones, — compare the simple form as it occurs in the lower part in measures 6, 7; Part II has, apparently, a new Motive throughout, but careful scrutiny reveals its origin in the modified Contrary motion of the first Motive.

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

The above superb illustrations of the 3-voice Invention-species are to be analyzed with more than ordinary attention and minuteness.

Bach, Organ Comp. (Peters compl. ed.), Vol. I, Sonata No. I, 2nd movement; M. one measure, upper part, followed by another measure of episodic extension (related to par. 72c); Part II, after 5 measures’ exposition of the Contrary motion, corresponds closely to sections of Part I, but in different order, with inverted voices, and (partly) transposed. To be minutely analyzed.

Bach, Suite, Peters ed. 214, No. 3, “Gigue.”

Bach, Suite, Peters ed. 214, No. 5, “Gigue”; M. 3 or 4 beats, in lower part; curious insertion of auxiliary tones, before Imitation in each of the other higher parts.

Bach, English Suite No. III, “Allemande”; M. one measure, lower part.

d’Albert, Pianoforte Suite, op. 1, movement 5 (“Gigue,” — excellent example).

Händel, Suite No. VIII, “Gigue.”

Händel, Suite No. VIII, “Courante”; largely harmonic in general character, and at times definite 4-voice texture; the original motion of the M. recurs in measures 18 and 19 of Part II.

Händel, Suite No. XIII, “Gigue.”

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

Bach, 3-voice Invention No. 10; Part (Section) I closes, a little indefinitely, in measure 11, as already seen; Part II embraces two Sections, closing respectively in measures 22 and 25; in measure 26 a vague, but probably sufficient, intimation of “the return to the beginning” (the distinctive condition of a “Third Part”) is recognizable.

Bach, Well-temp. Clavichord, Vol. II, Prelude 3, second tempo (3/8 time); Section I ends in measure 10; Section II, based chiefly upon the Contrary motion of the M., closes in measure 17; the remaining (Third) Section is sufficiently indicative of a recurrence of the early contents of Section I to represent the 3-Part form.

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

Bach, French Suite No. 1, “Gigue”; Part II, based on the Contrary motion, terminates 7 measures from the end, upon a strong Dominant semi-cadence; what follows is a very obvious (though somewhat disguised) Third Part, or recurrence of the beginning; it opens with several stretto Imitations, in the original motion, and, in the second measure, in Contrary motion (upper voice); the last two measures correspond to the ending of Part I.

Bach, Well-temp. Clavichord, Vol. II, Prelude No. 5; M. one measure long, with an episodic extension of one well-contrasted lyric measure, which reappears at the beginning of Parts II and III, but does not participate essentially in the thematic development; Part I has a Codetta of 4 measures; Part II begins with the Contrary motion, but utilizes the original motion also; its ending, and the announcement of Part III, are very distinct; the latter diverges into the Sub-dominant key, in its 3rd measure, and thereafter follows almost exactly the line of Part I, transposed, of course, to the principal key.

Bach, Well-temp. Clavichord, Vol. II, Prelude 21; based throughout upon three brief Motives (announced in measures 1, 9, and 13, respectively), — see par. 52; Part II is 16 measures in length; Part III begins very definitely; a curious series of double-announcements of the principal Motive, in simultaneous original and Contrary motion, appears in measures 12 to 7 from the end.

Bach, Peters ed., Supplement (No. 1959), page 63.

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: *

Bach, Well-temp. Clavichord, Vol. I, Prelude 9; M. 7 beats long, followed by an episodic (lyric) extension; the first Imitation is in measure 3 (lower part); Part I ends in measure 8; Part II ends in measure 14; Part III is a nearly exact transposed recurrence of the First Part, ending, with an evaded cadence, in measure 22, and followed by a brief Codetta, or plagal extension.

