,I,.

A COMPANION TO BACH'S 'ART OFFUGUE'

THE student should make his own analysisof Die Kunst derFuge; but his results will need verifying,and the following

pages will serve his purpose.Theorists are on solid ground when they tell us that the

scheme of Die Kunst der Fuge (hereinafter called K. d.F.)involves some discrepancy between matter and form; but it isa mistake to assign this discrepancy to the technical difficultiesBach deals with. None of them are difficulties to him; withsome of the apparently artificial schemes even the difficultiesfor ordinary mortals have been grossly overrated; and the firstelement' of conflict comes where we least expect it-in thesimplest fugues. For Bach uses the same subject in all; and asubject capable of the most elaborate stretti cannot be the kindof subject Bach would normally choose for a simple fugue. InDas Wohltemperirte KZavier (hereinafter called W. K.) thefugues that are as simple as Contrapunctus I and Contra-punctus II are the E major, Bk. I, NO.9; and in Bk. II theC major, No. I; the E minor, No. 10; the F major, No. II;the F minor, No. 12; the G major, No. 15; and the A major,No. 19. All the others have some such features as counter-subjects, identifiable recurring episodes, or stretti; and eventhe E minor and G major of Bk. II have rudimentary counter-subjects, while the recurring episodes in the F minor are veryprominent. Now try to imagine any of these fugues with aserious subject!

One of the paradoxes of K. d. F. is that Bach foundthe making of simple fugues on a severe theme so interestingthat he wrote no less than four without allowing himself anyof the devices for which that theme was designed. These firstfour fugues are as remarkable a tour deforce in composition as

I'!1II

'."

.I

~

...1.

rF'jid~

2 A COMJANION TO

the remaining fugues are in counterpoint. An elaboratecontrapuntal combination really greatly simplifies the com-poser's task. Ii:is like those Japanese paper pellets which whendropped into water unfold into flowers. The composer makesthe voices of his fugue announce the materials in separateexpositions, and then gradually combines them until he reachesthe final stage in which all the materials in combination gothrough their most effectivepermutations and come to an end.The actual art of composition in such a work lies in theminutest details of its joints: the general scheme seems tocompose itself. But a simple fugue is almost a pure effort ofcomposition: it gives the composer no apriori guidance exceptthat its subject is passed from voice to voice, and that thisprocess is relievedby episodesarising naturally from the subjectand its accompaniments. Obviously the art of compositionhere depends largely on the episodes; and if these are merelyconnective tissue without strong recurring features, the com-poser's power of rhetoric is indeed severelytested. Such is the

No. I. problem Bach sets himself in Contrapunctus I. The subjectEx.I.

~!:.:2~~~ -~~~ -~-~Ji&~'

is announced by the alto. Upon its last note the soprano enters

with a tonalanswer. The principle of tonal answer rests op.thefact that it is seldom desirable that each voice should crudelytranspose the subject into its own key. Accordingly a tonalanswer begins by lying on the dominant rather than in thedominant. Or, in other words, the 5th from the tonic tothe dominant corresponds to the 4th from the dominant tothe tonic, and not to another 5th. A tonal answer shows itscharacter at the first convenient note, and afterward,sproceedswith the subject normally transposed, unless the subjectmodulates to the dominant, in which case the answer mustcontrive to return to the tonic. In the exposition (i.e. until all

I,

BACH'S 'ART OF FUGUE' 3the voiceshave entered with the subject) the only regular formof answer is that which lies on or in the dominant, as

Ex.2.

r~~~-=§~ ~~~~~~~but, as the flat at the end of Ex. 2 shows, Bach does not allowpedantries to interfere with his harmony. Many fine modu-lations arise from 'irregular' later entries. .

In the exposition of Contrapunctus I Bach has no gapsbetween the entries of subject (S) and answer (A), and so thefirst 16 bars consist of Alto, S; Soprano, A; Bass, S; andTenor, A. The counterpoint is not only simple but often ofa kind that hardly occurs away from keyboards. Often itssense lies (like the quasi-counter-subject in the G majorFugue, W. K. II, 15) rather in the combined result of the

rhythms;. f J. f and ~n J~n J than in either of thecomponent parts. This kind of counterpoint continues, afterthe exposition, from bar 17 to 24 while the alto rests. Thesebars, then, are the first episode. In bar 24 the alto enters withthe subject. A merely interstitial episode separates this from anentry of the subject in the soprano in bar 29. This is not ananswer, but a real transposition into the dominant, A minor.It overlaps by one bar (32) anew kind of answer in the bass,whereby the key swings round to G minor the subdominant.The overlapping by one bar does not amount to a stretto; butBach had already in bar 29 been unable to resist a three-notehint of a close stretto in the bass. It is very important withBach that we should never confuse such hints with his definitecontrapuntal devices. He alwaysworks his schemes out to thelast note as to completeness, however free he may be as tovariation. For instance, the theme of this fugue and of all theothers in the work, is always continued right to the first noteof its fifth bar. Again, a regular counter-subject is a higWycharacteristic feature constantly accompanying the subject in

I

f

'~

t

: ,tI,~

I,'I.~

I,!

lIIiliI

!~,!I

l

"'~, -

4 A COMPANION TO

various positions. We must not give the name to the counter-point of bars 6-8 in this first fugue merely because Bach doesnot trouble to invent something different for the bass of bars14-16.

