REGULAR COUNTERSUBJECTS IN FUGUEWalter Hilse, FAGO

Ex.la.

regular countersubject

Ex. lb.

i

third entry /fof sUbject/

r i

~ regular countersubject

Initial tonaladjustment in answer

third entryof subject

T HIS ARTICLE is designed to be a sequel tomy essay, "The Fugal Answer," foundin the April 2006 issue of TAD. Refer

back to that article for definitions of, and dis­cussions on, "tonal" and "real" answers and"initial" and "terminal" tonal adjustments(and please correct the unfortunate musicaltypo in Example 1 of that article: the clef ofthe lower system should be a transposedtenor clef, not a bass clef!). If you do not haveaccess to this article, please refer to a stan­dard text on fugal composition. I will, how­ever, restate the definitions of "initial" and"terminal" tonal adjustments here. In a fugalanswer, an "initial" tonal adjustment is thealteration of one or more pitches near the be­ginning of the fugue subject to highlight therelationship between the tonic and dominantpitches in the home scale, and/or the keysbuilt on those pitches; in the answer of afugue with a modulating subject, a "terminal"tonal adjustment is a pitch adjustment, gen-

52

erally toward the end of the subject, designedto steer the answer back to the tonic key (af­ter it had commenced in the dominant).

A "countersubject" is, as the word sug­gests, a melodic idea-any melodic idea,whether or not it recurs-which appears as acounterpoint to the subject of a fugue. Acountersubject is "regular" if, after being in­troduced during the second statement of thesubject [i.e., the answer), it reappears duringall subsequent subject entries in the exposi­tion section of the fugue, and during a clearmajority of later statements (not necessarilyevery statement) of the subject. It acts, in ef­fect, like a steady companion or shadow ofthe subject. In the exposition, it always willappear in the voice that had just stated thesubject previously. Thus, Voice 1 will pre­sent the regular countersubject while Voice2 states the subject; Voice 2 will then presentthe regular countersubject while Voice 3states the subject; if there is a fourth voice,

Voice 3 will present the regular countersub­ject while Voice 4 states the subject; etc.

A regular countersubject, in order to be alaw-abiding element in the polyphonic fab­ric, must obey all traditional rules of coun­terpoint (the 18th-century variety, since welook, above all, to Bach's fugues as models):parallel octaves, fifths, and unisons with thesubject (or any other voice) must be es­chewed, dissonances properly prepared andresolved according to late-Baroque guide­lines, and the total range covered by themelody should be modest, generally not ex­ceeding a twelfth. To enjoy a profile suffi­ciently independent of the fugue subject, thecountersubject should offer significant con­trast to the subject in matters such asrhythms featured, pitch contour, andmelodic interval content. More often thannot, it should run in contrary or oblique mo­tion relative to the subject. While not neces­sarily as distinctive or memorable a melodic

THE AMERICAN ORGANIST

7

Ex.3a.initial tonal adjustment in answer

regular countersubject

regular countersubject~....- ....- .....

Ex.4b.

third entry!of subject

conception as the subject, it should nonethe­less be easily recognizable. In addition,since, during the course of the fugue, the reg­ular countersubject will inevitably have oc­casion to appear both above and below thesubject, it must obey the traditional laws ofdouble ("invertible") counterpoint, in orderto behave acceptably in both vertical ar­rangements. Thirds, sixths, octaves, unisons,and their octave compounds may be em­ployed as consonances as always, since theirintervallic inversions within the octave arealso consonant; seconds, sevenths, ninths,diminished and augmented intervals, andtheir octave-compounds can also be used, aslong as they follow traditional behavior asdissonances [i.e., are properly prepared andresolved). Perfect fifths, on the other hand,must be avoided, unless prepared and re­solved as if they were dissonances, sincetheir inversions are fourths- dissonances in18th-century language. (Please note: I am re-

MARCH 2008

splice pointin countersubject

stricting my discussion to double counter­point at the octave, which is only one,though by far the most common, of three tra­ditional species of double counterpoint. Theother two species, double counterpoint at thetwelfth and at the tenth, are rarely found infugues-Fugues 9 and 10 of Bach's The Artof Fugue are notable exceptions. In thoseother two species of double counterpoint,different vertical intervals must be avoidedor given special care.)