Bach, Well-temp. Clavichord, Vol. II, Prelude 4; Part I, closing in measure 17, manipulates the principal M. (upper part, measures 1–5; lower part, very much modified, measures 5–7); Part II begins with a new (2nd) Motive, two measures in length (inner voice), which is carried through the first of its Sections (to measure 27); in measure 27 a third Motive appears (1½ measures, upper voice), derived from the auxiliary Bass at the beginning; this is retained to the end of Part II (measure 33); see par. 52; Part III (measure 33) is, for 7 measures, a transposed recurrence of the first 7 measures of Part I, with the M. transferred to the inner voice; thereupon it returns to the beginning and reproduces these 7 measures in the original key, with slight changes. The remainder of Part III embraces the following factors: Measures 45–49, an episodic passage, largely sequential; measures 50–55, a transposed reproduction of the Second Section of Part II; measure 56 to end, a reproduction of the last 7 measures of Part I, the upper and inner voices inverted. See, again, par. 58.

Bach, Well-temp. Clavichord, Vol. II, Prelude 19; Part I is analyzed in Example 116; Part II begins with Contrary motion of the M., and uses it freely during its two Sections; Part III (measures 22–30) is an almost exact reproduction of Part I, but transposed, and with inner and upper voices inverted (par. 58); a. Codetta of 3½ measures is added.

Bach, Well-temp. Clavichord, Vol. II, Prelude 22; the M. is 5 measures long, announced first in the inner part, and associated with contrapuntal fragments from its first members; an “Auxiliary figure” appears in measure 7 (inner part), which assumes vital importance in the total development; see par. 52a; Part II embraces three Sections, beginning respectively in measures 16, 24, and 42; Part III (measures 55–70) is an accurate reproduction of Part I, transposed, and with inverted inner and upper voices (par. 58); a Coda is added, the last 6 measures of which correspond to the ending of Section 2 of the Second Part.

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):

Example ex117-1

Example ex117-2

Example ex117-3

Example ex117-4

Example ex117-5

*1) The irregularity of rhythm at this place (16th-notes upon the accented beat only) is balanced and justified by the recurrence of the same figure two measures later; compare par. 22e. Further, the 16ths are called forth by the purpose of connecting the inevitable d♯ and d♮ as smoothly as possible.

*2) The First Part runs on thus in a fundamental rhythm of 8th-notes, interrupted three times as in measure 3.

*3) This figure of four tones is the evident thematic germ of the new, characteristic Counter-motive in animated movement, which begins abruptly at the outset of Part II. The figure was doubtless conceived and adopted by Bach as the Contrary motion of the first member of the principal Motive, in Diminution.

*4) The peculiar “cross-relation” between the inner and lower parts here (d♯–d♮) is justified by the structural joint (or light cadence) at the first beat; compare par. 19d, and Ex. 57, especially Note *7).

*5) This Counter-motive agrees with the preceding one throughout, but skilfully transposed to correspond to the interval of Imitation adopted for the M. in the upper part (the 5th); therefore, the contrapuntal calculation is identical, and harmonious union is assured.

*6) From here on the animated contrapuntal figure is transferred impartially from one voice to another.

*7) The animated rhythm is maintained, without a check, to the cadence of Part II, which is made with much emphasis upon a Dominant chord, in measure 37 (see Ex. 118). The 2nd Section of the Part begins (measure 25) with the Contrary motion of the animated Counter-motive (modified unessentially to conform easily to the altered conditions); this reveals more clearly the origin of the figure indicated in Note *3). The original is to be thoroughly analyzed, up to measure 37.

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:

Example ex118-1

Example ex118-2

Example ex118-3

*1) At the beginning of Part III the original rhythm of 8th-notes is resumed, abruptly; but after two measures the characteristic Counter-motive reappears. As a rule, the original rhythm should have more time than this, to re-assert itself.

*2) The rhythm of 16th-notes is carried on without interruption, up to the cadence-beats. There is no Codetta in this instance.

See also— briefly, and solely with reference to the rhythmic design of the three Parts and Coda—Bach, Well-temp. Clavichord, Vol. I, Fugue 19; Part I, measures 1–20; Interlude, measures 20–22; Part II, measures 23–42; Part III, measures 42–49; Coda, to end.

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.

