# Fugue (Prout)/Chapter 9

CHAPTER IX.
THE MIDDLE AND FINAL SECTIONS OF A FUGUE.
290. Hitherto our task has been comparatively easy. It is possible to give very definite rules as to the correct answering of a fugue subject, the treatment of the exposition and episodes, and the construction of stretto. But in dealing with those parts of a fugue which we are now approaching, we are met by far greater difficulties than any we have as yet encountered. These arise from the fact that as soon as in composing a fugue we get beyond the exposition (or counter-exposition, if there be one), we are left to a very great extent free to do what we please; and it is quite impossible here to give more than very general principles for the guidance of the student.
291. The first great fact which must be clearly grasped is, that every fugue, however much variety there may be in the details, is in its main outlines constructed in the same general form. This is the form which is commonly known by the name of Ternary or Three-part form. A movement in ternary form can always be divided into three principal sections. In a piece other than a fugue (for instance, in the slow movement of a sonata, in which this form is frequently used), the first section will be mostly in the key of the tonic, and will close either in that key, or in one of the most nearly related keys—probably the dominant if the movement be in a major key, and the relative major if it be in a minor key. The second part of such a movement generally consists of an episodical subject, but is invariably in a different key from the first part; while the third section usually repeats the subject of the first in the tonic key.
292. We can best show the ternary form by a diagram—
| 1st Section. Chief subject. (Tonic key.) | 2nd Section. Episode. (Related key.) | 3rd Section. Chief subject. (Tonic key.) |
This skeleton form can be filled up in an almost infinite number of different ways, as regards variety of detail; but the broad outline given above can always be distinctly traced.
​293. The same form, though with some modifications, which we shall proceed to point out, is clearly to be seen in every well-written fugue. Its first section comprises the exposition and counter-exposition, when there is one, or (if there be no counter-exposition) it may also include an entry of subject or answer after the first episode, provided such entry be in either of the keys of the exposition. It will be remembered that the whole of the exposition oscillates, if we may so speak, between the keys of the tonic and dominant. If at the end of the exposition, the first episode modulates, so as to introduce an entry of the subject or answer in a new key, then the first section of the fugue ends with the exposition itself. For an illustration of this, see the passage from Bach's fugue in C minor, quoted in § 215. Here the exposition ends on the first note of the ninth bar, and the following episode, which modulates to E flat, to introduce the next entry of the subject, is the beginning of the middle section of the fugue. But if the first episode does not modulate away from the tonic or dominant key, but leads either to the counter-exposition, or to an isolated entry of subject or answer in the original key (as in our example (a) § 222) this episode and the following entry belong to the first section. To put it in general terms—The first section of a fugue extends as far as the end of the last entry of the subject or answer in the original keys of tonic and dominant. As a natural corollary of this, the second section begins with the commencement of the first episode which modulates to any other key than that of tonic or dominant.
294. The length of the middle section varies greatly in different fugues. In some it is very short, containing only one or two entries of the subject, connected by episodes of only a few bars' length. For instance, in the 31st fugue of the 'Wohltemperirtes Clavier,' a somewhat long exposition is followed by the counter-exposition in stretto which we quoted in § 270. Thus far all belongs to the first section of the fugue, because we never get away from the tonic and dominant keys. If the student will examine this piece he will see that, out of 70 bars which it contains, the exposition and counter-exposition extend to bar 44, or nearly two-thirds of the whole. There is only one episode in this fugue (bars 44 to 53), followed by an entry of the tenor in the key of the subdominant (bars 53 to 58), after which the reintroduction of the subject and answer in the tonic key (bars 59 to 70) form the final section of the fugue. The whole will therefore be analyzed thus—
First Section—Exposition and Counter-exposition (bars 1–44).
Middle Section—Episode and entry of subject in subdominant (bars 44–58).
Final Section—Return of subject and answer in tonic key: Coda (bars 59–70).