At bar 36 another episode begins. It lasts orJy 4 bars, andat bar 40 the tenor (after 5 bars rest) enters on the dominantof D with another answer-form of the subject, landing it inD minor. An episode 5 bars long leads to a similar entry inthe soprano, preceded by an anticipation of the first two notesof the theme by the alto in bar 48. Three bars after the sopranohas finished the subject, the bass, having rested 6 bars, entersin D minor (the soprano having, in bar 55, made another pointof a premonitory two notes). The bass carries the figure of the4th bar down for three steps to the subdominant, from whichit moves to a dominant pedal. Meanwhile, with bar 60the lastepisode begins. It develops for 14 bars which end in anemphatic close spaced out with rhetorical pauses. This closeends on a tonic pedal over which, with subdominant tendencyand a major 3rd (tiercede Picardie),the tenor givesa finalanswer-form of the subject, of which the last note (as usuallyin K. d. F.) arrives with the last bar. The grandiose full closein bars 70-4 is actually the only closein the whole fugue. Thelast 5 bars are not in the 'Berlin autograph', which representsBach's first version, ending as follows:

(72) (74)'"".---

d~l ~.J.G-=--~--. ~""'

It is evident that the important thing in this fuguc::,isthe wayin which it is spaced out. The uninterrupted exposition weldsthe first 16 bars into a big symmetrical unit. The next 6 barsof episode relieve the regularity. Then there is an entry of the

BACH'S 'ART OF FUGUE' 5

subject (which alwaysaccounts for 4 bars) with a gap of 2 barsbetween it and the next entry, which, however, in its turnoverlaps the next by one bar. We thus have a series of threeentries with a distinct effect of compression. Three otherentries follow, each after a short (4 bar) episode, with a notice-able tendency to arouse anticipation in other parts; and at lastwe have a long episode of 14 bars making a climax and comingto the only (and therefore final) closein the composition. Thecounterpoint has given the composer no help whatever. Eachentry of the subject is preceded by a rest, and each long rest isfollowed by an entry of the subject.

Contrapunctus II also has no definite contrapuntal device No.that can serve to shape the composition. But the counterpoint II.is givena strong character by means of dotting the fourth bar ofthe subject and deriving many sequences from its figure withthe short notes boldly tied to the longer ones in systematicdefiance of a common rule of rhythm in counterpoint. (Seebar 5.) Where each part is played or sung by a separate person.that rule is practical common sense; but in keyboard counter-point there is no awkwardnessin playing the eccentric rhythmwith some fingers and the accented beats with others. Theexposition, in the order Bass, Tenor, Alto, Soprano (herein-after called B, T, A, S), again accounts for the first 16 barswithout interruption: after which, 6 bars of episode end ina well-marked half-close on the dominant. Then in bar 23 A,imitated by the lower voices, appears to be starting anotherepisodic figure in the dotted rhythm, but proves to havedrifted into the subject, thus starting a counter-exposition inthe order A, S (answer), B (after 1 bar), and T (after 3 bars).Two bars after T has finished, S enters high up with thesubject in F major. (The rule about entries and rests is observedno longer in K. d. F. A part will often drift into the subject,and may enter with casual counterpoint" after a long rest.)A answers S with a twist into G minor, immediately followedby B with a twist into B flat major. After 4 episodic bars B

'ff!!fi4

6 A COMPANION TO

enters again in D minor. Another 4-bar episode separates thisfrom an answer, syncopated, in T, after which 6 bars of episodebring us to the final entry in S.

A point of great interest in the history of the work is that inthe Berlin autograph this fugue ended with a half-close, sub-

17\

stituting the chord ~~-~ for bar 78. This showsthatBach at first had thoughts of playing some of the fugues insequence. It is unlikely that he ever thought of performingthe whole series at once: the very nature of the scheme is nomore favourable to good contrasts than the plan of a dictionary.In the Berlin autograph this fugue is followed by Contra-punctus V. This fits the dominant close of II; and thepresent IV, which also fits it, was not yet projected.

The composition of Contrapunctus II depends even morethan in Contrapunctus I on fine rhetorical detail. The studentcan easily see the power of such detail by the effect in situ ofthe return to D minor in bar 61. It would be very exciting toachieve such a climax in an exercise.

No. ContrapunctusIII is one of 'Bach'smostbeautifulpiecesofIII. quiet chromatic slow music. (In the Berlin autograph it is

No.2 and ends two bars earlier, at bar 70.) Counterpointemerges from the matrix of the keyboard style. The subject isthe inversion of Ex. 1-

Ex.3.

~ j::2t:: jt~~ r ~,

and Bach begins with the tenor, in the position of an answer toEx. 3. In other words the subject of this fugue modulates atonce to the dominant and back, and has Ex. 3 for its answer.The opening modulation has a mysterious effec.~,which isenhanced by the chromatic counterpoint which accompaniesthe answer. This. counterpoint, unlike the indeterminatecounterpoints of the previous fugues, is preserved as an

,~

'ilJ;~"

I

BACH'S 'ART OF FUGUE' 7accompaniment to most of the later entries, and naturallyoccurs in the voicethat last had the subject. It thus constitutesa regular counter-subject (hereinafter called c.-s.). An episodeof 2 bars intervenes between the third entry (S) and the fourth(B). Theorists callan episodeacodettawhen it occurs beforetheend of the exposition. The distinction is not only useless butconfusing when such an episode recurs later in the course ofthe fugue. Outside K. d. F. Bach seldom has an expositionunbroken by episode, and the I6-bar regularity of the first twofugues here is a special effect intended to give breadth to thoseotherwise restricted compositions.