See Bach, English Suite No. VI, “Prelude,” allegro-movement. The Introduction of 37 measures is not to be analyzed at present. Section 1 extends to the 11th measure; Section 2 utilizes the Contrary motion of the Motive; Section 3 (measures 20–49) is preponderantly two-voice texture, and contains several effective episodic passages, more in the style of harmonic figuration than polyphonic development; this closes with a strong Tonic cadence in the principal key, and terminates the First Division. The following five sections constitute the Middle Division or “Trio” (up to measure 110); Section IV (measures 49–61) is mainly episodic, and suggests the presence of an Auxiliary Motive; Section V (measures 61–76) reverts emphatically to the principal M., and contains a reminiscence of Section III; Section VI (to measure 90) begins with a novel treatment of the M., and then (measure 80) corroborates the main contents of Section IV; Section VII (to measure 106) begins with a new form of treatment, but soon runs into the current of Section III, to which, especially during its last 6 or 7 measures, it bears close resemblance; Section VIII (to measure 110) is a brief Re-transition. The remaining three sections (measure no to the end) are a literal recurrence of Sections I, II, and III, i.e., the First Division.

Bach, English Suite No. II, “Prelude.” This is preponderantly two-voice texture, and its First Division has already been analyzed in Exercise 13. The Middle Division (measures 55–110) begins with an episodic passage, based upon a new (Auxiliary) Motive which distinctly governs the Division, though the principal M. asserts itself from time to time,— somewhat analogous to par. 48c; in measure 87 a 4-measure Section occurs, corresponding exactly (excepting in key) to the Codetta of the First Division; it is immediately repeated, with transferred register and other unessential changes; in measure 95 the Auxiliary M. again resumes its sway, and leads to an unusually impressive cadence in measure 110, in the Relative key, — followed immediately by the literal reproduction of the First Division, as “Da capo.” It is almost certainly only an accidental coincidence that the three Divisions should each contain the same number of measures (55).

EXERCISE 21.

A. Write a complete example of the 3-voice Invention in 2-Part Song-form (broad design, par. 69b), employing the same Motive in Part II, chiefly in the original motion (par. 48a). An original M. is to be used, — preferably in major.

B. An example of the 3-voice Invention in the 2-Part Song-form, as “Gigue” (par. 69c), — Contrary motion of the M. as basis of Part II. Original M., preferably in minor, and 6/8 time.

C. Two examples (major and minor, but in different species of measure from each other and from those above) in the 3-Part Song-form, par. 69d and [par.] 69e. Thematic basis of Part II optional. Motive original

D. An example (preferably major) in the 3-Part Song-form, with characteristic counter-motive in animated rhythm during Part II, — par. 70a and [par.] 70b. Either Motive 3 of Exercise 19B may be used, or an original one of similar stately character.

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.

This is clearly illustrated in Bach, 3-voice Invention, No. 11, which is to be carefully analyzed; the thematic Figure of four (or five) notes stands at the beginning of the principal melodic part, but its connection with the latter is thereafter, almost constantly, purely incidental; the lyric sentences are built upon, not derived thematically from, this Figure. The character of this Invention is distinctly lyric; its form is Sectional.

See further, briefly: Bach, Well-temp. Clavichord, Vol. I, Preludes 9 and 17; Vol. II, Prelude 21.

e. These distinctions of Style must be adopted and applied in a very general sense only. It is as impracticable as it is obviously undesirable, to coerce a polyphonic composition into such definite agreement with the essential conditions of “Style” as is found in some free homophonic structures. Consequently, even the analytic definition will often be found doubtful and difficult, because the related phases overlap so widely that both styles may be distinctly represented in the same composition; a lyric Invention may incline toward either the light or the serious style; and even these extremes may touch, — a serious Invention may contain vivacious episodes, and vice versa.

Furthermore, the number of parts employed influences the style to a certain extent; two-voice texture is most appropriate for the Light styles, three-voice for the Lyric, and four- (or more) voice for the Serious. Examples in two-voice texture have been cited in pars. 51 and [par.] 53. Three-voice texture is the only kind that may be adapted to all three styles.

Finally, in an Invention expressly designed to represent one or another of these styles, the episodic passages are apt to predominate somewhat, both in extent and character; for the relief from strict thematic treatment which they afford contributes to the realization of the specific purposes involved. And, in general, the structural (formal) details advance proportionately in significance, and are defined more distinctly than in the more neutral varieties of polyphonic development. Compare pars. 45 and [par.] 53.

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:

Example ex119-1

Example ex119-2

*1) The Pedal-part is based upon this independent M. throughout.