295. The disproportion in the length of the middle and final sections of this fugue, as compared with the first section, is ​very unusual, and we have purposely given it as an extreme instance. More frequently the exposition will be comparatively short, and the middle section will contain at least two or three entries, or groups of entries, of the subject. We will take the 21 st fugue of the 'Wohltemperirtes Clavier' as a fair average specimen of the relative lengths of the three sections. The opening bars of this fugue were quoted in § 173.
296. If the student will take his copy of the fugue, and number each bar for reference, he will find the following analysis of its form perfectly easy to follow.
First Section (Bars 1 to 17)—Exposition, including an additional entry in the treble (§ 187).
Middle Section (Bars 17 to 41)—This section contains four distinct features:—(a) First episode (bars 17 to 22); a sequential extension of the last part of the subject, modulating to G minor; (b) First group of middle entries (bars 22 to 30), viz.: subject (alto) in G minor; answer (bass) in C minor, both entries being accompanied by the two countersubjects; (c) Second episode (bars 30 to 35); a modification of the first, in the first bars of which we see a free inversion of bars 19, 20, the change in the quaver figure of a fifth to a third, causing the double counterpoint to be partly in the octave and partly in the thirteenth; (d) Second group of middle entries (bars 35–41). This commences with a fragmentary entry of the answer in the alto, followed by a complete entry of the subject in E flat.
Final Section (Bars 41 to 48)—Return of subject (alto) in the tonic key, the first notes being altered to connect better with the key of E flat (bars 41 to 45); coda (bars 45 to 48).
297. The analysis of another fugue from the same work will assist us in understanding the construction of the middle section. We select No. 34 in E minor. This fugue, of which we quoted the subject and countersubject in § 168, has a real answer. In such a case, it is impossible to distinguish between subject and answer, excepting by observing the distance of entry. If a second entry is a fifth above or fourth below the first, we know that the first was the subject and the second the answer; if the second were the fourth above or fifth below the first, then the first would be the answer and the second the subject. But with single entries, or entries at other distances, there is no means of distinguishing; we therefore shall always speak of the theme as the subject in doubtful cases. If the answer be tonal, as in the fugue last analyzed, the difference in its form shows at once which it is; though even in this case we often find a real instead of a tonal answer in the later sections of a tonal fugue.
298. The fugue in E minor is so instructive that we give it in full, writing it in open score. We most strongly recommend to the student the putting fugues into score; he will get a far deeper ​and more accurate insight into their construction by this means than by any amount of mere reading or playing them.
J. S. Bach. Wohltemperirtes Clavier, Fugue 34.
299. The first section of this fugue contains only the exposition. Though the subject is announced in an outer part, we do not find here the additional entry spoken of in § 186; perhaps because of the extent of the subject, which is the longest of any in the 'Forty-Eight.' The exposition ends in the 18th bar, and is immediately followed by the first episode (bars 18 to 23). As this episode does not introduce a new entry in either tonic or dominant key, but modulates to the relative major, we see ​that it belongs to the middle section of the fugue, and not to the first (§ 293). This first episode is formed from the last bar of the subject, continued sequentially in the bass as far as bar 20, and accompanied by a figure, evidently founded, as regards its rhythm, on the third and fourth bars of the subject, and treated by free imitation between treble and alto. The second half of the episode contains a new sequence in the bass—a modified form of the treble of bar 7—accompanied by the last notes of the subject, given alternately by inverse motion in the treble and direct motion in the alto.
300. The first episode, ending, as we have seen, in G major, leads to an entry of the subject in that key (bar 23). It is accompanied by the countersubject, which enters in the alto at bar 26, and which here for the first time appears below the subject. At bar 29 the answer enters in the alto. That it is to be looked at as an answer here, is shown by the fact that it is a fourth below the preceding entry in the treble. The countersubject is given, as usual, to the voice which last had the subject. The bass accompanies with a free part, the material of which is taken partly from the treble of bars 7 and 8, and partly from the last notes of the subject. These two appearances of subject and answer form the first group of middle entries, which extends from bar 23 to bar 35.