The exposition of this third fugue, then, is inthe order T, A(with counter-subject in T), S (c.-s. in A), and, after a 2-barepisode, B (c.-s. in S). A chromatic and sequential episodenow follows; a I-bar sequence in which the soprano and altointerchange parts at each step. This is a simple form of adevice by which Bach in other highly organized fugues is ableto make a straight sequence of many steps without monotony.In the present instance the bass never exchangeswith the otherparts; but similar episodes in other fugues are in triple counter-point, with six possible positions (see the F sharp major fugue,W. K. II, 13). And the last episode in the 6-part fugue ofDas Musika/ische Opfer is in quadruple counterpoint, with 24possible positions. It is important to realize the purpose ofthis device,viz. the grand simplicity of a long sequence under-lying a constantly changing surface.

Call this passage(bars 19-22) the second episode. At bar 23,S(with c.-S. in A) gives an ornamental variation of the subject,with syncopations and passing-notes.

Ex.4.

F ~~~~~Such a device is unkno~ to the text-books, but is quiteimportant in Bach's systems of fugue. You will find a very

"', /:/,"

-, ;."",",-."!'c"'::':4",";}'L'1!J!!ffJI~~~II

8 A COMP~NION TOregular example carried through all four voices in close two-part stretti in the E major fugue, W. K. II, 9, bars 23-6.Here in Contrapunctus III Bach makes Ex. 4 an integralpart of the fugue. After a 2-bar episode T has it in A minor(c.-s. again in A) and then again, after 2 bars, in F major(without c.-s.).

And now the composition begins to show symmetry byresuming Ep. 2 (bars 39-42). S, which has been restingfor 12 bars, then enters with the plain s).lbject in A minor(c.-s. in A). A new episode of 4 bars drifts into E~ and Cminor, from which point B (after 4 1?arsrest) moves intoG minor with an entry of the plain subject. A replies in Dminor with the variation Ex. 4 unsyncopated, entering acrotchet earlier (c.-s. in T). This overlaps by I bar with S,also in unsyncopated variation, and with a chromatic alterationin its last bar. After an interstitial bar the subject, unvaried,enters for the last time in T, and six more bars closethe fugue.The Berlin autograph is two bars shorter, representing bar 70by the following final chord:

~=I-----

I~I '.~

. c:::r\V

I

No. Contrapunctus IV is later than the Berlin autograph. It isIV. one of Bach's greater fugues and is a very lively st~dy in

episodes. They all arisefrom the quavers in the last bar of Ex. 3,direct and inverted, i. e. going up or going down, together witha cuckoo-likefigureof a descending3rd whichisfirst representedby its characteristiciambic rhythm J d. IJ J J in the counter-~

points of the exposition, and which afterwards!'develops inways easier to appreciate by ear than to describe.

The exposition is in the order S, A (with a characteristic

~

BACH'S 'ART OF FUGUE' 92-bar interlude), T, B. Episode I fills the 8 bars from 19to 26.Then four entries follow without break; S in F, A in C, T inG minor, B (as answer) in D minor. Episode 2 begins byturning the parts of Ep. I round, the quavers being now inS and A, and the iambic 3rd in T and B, instead of viceversa. In 10 bars it comes (in A minor) to a full close (alwaysa remarkable incident in a fugue) and proceeds on a new linefor another 8 bars (53-60). Now comes a series of entries withwhat may be called an enhanced form of the subject. In a tonicposition this splendid device would run thus, with the ex-planatory harmonies:

Ex.5. .d. .

F~~~. ~ r

It has a powerfully rhetorical modulating effect. It first appearsat bar 61 in B, starting in F and reaching G minor, where it isimmediately answered by T, which thereby reaches the domi-nant of D. Four bars of episode intervene. The cuckoo-like3rds, which have been making an insistent (though not fixed)counterpoint to the enhanced subject, now become rising 6ths.A enters with the enhanced subject in D minor moving to thedominant of A; and S followsin A minor going right over thedominant of E minor, a very bold venture. Episode 3 beginsby inverting the treble of bars 45~-8t and swinging roundto C major with a full close. Hereupon the lines ofEp. I areresumed and developed for another 16bars closing in G minor(bar 10;3),after which the episode continues with the line takenin the latter part of Ep. 2 for 4 bars, having lasted 26 in all.

Bach is not allowinghimself to use any of the contrapuntaldevices for which his theme was designed; but he now gives ita treatment which is not exactly a stretto, but a kind of synco-pated doubling in 3rds. At bar 1°7 T, in D minor, leads,doubled in syncopated lower 3rds by B. This combination isimmediately answered by Sand A. S, which is in the normal

~c""~"~~""""""", ".='I'!'

10 A COMPANION TO

position for the answer, is syncopated, while A is on the beata 6th below. The last episodebegins at bar I I5 on the prevalentlines of the scaly runs and the cuckoo-figure. But after 4 barsit proceeds to develop the beginning of Ep. 3, reinverting Sof bars 451-8l and 81-4 in B of bars 119-22, inverse answerin A. After I4 bars T enters in G minor with the enhancedsubject, which closes into D minor, where a final entry in A,plus 2 bars, ends the fugue, over the usual tonic pedal.