*2) Here the Pedal has, constantly, a simplified form of the first member of the principal Motive. For further illustration:

See Bach, 3-voice Invention No. 5; there are several brief thematic figures, the principal one of which is first announced in the upper part (one measure long); the form is Sectional, the style Lyric; during the last 8½ measures, the inner part corresponds exactly to the upper part of the First Section. The Bass is an independent auxiliary part throughout, in uniform harmonic Figuration.

Bach, Well-temp. Clavichord, Vol. I, Prelude 24; the Bass is an auxiliary running part in 8th-notes, with two or three brief interruptions; the consistency of its formation is noteworthy; the M. of the two other voices is one measure long, first announced in the inner part, and imitated mostly in stretto; in Part II the original M. is abandoned, and in its place the modified Diminution is adopted as thematic basis, resulting in greater rhythmic animation throughout the Part.

Bach, 30 Var. for the Clav. in G major; Var. 2.

Bach, Organ Compositions (Peters compl. ed.), Vol. I, Sonata No. IV, 1st movement; the form embraces 3 Sections, with Coda, and an independent Introduction; the M. is 6 measures long, first announced in the inner part; the Pedal-part (Bass) is entirely independent of the thematic voices; Section 3 (measure 25 from end) is wholly episodic, but corroborative of the foregoing Sections.

The same Sonata, 2nd movement; Pedal entirely independent; design embraces 9 brief Sections; principal M. of two measures, announced by the upper part, carried through first 2 Sections (measures 1–11); an auxiliary M., one-half measure in length, is adopted as sole basis of Section 3 and (in Contrary motion) of Section 4; Section 5 (measures 22, 23) is episodic; the remainder is practically a reproduction of the foregoing, transposed, — Sections 6, 7, and 8 corresponding closely to 2, 3, and 4, extended by a 9th Section based on the principal Motive (last 5½ measures).

The same Sonata, 3rd movement; 4 Sections and repeated Codetta; M. 8 measures; the Pedal takes the M. twice, — as regular third announcement (measures 21–27), and again near the end, — in a simplified form, convenient for pedal-technique otherwise the Bass is independent.

Bach, same Volume, Sonata No. I, last movement; 2-Part Song-form, “Gigue” species; the Pedal has occasional fragments of the M., but is chiefly independent; Part II, after 15 measures devoted to the exposition of the Contrary motion, corresponds to the latter portion of Part I, but transposed, and with inverted voices (par. 58).

The same Sonata, first movement; 2-Part Song-form, closely corresponding structure; M. 1½ measures; the Pedal is independent, excepting a very few imperfect imitations of the principal figure of the Motive.

Mendelssohn, Pianoforte Capriccio, op. 5, middle Division (measures 135–290); M. 8 measures, upper voice; running Bass during Part I; M. in Contrary motion and running upper voice during Part II; after 28 measures (3 complete announcements) the M. appears in sequential succession, each time contracted more and more at the end (up to the where another complete announcement is made); in Part III the original motion of the M., and the running Bass, are resumed.

Mendelssohn, Prelude (Pfte.), op. 35, No. 4; 3-Part Song-form; Part I, Double-Period with Codetta; Motive, 2 measures; Part II is based upon a new M. of 2 measures, in stretto Imitations, but also announces the principal M.; Part III like I, but abbreviated to Single Period with Codetta, and extended by a Period taken from Part II, and brief Coda; the Bass is a running auxiliary part throughout, and consists in strictly uniform harmonic Figuration.

EXERCISE 22.

A. Write a complete 3-voice Invention, with consideration of the essential conditions of the Spirited Style (par. 72a), and the Serious Style (par. 72b), as follows: Adopt the design of the 3-Part Song-form; develop the rapid M. during Parts I and III, and the stately M. during Part II; the second M. may be quite new (par. 48c), or it may be developed out of the first Motive by Augmentation (of a portion of the latter),— see par. 31a. This arrangement of movements reverses the rhythmic order given in par. 70a.

B. Write an Invention in the Lyric Style, according to par. 72c, mode, tempo, and form optional.

C. An Invention with a Running Bass (par. 73b).

D. An Invention for the Organ, with Independent Pedal-part (par. 73b).