301. The second episode (bars 35 to 41) is made of the same material as the first—mainly the last notes of the subject, but with different combinations from the previous ones, and modulates to B minor. In this key, the next middle entry is made by the bass (bar 41), the countersubject now being in the alto, and the treble supplying a counterpoint mostly made from the last notes of the subject, direct and inverted. It must be noticed that all the middle entries after the first are isolated entries—that is, each one is divided from the following by an episode.
302. The third episode is the shortest of any (bars 47 to 49). It is a transposition a fourth lower (with a slight modification at the end) of bars 18 to 20 of the first episode, and leads to an entry of the subject (alto) in the original key (bars 49 to 55). In a large number of fugues a return to the tonic key is not found till we reach the final section of the fugue but we sometimes, as here, meet with a middle entry in the tonic. We see another instance in the third fugue (C sharp major) of this work. When an entry of the subject in the tonic is not followed by any entry in another key (except possibly the dominant), this tonic entry indicates the beginning of the final section of the fugue; if, as here, another subsequent modulation is made, the tonic entry forms part of the middle section. In the entry now under notice, the countersubject appears for the first and only time in the bass. Though this entry and the preceding (in bar 41) bear to one another the relation of tonic ​and dominant, we have not described the B minor entry as an answer, because it is separated from the next by a short episode.
303. The fourth episode (bars 55 to 59) presents us with the old material—the last notes of the subject sequentially treated in the treble—with new counterpoints for alto and bass. It modulates to A minor, in which key the last middle entry is made by the treble (bars 59 to 65), the alto having the countersubject.
304. The fifth, and last episode (bars 65 to 70), like all the others, shows the last part of the subject in fresh combinations. It leads back to E minor, to introduce the final section of the fugue, which will always be in the key of the tonic. The pause after the half cadence in bar 70 is rather rare in an instrumental fugue, but somewhat more common in a vocal one.
305. One introductory bar after the pause leads to the final entry of the subject (bass) in the tonic key (bars 71 to 77). In some fugues all the voices enter with either subject or answer in the final section. This is especially the case in fugues which have a stretto, a feature which, it will be seen, is wanting in the one now under notice. But in many of the fugues of Bach, the final section contains, as here, only one entry. This is followed by the coda (bars 77 to 86). A coda (Italian = tail) is a passage added at the end of a piece of music to bring it to a satisfactory conclusion. Sometimes, as here, it will consist of only a few bars; sometimes, as in many symphonies and sonatas, it will be of considerable length and importance. The chief feature of the present coda is the ornamented dominant pedal (bars 78 to 81); we also, quite exceptionally, find a second pause (bar 83), here on the last inversion of a dominant minor ninth.
306. Another point of importance is illustrated in this coda. In the 83rd and last bars will be seen the introduction of an additional voice. This is often met with at the conclusion of a fugue. Out of the 48 fugues in the 'Wohltemperirtes Clavier' we find such additional parts in sixteen, mostly in approaching the final cadence, but occasionally (e.g., in fugues 35 and 39) earlier in the coda. Let the student examine, as striking examples of this procedure, the last bars of the fugues in A minor (No. 20) and C sharp major (No. 27).
307. We will now tabulate, for future use, the entries of the subject in the fugue just analyzed, noting the succession of keys, and the voice to which each entry is given.
I. Exposition. :
| | 1. Subject (treble)—bar 1. | E minor. |
| | 2. Answer (alto)—bar 6. | B minor. |
| | 3. Subject (bass)—bar 12. | E minor. |
| II. Middle Section. ||
| | 4. Subject (treble)—bar 23. | G major. |
| | 5. Answer (alto)—bar 29. | D major. ​ |
| | 6. Subject (bass)—bar 42. | B minor. |
| | 7. Subject (alto)—bar 49. | E minor. |
| | 8. Subject (treble)—bar 59. | A minor. |
| III. Final Section. ||
| | 9. Subject (bass)—bar 71. | E minor. |
It will be seen that no two consecutive entries are for the same voice, or in the same key.