A persistent repeated figure in bars 5 and 6 has often aidedthe cuckoo-figure in giving rhetorical force to the counter-point, but it does not amount to a steady counter-subject.

A word must be said about the tempo of these fugues. Thetime-signatures ~ and C are no clue as Bach uses them, and inthe present edition they -are, with due warning in footnotes,altered according to their meaning in modern music. Nobodywith a sense of beauty would want to take an alla-breve tempofor the lovely melancholy of Contrapunctus III; but anybgdywho thinks that in Contrapunctus IV such a passage as bars53-60 could be slower than a fairly lively alla-breve must be inthe state of mind imputed by Strachan-Davidson to the school-boy who 'believes in his heart that no nonsense is too enormousto be a possible translation of a classicalauthor'.

No. We now come to the fugues for which the theme was de-V. signed. Bach henceforth fills out the intervals as in Ex. 4

but without syncopation and without the graceful G beforethe B~.

Contrapunctus V is astretto-fugue in contrary motion.'-Wemay as well use the signs invented by Wesleyand Horn for thefirst English edition of the W. K.: viz. 1\ £or the normalsubject, and V for the inverted subject. With K. d. F. it willbe convenient to take these signs in relation to the work as awhole. On this reckoning Contrapunctus V begin,uvith V inA, which is answered after 3 bars (instead of 4) by 1\ in B;whereupon, still at 3-bar intervals, S enters with 1\ answeredby V in T. A 3-bar episode, arising, as usual, from the quaver

-";'jiib.",

BACH'S 'ART OF FUGUE' II

figure, leads to a counter-exposition at 3-bar intervals, in theorder S V (answer in A minor), T 1\ (A minor), B V (Dminor) A 1\. Another 3-bar episode leads to F major, wherethe stretti begin. Bach knows of no such rule as that the strettishould make their climaxes by appearing in gradually closerorder. He does not think that climaxes depend' on any such

principle, and here he begins (in bar 33) at once with theclosest stretto, B 1\; answered at half a bar by S V. Another

3-bar episodebrings us to the conversestretto in G minor, TV;answered by A 1\. Another 2 bars (or It) takes lis to B~,where Band T give a new stretto in th<?octave at a bar and ahalf, both parts with V. And noW comes an episode on thefigure of bar I in close 4-part canon (at crotchet distances) onthe first figure of V. Bach would certainly not call this astretto, but a mere imitative episode; though it is exactly likethe passages in Handel's Amen chorus, on the strength ofwhich Rockstro tells us that that most improvisatory offugues is a marvel of close stretto. Bach makes 4 bars ofthis episode lead to the inversion of the second stretto, S 1\ inD minor, answered at It bars an octave lower by A 1\. (Thesoprano entry shows, like the tenor entry in bar 41, howBach uses the idea of a tonal answer to swing from one key toanother by substituting a 4th for the inirial 5th. The studentshould note other cases for himself. This is one of the simplesubdeties by which fugues I and II are kept alive withoutfurther apparatus.)

Another-interstitial episode now leads in 3 bars to an inver-sion of the 4-part canonic passagethat forms the only charac-terized episode in this fugue. In bars 65-8 the figure of 1\ isthus worked into canon at crotchet distances. The parts arenot in the exact reverse order of bars 53-6, though they couldhave been so arranged. But such 'mirror' inversionsbelong toa later problem. This episode leads back to D minor, wherewe have a third plan of stretto, in the 8ve at I bar. (Thisrequires accessoryparts to support the 4ths which come on the

"illi!"'" ,'~'~".::;..,;::"~,""!!I:ii!!ti&~~,,i;cili."ITiJ!~i

12 A COMPANION TO

beat in the only possible position. Other positions wouldresult in consecutive 5ths.) First, bars 69-72 show S Vanswered by TV. The usual 3bars of interstitial episode inter-vene before we come to the converse stretto, T V answeredby A I\. The bass should normally have led here, but Bach(who never lets machinery interfere with good music) isreserving it for the final entry, which follows after a 4-barepisode. Tl-,ismakes an emphatic closeinto a final tonic pedalover which,with a major tierce de Picardie,the voicesbreakinto 6 parts and the alto with the upper bass give the direct and

inverted themes simultaneously; O. Great rhetorical power isnot to be expected from this fugue. Its stretti are all extra-ordinarily smooth, and not (in Bach's estimation)very differentfrom eachother. The structure ispunctuated by the half-closesat bars 52 and 64 before those imitative episodes which are thebackbone of the composition. Otherwise, smoothness is themain point of the whole. Bach has made incalculable progresssince the early stretto-fugues in D~ minor and A minor whichhe admitted into Bk. I of W. K. Such crudenesses as thefollowing, from the D~ minor fugue- f

Ex.6.

~'~ ~I~~~:JF~.J.~~ i' t:J W ,--,' [I

would be wholly inadmissible in K. d. P., though the alto inthe fifth bar of Ex. 6 would certainly sound more convincingifit could have been played without skipping to the higher 8ve.But playability is as strict a condition in K. d. F. as in W. K.

No. Contrapunctus VI is a solid mass ofstretto with,tpe subjectVI. not only direct and inverted but alsodiminished in both forms.