308. Before proceeding to lay down any general principles, we will analyze another fugue from the same work, constructed on a different plan, and illustrating several points not shown in the fugue in E minor.
J. S. Bach. Wohltemperirtes Clavier, Fugue 29.
This splendid fugue—one of the most perfect of the 'Forty-Eight'—is a remarkable example of Bach's power of letting art conceal art. There is not one which flows more naturally and unconstrainedly, and yet there is not one which is fuller of scientific device. This will appear from our analysis.
309. Let us first look at the subject. We see here an exception to the general rule given in § 29, that with a downward leap of a fifth the first note will be dominant, and the second tonic. The subject begins with a leap from tonic to subdominant, and consequently takes a real answer. Had D been a dominant, the key of the fugue would have been G, and the answer
As C sharp is not used in the subject, the key is doubtful at first; in such cases the answer always decides the point.
311. The exposition foreshadows the treatment by stretto which Bach intends; for the entry of the bass in bar 6 is half a bar sooner than its regular place. The exposition ends at the 7th bar, and the first episode is made from the figure just quoted, by close imitation, in all the voices at one crotchet's distance.
312. As the following entry of the subject (bar 10) is in E minor, we should expect the episode to modulate to that key. Bach, however, does not do this, but makes his modulation on the first notes of the subject itself. As the original keys of tonic and dominant are not quitted till after the episode, we include this in the first section of the fugue, and consider the middle section to begin in bar 10.
313. The first group of middle entries, bars 10 to 13—subject (alto), answer (treble)—is followed by the second episode, only one bar in length. We count this as an episode because it effects a modulation from B minor to A. At bar 14 the first stretto is introduced. It is for two voices only, in the fourth above, and at a distance of half a bar. It is seldom that so early a return is made to the tonic key; but it may be said here, that in fugues containing much stretto, we often find a much greater prevalence of the original keys, and less modulation, than in fugues in which there is no close imitation. Nos. 1 and 4 of the 'Wohltemperirtes Clavier' are illustrations of this.
314. In the third episode (bars 16–21) we see the figure of the second, a sequential prolongation of the first, treated by close imitation in all the voices. It leads to the second stretto (bars 21 to 23). We said in § 251 that when there were several stretti, their interest should gradually increase. We see this illustrated here. Three voices now take part in it; the treble enters one bar after the tenor, and the alto half a bar after the treble. The intervals of entry (fifth and octave) are again regular.
315. Bar 24, though not containing subject or answer, cannot be considered as episode, because it does not modulate to a fresh key, but introduces an entry which clearly belongs to the preceding group, being the regular answer to the last preceding entry—the subject in bar 22. We therefore regard bar 24 as a codetta, similar to that so often seen in an exposition.
​316. At bar 27 the third stretto is introduced. The interest is here heightened by bringing in the imitations at a closer distance—one crotchet instead of half a bar. Variety is also obtained by introducing all the voices in the octave. We have marked the entries with 'A' instead of 'S,' because the G natural of the tenor in the 28th bar proves the key of the music to be D. The 'A—?' in the alto of the same bar indicates an incomplete entry. Another, similarly marked, will be seen in bar 44.
317. Another series of close imitations will be found in the fourth episode (bars 29 to 33). This leads to the fourth middle entry—another stretto for three voices, each a sixth above the preceding, and at a crotchet's distance. This stretto is an advance upon the preceding, inasmuch as now all the three voices complete the subject.
318. The fifth and last episode leads to the final section of the fugue, in which the subject is once more introduced in the tonic key (bar 40). It is now accompanied with simultaneous double counterpoint in the tenth and octave (compare bar 40 with bar 3). The entry of the answer at bar 43, with chromatic alterations, leads to the last and closest stretto. This is the stretto maestrale, already quoted and described in § 278, and it is followed by a short coda, in which the figure of imitation, so often referred to, is maintained to the very last note.