Wesleyand Horn use the sign 0 for diminution, and we mustcombine it with the other signs. Thus the exposition brings in

~

BACH'S 'ART OF FUGUE' 13

three parts within 3 bars; B /\, S -&'A 1'. Two bars after Bhas finished its full-sized subject T enters with ~. Theepisodes are mere interstitial though they make excellent useof the first figure of the diminished subject. For the rest thefugue is uninterrupted stretto; and when the student hasamused himself by putting the abovesigns into the score (beingscrupulous in not so labelling mere fragments) he has analysednearly all that is meant to be studied. He can penetrate intodetails by labelling the first 4 or 6 notes ofthe subject '(a)' andthe last 5 notes (the final turn) '(b)'; and this will enable himto see that the episodes and interstitial counterpoints are notwithout organization. He may label the short demisemiquaverruns (in the style of a French overture) with the letter x if heagrees with me that Bach is not intending to derive themfrom (b).

I do not recommend a solemn attitude towards these

three stretto fugues V, VI, and VII. Yet it is impossible tooverrate the mastery shown in their perfect smoothness. Andto make reasonably effectivecompositions out of such uniformmasses of stretto is almost as great a tour de force as to makethem, like fugues I and II, with no fugue-devices at all. Onthe wholeNos. VI and VII are aesthetically about as importantas No. I, which No. VI resembles in the feature of reserving itsone full close for the, final climax. (You must not call everytonic chord a full close when it is preceded by a dominant: thatincident in bars II-I2 does not stop the flow.)

Nothing is more overrated than the difficulty of makin~contrapuntal combinations. There is no difficulty: your com-binations will work automatically if they are going to work atall. An experienced composer acquires an instinct for combina-tions that work. An inexperienced composer, if he is con-scientious, says to preconceived materials ']I,1arche,au jet'assomme',and, like Adam de la Hale, 'rough-hews the mainaccents into concord. If he is one of our noble liberators fromclassicalprejudice, he simply says '9a marche'over any number

~{j._, .. . . - ,.,--_.

.' H"H',"","' '" 'H' ',,"'e..:!!:'!,-:!!!,,'

14 A COMPANION TO

of things he chooses to put together, and thunders his anathe-mas at any critic so blasphemous as to object. All the ingenuityof K. d. F., except a few freakish fireworks,was settled oncefor all when Bach invented first that wonderfully plastic subjectand, secondly-to-seventhIy,certain other subjects that combinewith it. At present he is engaged in the comparatively trivialtask of co~bining it with itself; and he is unable to pile up hisstretti to noble climaxes like those of the stretto fugues in\'(7.K. I, C major and W. K. II, D major, simply because thereare too many of them here. These fugues are restricted not bytheir ingenuity but by what is for Bach their ridiculous ease.

No. Contrapunctus VII adds augmentation to the diminution,VII. and has no episodes at all except bars 32-4. Its composition

must have been a very simple process, after Bach had collectedhis material for the whole K. d. F. to begin with. He probablyfirst wrote the 4 bars which lead to the entry of the bass withthe augmented inverted subject. (Wesley and Horn use thesign = for augmentation.) Then he wrote out the bass in thefollowing 8 bars, properly spaced to leave room for 16notes toa bar. He then put whatever entries and counterpoints camehandy above this: including the double-diminution of (a).

Ex.7.

~--

~ ~-~~ ---~

BACH'S 'ART OF FUGUE' IS

student should note other cases for himself, and should notfail to observe how all suspicion of tautology disappears in thegeneral result. Bach never uses a rule as a substitute for hisown judgement. This particular rule is as powerless to avoidtautology as a ru1e for calling Bach 'the Leipzig Cantor' and'the master-contrapuntist',1Xc., &c., in alternate sentences.)

At bar 23, Truns into ~ in F major, and this settles thebusiness of the next 8 bars. Mter the only episode of 3-bars'

length, A enters in D minor with Vagainst the I i-bar strettoof 1\ at the 8ve. Then 7bars of the diminished subject lead to1\ high up in S by way of climax. Four final bars come to the=close. There are no other closes.

The C major organ fugueEx.8.

~ ~~~.- --.-'---"

I

Of course the diminished subject can slip in some two or threetimes while Vis booming in the bass. This takes us to bar 14.Bach probably blocked out the rest of the fugue in the sameway from each augmentation to the next. From bar 14 heproceeds with the ordinary and dL.'1linishedsubject for 9 bars.Note the running catch-up in the course of V in A, and also

the fact that Bach does not mind giving 'it twice infthe sameposition to T, with only one intervening bar. (This is anextreme case of Bach's deliberate contempt for a rule aboutwhich some eighteenth-century theorists were very strict. The

shows how such a stretto-scheme can be given a grandrhetorical effect. It reserves the augmentation for a long-delayed first entry of the pedals, to which the augmentation isconfined, and which devote themselves to it exclusively. Sucha devicewas not open to Bach in the scheme of K. d. F.; butI found myself driven to use its aesthetic equivalent in myconjectural finish of the great quadruple fugue.

Now we come to the central business of K. d. F.; the fugues No.in double and triple counterpoint, or fugues in which the VIII.motto-theme is combined with others. Such fugues are thosewhich Bach most enjoysworking out on a large scale,and thereis nothing in the scheme of K. d. F. to prevent them frombeing pure works of art. Accordingly these examples areamong his greatest compositions and must be taken on theirindividual merits.

Contrapunctus VIII is a triple fugue- with three stronglycontrasted subjects. And here it is well to call attention tothe real nature and purpose of polyphony. Much vexatious

16 A COMPANION TO

damage is done to the enjoyment of music, even for musiciansthemselves, by the mista.~ennotion that in order to understandpolyphony you must be able to attend to all the parts at once.No such mistake was made by the sixteenth-century theoriststowhomPalestrina's polyphony wasthe finaloutcomeof a tradi-tion as ancient to them as Bach is to us now. Theyanalysedtheir harmony as between two parts at a time; and this wasadequate. For every fault of harmony existsbetween two parts;and if it at the same time concerns more, we can call it morethan one fault. If in the 6-part polyphony of the Missa PapaeMareilli or the 4o-part polyphony of Tallis's Spem in aliumthere are no faults, then our enjoyment of the euphony doesnot depend on our attending to the individual parts. It is thesame with combinations of themes: a piece of triple counter-point is, or ought to be, a satisfactory mass of harmony in thefirst place. Second!y, this harmony happens to be producedby three pregnant melodies so disposed that any can be a bassor treble to the others. Consequently this mass of harmonycan be presented in six positions, every one of which has adifferent surface or bass. To complain that we cannot attend

. to all three themes at once is like arguing that no picture orightto be larger than a postage-stamp because that is fully as largean area as the eye's centre of clear vision can comprise.

In point of fact, Bach's triple counterpoints(likethe eoupd'a;il of a big picture) produce an immediate effect before wemake any effort of attention. The themes are so contrastedas to be transparent to each other. One will trickle along in arapid movement which would be audible even in an undertoneagainst the others. Another will have wide skips which willalways attract attention even in an inner part. The third willperhaps consist of some long notes in a chain of suspendeddiscords; which is as much as to say that it provides, ,the mainharmonic effect. Or it may have some peculiar rhythm. Seethe combinations of a subject with two counter-subjects inW. K. I, C mi., q~ ma., Bb ma.

0""

BACH'S 'ART OF FUGUE' 17

Contrapunctus VIII is on the lines of W. K. I, C~ mi. andII, F# mi.; in which three subjects are given eq1;1alprominenceby being introduced in separate sections, their complete com-bination being reserved for a later stage. (In the great C# minorfugue the third subject soon joins the second in making triplecounterpoint with the first; and the final stage is devoted topiles of stretto on 1\ + 1\.)1 3

The composer's first task in such a fugue is to make his finalcombination. The listener will understand the aesthetic valuesof the work much better if he regards this combination as asingle idea than if he persists in trying to keep its threadsseparate; in other words, than if he refuses to follow thecomposer's intention of pulling the whole together.

Here, then, is the 'idea' of Contrapunctus VIII:Ex.9.

1\ A1V

1

~1J-J-~2 1\

~~=#=t-m~~~=d==r i~

Like all good triple and multiple counterpoints these threeneither begin together nor end together. They are perfectlytransparent to each other. The quickly-moving 1\ makes2

.suspended discords with 1\. And 1\, which is the inverted1 3motto-theme of K. d. F., is conspicuous by its broken rhythm,a delightful instance of Bach's power of variation, and verysuggestive of Brahms.

Three such themes are enough for a very big fugue; and sothis is one of Bach's biggest. The first section is a broadexposition of the topmost theme of Ex. 9, led off by A. The;~ap of It. bars between the very first voice and its answer is

- rare ill Bach: it here has the effectof prolonging the subject, asau thr~e parts at first use the figure it contains. The rest of thecounterpoint does not form a regular counter-subject, but its

18 A COMPANION TO

figures are used constantly. You may, if you like, derive thefigure of bars 7-8 by diminution from bars 5-6, though I doubtwhether this is Bach's way of thinking. At all events, if youletter the figure as (x), and the first notes of bar 9 as (y), youwill then be able to account for most of the quaver counter-points as made of x+y direct and inverted.