319. It will be seen that this fugue differs in many important respects from the fugue in E minor, and nearly every leading feature of a fugue which is not shown in the one is illustrated by the other. One point of difference is that in the former there are scarcely any rests; all the voices are almost continuously occupied. In the fugue in D, on the other hand, we find not only one, but in bar 16 two voices resting at once. It is generally better to give occasional rests to some of the voices. After such a rest, the voice that has been silent should enter with the subject, or with some decided feature of the counterpoint (see the entries in bars 17 and 18), and not drop in, as it were, incidentally, and without anything particular to say.
320. Another point to notice in this fugue is that nearly all the entries of the subject are preceded by a rest. That this is not absolutely necessary was seen from the fugue in E minor, in which very few of the entries are so approached; but it is nevertheless preferable as marking the entrance of the subject more clearly. Where this cannot well be managed, the next best thing is to approach the entry by a leap, as in the fugue in D, bars 27, 33, and 43.
321. In bars 16, 20, and 27 of the fugue in D will be seen full cadences, and at bars 10, 33, and 44, inverted cadences. The latter are very common, the former are rarer. It must be remembered that when a full cadence is employed in a fugue, the music must never come to a standstill; the last note of the cadence must always be a starting point for a new entry, ​either of the subject (as at bar 27) or of some important figure of counterpoint (as at bars 16 and 20). Occasionally in old fugues, we meet with a full close in some related key just before the final stretto; but this is not to be recommended.
322. To what keys, and in what order, is it advisable to modulate in the middle section of a fugue? To this important question it is not possible to give more than a general answer. The rule given by the old theorists was that the modulations in a fugue should be confined to the nearly related keys. We quote Cherubini's remarks on this subject:—
"When a fugue is in a major key, the key into which we should modulate first is that of the dominant with its major third; then into the sixth—the relative minor key of the principal key; after that into the major key of the subdominant, to the minor key of the second, and to the mediant, also minor; and then return to the key of the dominant, in order to proceed to the conclusion, which should be in the principal key.
"It is permitted in the course of a fugue in a major key to change the principal key into the minor; but this permutation should be employed only for a few moments, and merely to bring in a suspension on the dominant, in order afterwards to attack the principal major key.
"When a fugue is in a minor key, the first modulation is into the mediant major key, which is the relative major of the principal key; then we modulate in turn into the dominant minor key, into the sixth major key, into the subdominant minor key, and into the seventh major key; and lastly from one of these keys return to the principal key."
323. We have quoted Cherubini somewhat fully, because it is well that students who are working for an examination should know what the old rules are; but when we come to apply to them the test of Bach's practice, we find that they will not hold water for a moment. In the whole of the 'Forty-Eight,' there is not one single fugue in which the order of modulation prescribed by Cherubini is observed. What is even more to the point—in the 'Art of Fugue,' a work written by Bach, to show the proper method of fugal construction, we also find no fugue written on Cherubini's plan.
324. Besides this, we find that Bach, though he generally keeps within the circle of nearly-related keys, has no hesitation about going into unrelated keys when he has a mind to. No. 4 of the 'Art of Fugue,' the key of which is D minor, contains a modulation to B minor. In the fugue in E minor (No. 10 of the 'Forty-Eight') there is at bar 30 an entry of the subject in D minor; and in the fugue in A flat (No. 41 of the same work), we see at bar 32 an entry in E flat minor. The great organ fugue in D contains entries in C sharp minor and E major, and the organ fugue in B minor has an entry in C sharp minor. It is quite clear, either that Bach did not know how to write fugues properly, or that the old rules need altering. Of course we choose the latter alternative.
325. The rules as to the course of modulation and the middle entries in fugues which we deduce from Bach's works, are as follows:—
I. It is best in general to keep within the circle of ​nearly-related keys, but an entry in an unrelated key is occasionally possible, if such key be naturally introduced, and not (to use Mozart's immortal phrase) "pulled in by the hair of its head."
II. A middle entry may either be isolated—that is a single appearance of subject or answer in one voice; or there may be a group of entries, two or more voices in succession giving subject or answer. In the latter case it is best, except in a close stretto (see bars 44, 45, of the fugue in § 308), that the entries should be at the distance of a fourth, fifth, or octave.