Ex. 10.

~~~=-r-~~J:!C :!C ,x x_y'---' , D '--'---'

Ex. II.

I~~-.-/Yv

Six bars after the exposition A has an entry of 1\ in A minor1with a suggestion of close stretto in B. But stretto is not thebusiness of this fugue, and imitative suggestions are all thatappear in it. A sequence is developed from the main figureof ~ in bars 28-3°, and at bar 35 B concludes the first sectionwith the whole theme, ending at bar 39. f

Now, as in the great C# minor fugue, 1\ makes its first2appearance already in combination with I\. It is in A, below1

1\ in S. Before answering 1\ B throws in a new figure (1\)1 1 z(not to be confused with the x y groups) in G minor. i

x

Ex. 12.

~=--~~~:P ,--- 1-:::= ----A

~

It then proceeds with 1- in that key, S having~. After aninterval of 2 bars from the end of this, we have a third entry inA minor (A 1\, B 1\). Then there is a 7-bar episode developing1 21\ and Vz. At bar 61 we have S 1\ with A 1\ in F major,Z 1 2

followed, after a 2-bar interlude at B 1\ with S 1\ in B flat,1 2

',_~~n~ ".., n' , " .

a

BACH'S 'ART OF FUGUE' 19

making a close. The next episode begins with the ~+Vdevelopment, but at bar 74 it takes up the figure of 1\, which2is in any case a sequence that can be prolonged indefinitely,so that no line can be drawn between the fixed theme and its

episodic developments. This gives a subtle and perhapsintentional point to casual resemblances to 1\ (with reversed1accents) in bars 74-6. An unmistakable but unfinished entryof 1\ comesin A at the end of bar 79; B having already begun1to unroll the figure of 1\. After two bars S takes the point up2

with a complete D minor entry of 1\ over 1\ in A; and the2followingepisode brings this second sectlOnto an end with aclimax. Beginning with the ~+Vmatter, it treats the figureof 1\ in close imitation while B alludes to 1\; and then the2 1episode comes with a flourish (implying a big rallentando)toa half-close (bar 93).

~ in B (followedby the long-forgotten x) answered by V inS (which continues with 1\), form free counterpoints to 1\;Y 3our K. d. F. theme inverted, with a charming new brokenrhythm. The figure of 1\ (but not the whole theme) also joins2the counterpoints. After a bar's interlude B gives the answerof 1\; and after a 2-bar interlude S has it, also in A minor.3

The next episode develops Ii- and V for 5 bars and thensuddenly plunges into what sounds like 1\ over 1\ on2 1

a tonic pedal D. But this turns out to be only a sequence,which starts the episode on a new imitative development of thefigure of 1\. This leads to a close in A minor. The figure of2

~ is resumed in B and answered by the whole theme ~in Sin an abnormal relation to 1\ which appears in A, partially but1effectively doubled in 3rds by B. (The abnormality in thisrelation of 1\ to 1\ consists in the fact that it is not only at2 1

a different pitch, which in itself would mean inversion in adouble counterpoint other than in the 8ve, but that it combines

"1"'"1.""'1,,, n""""""

A COMPANION TO

at a different point, a device for which the books have noname.)

The old extra bars (5 and 6) reappear. B answers, with 1\ in2A at the normal point and pitch. Then a 12-bar episode on 1\zand Vleads to the stage for which this fugue has been preparing

for 146 bars. With bar 147 the triple counterpoint begins.According to the position of the themes it shou1O.be in F major,but a bold handling of accidentals(unknownin principle to text-books) warps the first 3 bars into A minor, and very boldlywarps the answer into E minor. Only the third entry is normalto its key of G minor. These entries,with the wholelast sectionof the fugue, are best tabulated as follows:

B", 147-51{~ F (&guh,d as Ami.)

B", 152-6 {g C (di,gui'od as E mi.)2 bars (It) interlude

B= 158 CODd)-63{~ G mi.

7 bars episode on new lines, ending with figure of 1\. ,2 .

B= 170-5{~D mi.8 bars episode on lines of the previous one.

B" 182 (,nd) to ODdoffugu, {~

20

a

BACH'S 'ART OF FUGUE' 2I

, ContrapunctusIX is in double counterpoint(hereinafterNo.called D-C) at the 12th. The object of this device is to obtain IX.two different harmonic schemes from one pair of melodies.Ordinary interchange of parts by an octave or two does notalter the roots of the harmony; but a properly managed D-Cin 12th produces two markedly different harmonic effectsbesides changing the expression of the shifted theme. Theconcord of the. 6th inverts into a 7th, and the shifted themeassumes a new colouring of dominant or subdominant accord-ing to circumstances.

In the Berlin autograph this fugue is NO.5, which shows onlythat it probably occurred to Bach before others which shouldprecede it. But its notation gives the K. d. F. theme in itsnormal time, and so we may use it in the following paradigm:

Ex. 13.

InI2th. ¥&,)'~-# '- ~

~

fFC~ F -L r~ -=;j

Original. ---.

position.I~-~~

~ . n