III. No two successive groups of entries should have the same order of voices.
IV. No two groups of middle entries should be in the same key, nor should the same voice have subject or answer twice in succession.
326. This last rule is not always strictly observed. A remarkable exception will be seen in the 19th fugue of the 'Wohltemperirtes Clavier,' where the bass gives the subject in bar 4, and the answer immediately after in bar 6. Another example will be seen in the fourth fugue of the same work, where at bars 19 and 22 there are two consecutive entries of the subject in the tenor. The rule is, nevertheless, a good one, and the student will do well to adhere to it carefully.
327. It is not necessary that all the voices should take part in a group of middle entries. In a two-part fugue it will of course be needful, but in one with more than two voices, one at least may rest, if desired. This, in fact, is often expedient, for the sake of obtaining the contrast of thinner and fuller harmony. For an example, see No. 15 of the 'Forty-Eight,' bars 34 to 46, and 51 to 55. In the final section of a fugue, which always begins with the last return of the original key, it is imperative that all the voices be engaged, though it is not necessary that all should have subject or answer. If, however, the fugue contains stretti, it is best that all the voices take part in the final stretto, which should also be the closest.
328. We have already seen that there is no fixed number of groups of middle entries, which may vary from one or two to five or six, or even more. Neither is there any rule as to the order of voices for these middle entries, except in so far as concerns the point referred to in Rule III., § 325. It must not be forgotten that if stretti are used, their interest should always be cumulative.
329. When a pedal point (either dominant or tonic) is met with in a fugue, it is almost always in the final section. Occasionally we find a pedal earlier in a fugue, as, for instance, in No. 35 of the 'Wohltemperirtes Clavier,' and in the choral fugue, "For holy blood must be" in Schumann's 'Paradise and the Peri.' Such cases are, however, exceptional, and the student, if he wishes to use a pedal point, had better reserve it for the final section, as it is seen in the fugue in E minor in § 298. In a fugue containing stretti, the last is often made upon a pedal, ​which sometimes in this case is an additional voice, as in fugue 20 of the 'Forty-Eight,' bars 83 to 87.
330. A few general principles will conclude this part of our subject. We have already (§ 321) spoken of the necessity of continuity in fugal writing. This necessity will be best shown by quoting a passage from Mozart's 'Musical Joke,' written as a burlesque of unskilful composers. This work is full of the most ludicrous mistakes in composition, intentionally introduced. Consecutives, passing notes quitted by leap, and similar atrocities, abound in it, but treated so skilfully that the joke is always perceptible. In the finale, Mozart introduces a little bit of fugue, thus—
Mozart. 'Ein Musikalischer Spass.
The student will see that there is here a subject, a countersubject, and a regular exposition; and yet how ludicrous the ​effect of the whole is! This is because of the want of continuity; the piece is chopped up by the full cadences into lengths of four bars each. A full cadence in a fugue (which should in all cases be sparingly used) must always be a point of departure for some new entry, if not of the subject, at all events for some important feature of counterpoint. We have referred to this above, but we repeat it as a point of vital importance in fugal writing, which will be enforced by the example just given.
331. We saw in the fugue in D (§ 308) the expediency of occasional rests in the voices (§ 319). After a rest, the voice which has been silent may enter on any part of the bar; but it should always end before a rest, on an accented beat.
332. One final point remains to be noticed. It has several times been incidentally said that a fugue is essentially a polyphonic composition. It is therefore of great importance that each voice should preserve its individuality. Passages for two parts in thirds or sixths, though not absolutely prohibited, should be sparingly used, and, in any case, not for long together. Passages in which a subject is accompanied by plain chords are also seldom advisable, though they are occasionally to be used, even with good effect, as in the following example—
J. S. Bach. Wohltemperirtes Clavier, Fugue 18.
The student will do well in his attempts at fugue to keep to the strictly contrapuntal style.
333. The student may now begin the composition of a complete fugue. To show him how to set to work, we shall write three fugues for him, one in two parts, one in three, and one in four. We will take the subject we wrote in § 254 to illustrate stretto, as this will give us the opportunity of introducing several stretti at different intervals and distances. The student had better begin by writing a few two-part fugues, as these are easier than those with three or four voices. He must remember not to introduce any progressions between the voices which would not be allowed in free two-part counterpoint. He should also always bear in mind the harmonic progressions indicated by the outline harmony.
​334. The first thing to do is to lay out clearly in the mind the general plan of the fugue. We know that the first and the final sections will be in the keys of the tonic and dominant; but we ought also to decide on the keys and order of the middle entries, and not start on our journey like Abraham, not knowing whither we go, and trusting to luck to come out somewhere. As we do not intend any of our specimen fugues to be very long, we will content ourselves for the one in two parts with two groups of middle entries—one in A minor and the other in F major. The outline of the fugue will therefore take the following form:—
(1) Exposition, to which, as there are only two voices, we shall add a counter-exposition.
(2) First episode, modulating to A minor.
(3) First middle group of entries in A minor, with first stretto.
(4) Second episode, modulating to F.
(5) Second middle group of entries in F, with closer stretto.
(6) Third episode, modulating back to C.
(7) Final section of fugue; entries in C, with closest stretto.
335. Some such outline as this ought to be clearly in the student's mind before he begins to write. We now give the complete fugue.
​The rule given in § 325 that two successive entries should not be in the same voice does not apply to two-part fugues; for if it did, the same voice would have either subject or answer mostly all through a fugue. We shall therefore modify the rule in this case, and say that in two-part fugue "the same voice should not have subject or answer twice in succession, unless separated by an episode."
336. We have written a countersubject against the answer (bars 5 to 9), but shall be unable to make much use of it in the middle and final entries, because of the stretti; for the countersubject must evidently be discontinued when the voice that is giving it has to take up the subject or answer. But fragments of it will be seen in bars 26 and 34.
337. In the counter-exposition (bars 10 to 18) the treble which first had the subject leads with the answer, and the bass replies with the subject. The first episode (bars 18 to 21) is made from the inversion of the last three notes of the subject, treated sequentially by the treble, and imitated in the fourth below by the bass.
338. The first group of middle entries (bars 22 to 28) is led by the answer, and imitated in the octave, also by the answer, at two bars' distance. The leading voice is here able to complete the answer. The second episode is founded on the fourth bar of the subject, imitated in the fourth above; it will be remembered that the imitation in the first episode was in the fourth below. This second episode is only two bars in length.
339. In the next group of middle entries (bars 30 to 35), the subject in the bass is followed in the regular interval by the answer at one bar's distance. The third episode is a sequential treatment by the treble of an ornamented form of the countersubject in bar 8, imitated in the fifth below by the bass. The final section of the fugue contains the closest stretto (bars 40 to 45) at half a bar's distance, the answer being lengthened by the repetition in bar 43 of half a bar, to bring the piece to a satisfactory close.
340. We will now write a three-part fugue, and for the sake of variety will take the answer of the last fugue as our subject. As this answer was in the key of the tonic, it follows that the present answer will be in the key of the dominant, and will consequently be identical with the subject of the last fugue. We will write an entirely new countersubject—this time, for a change, in double counterpoint in the twelfth, and will begin the fugue with the middle voice, so as to show the countersubject in both positions in the exposition. Our plan of modulation shall be the same as in the last fugue, with middle entries in A minor and F, and each group of entries after the exposition shall contain a stretto.
341. After the explanations given of the last fugue, this will need but few remarks. Note that in all the stretti the last voice to enter always has the subject or answer complete (§ 252). Observe also, as showing how much variety is possible in a subject well adapted for the purpose, that none of the stretti here given are identical with those in three parts made from the same subject in §§ 264, 265. The incomplete entries are, as before, indicated by S——? Where the entries are at irregular distances, they are marked with S, whether they resemble subject or answer.