~~~~~

\I~{I~w

~~~~

The shifting tonality of the running theme when it is placeda 12th higher is very interesting and, as the alternative acci-dentals show, capable of some free play.

Bach, feeling that the semiquavers might suggest too quick

22 A COMPANION TO

a tempo, changed the notation, doubling the note-values andhalving the bars. We should, however, misinterpret him if wetook his new C time-signature to mean 4 in a bar: it must besufficiently like alla breve to account for his ever having thoughtof semiquavers at all. But not too fast for the details of bars20-1. I cannot account for the manifest perversity of Bach'suse and non-use of the alla-breve time-signatures. But thechoice of note-values is another matter with method in it. A

notation in quavers and semiquavers has its advantages in key-board polyphony; for the quaver-bars often show the con-tinuity of a part that moves from one stave to the other, whereascrotchets and minims show no connexion. In open score thisadvantage disappears; and the engraver (whose point of viewBach thoroughly understood) merely has some 30 per cent.more work with those troublesome heavy lines. Moreover, theopen score, with its four vocal clefs, is associated with choralmusic, and Bach accordingly changed to the characteristicchoral note-values when he decided to put the work into score.It is a melancholy reflection that if the Berlin autograph hadremained our only text of K. d. F. we should have sufferedfrom no nonsense as to its not being practical keyboard music,and should not even have been led to lay more stress on itstheoretical aspect than is implied by its title and its use of onetheme throughout all its numbers.

Bach changed his notation in similar ways elsewhere; e!g. inthe A major organ-fugue, and in the 48th prelude ofW. K.! Inlater music there is the interesting case of Mendelssohn re-writing the alla-brevebars of the Midsummer Night's Dreamoverture as common-time bars of twice the length in his piano-forte arrangement; and Wagner, in Isolde's Liebestod, tran-scribes 100 alla-breve bars of the duet in the 2nd Act as 50common-time bars. ' ,,

Contrapunctus IX beginswith an uninterrupted exposition ofits running theme (whichwewill call 1\), in the orderA,B,S, T.1A 6-bar episode (the student can letter its figures already in the

BACH'S 'ART OF FUGUE' 23

running theme) leads to the entry of 1\ in S with 1\ in T. This2 1

is followed(with only a 2-bar interlude) by the inversion in the12th in F major, 1\ in T, 1\ at 12th in A. Another 6-bar2 1episode returns to D minor, where we have the original com-bination, /\ in A, /\ in B. Again a 6-bar episode leads to A

2 1 .

minor, where the inversion in the 12th is again given to A andT. The next episode takes 8 bars, and, as in Contrapunctus I,hints of the K. d. F. theme are givenby premonitory rising 5thsor 4ths. At bar 89 the twelfth-position appears, 1\ in B with2/\ at 12thin S. This is immediately followed(with only I bar's1interlude) with the same thing in G minor between T andA, who have thus had it 3 times out of 4. Then fol-lows the last episode, 12 bars long, which leads to thefinal entry of the original combination, 1\ in A and /\ in T,2 1and so to the end of a very brilliant and straightforward fugue.

Contrapunctus X is in D-C at the loth. The mere inversions No.at this interval have no distinct character; but they have the X.advantage that they can be used with the original positionsimultaneously. Consequently they make it possible to doubleeither or both of the melodies in 3rds or 6ths. Perhaps thethree finest examples in the world are this fugue, the G minorfugue in W. K. II (which is also in the 12th and makes magnifi-cent use of the turning of 6ths into 7ths), and the Pleni suntcoeliof the B minor Mass, where in one of the positions themain theme is in the bass doubled three 8ves and a 3rd higherby a trumpet, while the other theme is in close 3rds for innervoices.

Bach originally began Contrapunctus X at bar 23 with Salone as a normal fugue-opening, with the answer in T as atbar 26. This early version was mistakenly included in theoriginal edition and most others. Even Rust, in the Bachgesell-schaft edition, could not resolve to remove it to the appendix.There is really no reason why it should be printed at all; thepurposes of the most exhaustive edition would be served by

,"'."'" "'~"",.. "",""'.

24 A COMPANION TO

a list of its trivial differencesfrom the final version, apart fromwhat has just been said.

The page which Bach added to the beginning is one of theprofoundest and most beautiful he ever wrote. The brokenrhythm and varied tonality of the new theme, with its wistfulrun up to Cq, give an effectof poetic mystery deepened by thepeculiar structure of the exposition. To begin with, Bachbreaks an old rule which he was never concerned to keep, butwhich the main theme of K. d. F. keeps for him, the rule thatthe first note of a fugue must be either the tonic or the domi-nant. But now his new theme, announced by A, begins withthe leading-note; and the answer by T is in the subdominant,breaking the rule that allowsonly the dominant as a modulationduring the exposition. (In W. K. the fourth entry of the greatC:Ij:minor fugue breaks this rule, and so does the subject,already beginning on the leading-note, of the F:Ij:major fuguein Bk. II.)

Then B inverts the subject and is answered in stretto at'It bars by S. Mter an interlude of 2t bars there is anothervery close stretto at the half-bar between /\ in A (with animpressive subsidence from A minor to G minor) and V in T,5 more bars bring the section to a half-close (bar 22). S thenenters with /\, which is the inverted K. d. F. theme as inContrapuncU:s V. A answers in partial stretto at I bar in the4th (apparently the 5th, to the first note, but it is a tonalanswer). This stretto has not occurred before in K. d. F.,because it cannot be carried through; but it makes its' pointhere. In due course T answers, and the accessory voices rest.The figure in bar 28

Ex. 14. ~x r:~ =r(i")~~... ,I"~1["1.

does not form a regular counter-subject, but is afterwardsgiven extraordinary prominence in episodes. (This fugue ranks

I

BACH'S 'ART OF FUGUE' 2S

with NO.4 as one of Bach's greatest examples of episodicdevelopment.)

In the exposition of /\ as it ran in the first draft, i.e. withoutIIthe accessoryA and B of bars 23-6, the voices expose /\ with-IIout break and always at 3-bar distances (as in NO.5), in theorder S, T, B, A.

Mter a 6-bar episode the first combination of f ~ appearsII

in A and T (bars 44-8). An interlude of 4 bars (introducing

{A/\

x in S) leads to the inversion in the loth, B A in loth.IIThe followingparadigm shows how the position at the lOth

can be used together with the original model:Ex. IS.

~-L~ .' =--

"II,,(~i i'~\U~ r' CTr=--~,----...

l~Such a schemehas any number of permutations; far more thanthe twenty-four of a genuine quadruple counterpoint. Either orboth themes maybe doubled in 3rds either aboveor below, or in6ths above or below, or, as here, in loths with one part in themiddle. And the two themes are very likely tp be invertible inthe 12th as well as in the lOth. This is the case here and alsoin the great G minor fugue of W. K. II, where Bach doublesboth themes at once. The present combination would be intoo stiff a rhythm without keeping one part free to move in itsown way. For this and other reasons not a quarter of even thetypical permutations are used, to say nothing of the stretti.

Bars 56-65 are an episode which takes the unorthodox form

E25410Windsor Public Library