342. Now let us look at the episodes. The first is made from the sequential inversion in the bass (bars 13 to 16) of the last notes of the subject, accompanied by sequential imitations in treble and alto of a variation of bar 4 of the subject, by direct motion. The second (bars 25 to 30) is a canon in the fourth below between treble and bass, founded on the first part of the countersubject, and accompanied by a florid counterpoint in quavers for the alto. The third (bars 36 to 40) is another piece of canonic imitation between treble and bass, now at half a bar's distance, made from the beginning of the answer in a varied form, while the alto has partial imitation (mostly rhythmic) of the first notes of the subject. Note in bar 43 the transient modulation to the subdominant, to avoid the awkward progression of a tritone in the alto and bass.
343. For our last illustration we write a four-part fugue. We take the first half only of our subject, so as to make the piece ​more concise. A short subject is frequently advisable with a larger number of parts; with a longer subject there is often danger of the fugue becoming straggling and tedious. As we intend to combine the theme with itself in stretto as much as we can, we will write no countersubject (§ 176). We will also introduce some points not illustrated in the preceding fugues. We will make a larger number of modulations, giving middle entries in G, A minor, D minor, F, and E minor (all the nearly related keys) before we reach the final section of the fugue.
344. In bars 5 to 7 we have introduced a codetta. There was no necessity for this, as the tenor could perfectly well enter with the subject in bar 5; but, as Bach frequently has such a codetta in his fugues, we have written this to show how to manage it, if it is desired. The first episode (bars 12 to 16) is made by inverting the codetta in the tenor and bass, and adding a sequential counterpoint in quavers for the treble. The first group of middle entries (bars 17 to 22) shows the first (partial) stretto, the bass entering half a bar before the regular time with the inverted subject. Here a modulation from G to A minor is made during the entries, instead of (as is more usual) during the episode.
345. The second and shortest episode is made from the beginning of the inverted subject in the treble, with a continuation freely imitated by direct and inverse motion in the alto and bass. Both first and second episodes are for three voices only.
346. The second group of middle entries, in the keys of A minor and D minor, gives a stretto at one bar's distance in all the parts—the alto entry being incomplete. It leads to the third episode, the most elaborate of the three (bars 30 to 35). It is a short canon 4 in 2, at one bar's distance, by contrary motion, and with inversion of the voices, founded on the first notes of the subject with a counterpoint of quavers. The third group of middle entries (bars 35 to 43) is again a stretto at one bar's distance; but it differs from the last, inasmuch as now all the voices have the subject complete. At bar 41 is a modulation to E minor, in which key a partial stretto, for alto and tenor only, at half a bar's distance is seen. The last short episode (bars 43 to 46) founded on a sequential continuation of the last notes of the subject, leads to the final section of the fugue.
347. This final section (bars 46 to 63) is far more extended than in the other two fugues. It begins with a stretto maestrale (§ 277), led by the treble, each succeeding voice entering at half a bar's distance, and a fourth below the preceding. At bars 51 to 57 a pedal point is introduced, with four voices above it (§ 329). Here there is a second stretto maestrale, the order of ​entry of the voices being now reversed, and the bass leading. The pedal is continued over a passage of free imitation founded on the treble of bar 35; and at bar 58 is a coda, with a final entry of the subject in tenths for treble and tenor, imitated by alto and bass in tenths in the following bar.
348. From the full analysis of the way in which we have written these three fugues, the student will probably learn as much as is possible to teach in a book as to fugal construction. More can be learned by analysis than in any other way. For this reason we shall follow this book by a companion volume on Fugal Analysis, which will contain a collection of some of the finest fugues ever written put into score and fully annotated. There is not room in this volume for a sufficient number of examples to illustrate the matter thoroughly. But mere analysis will not of itself suffice: the student must practise for himself, writing each separate part of a fugue (exposition, episode, stretto, &c.) till he has acquired fluency. Nothing but natural aptitude, aided by a great deal of study and hard work, will ever make a good fugue writer.