If the answer to a fugue subject is "real,"rather than "tonal," finding the correct formof a regular countersubject in its later ap­pearances poses no problem. It will simplybe an exact transposition of its original form:

See Example 1a and 1b

Since the regular countersubject is first en­countered during the second presentation ofthe subject, it will usually be mainly in the

.L

dominant key area at that point. The next ap­pearance of the regular countersubject will,however, be back in the tonic key, during thetime the third voice has its crack at the sub­ject. Thus, the second presentation of the reg­ular countersubject will essentially be atransposition of the first presentation downa fifth or up a fourth.

If the fugue subject is non-modulating, butits answer contains an initial tonal adjust­ment (cf. my April 2006 article), an exacttransposition of the first presentation of thecountersubject down a fifth or up a fourthstill usually fills the bill. A survey of regularcountersubjects in Bach's Well-temperedClavier reveals, surprisingly, that many ofthem do not begin their pattern of recurrenceuntil at least one beat after the start of thesubject. (Note, for example, the regular coun­tersubject in Example 1 above.) In the patternof recurrence, the most important aspect ofthe relationship between the two voices is

53

apparently not how th ey begin bu t rathe rthe ir int eraction as the cadence at th e end ofth e subject is approache d. Since most initialton al adj us tments involve only th e first orsecond note of th e subject, these adjus tme ntsare ther efor e ofte n co mplete d before th ecountersu bject begins. Cons ider, for exa m­ple, th e second and th ird ent ries in the Fuguein C-sharp Major, Book I:

See Example 2

In other cases of initial tonal adjus tments ,Bach finds it possibl e to preserve an exac ttransposit ion of the regu lar countersubj ecteven tho ugh there is an overlap between thebeginn ing of the countersubject (i.e., its pat­tern of recurrence) and th e ini tial ton al ad­justment: thi s can happen if a not e in th ecountersubject on an important part of a beatfun cti on s as a cons ona nce in th e firs t ap­pearan ce of the counte rsubject , th en as aproperly behaving dissonance in th e next ap­pearance (or vice versa ). Consid er , in th e fol­lowing example, the 16th note appearing inth e counters ubject again st th e fourth note ofth e sub ject:

See Example 3a and 3b

It is a sixth in its first appea rance , but aninth (accented passing tone) in th e next.

If the fugue su bject modu lates to th e dom­inant key, then things tend to be a bi t mor e

complicate d. The reg ular cou n tersubjec tusually must undergo a ton al adjus tme ntcorresponding to th e terminal tonal adjus t­ment found in th e answer. (An exce ption oc­curs whe n th e terminal adjus tment is veryearly in th e subject-e.g., in th e Fugue in G­sharp Minor, Well-tempered Clavier, BookI-in which case th e situa tion is similar to aqui ckly exec uted initial ad justment.) Fittedto th e tonal-answer form of th e subject in itsfirst appearance, th e regular countersubjectmu st now be fitte d to th e original form of thesubj ect. To acco mplish this , one mu st lookfor a "splice -poi nt" in the countersubject co­inciding (or almos t coinciding) with th esplice-point in th e an sw er. At th e splice­point you have chose n , begin to state all sub­sequent pitches one scale-step higher thanthey would hav e been in an exact transposi­tion, in order to wind up in th e dominant key(as the subj ect does in its third entry) ratherthan the subdominant :

See Example 4a and 4b

Regular countersubjects are not found inall fugues-in fact , among th e 48 fugues ofth e two books of the Well-tempered Clavier,over 20 [i.e. , close to 50% ) do not have th em.While an attractive regular countersubject isoften a major asset for a fugu e, the absence ofone is not necessaril y a shortc oming, and in­deed , some of Bach 's most masterly fuguesdo not have th em.

In par ticular, regular counters ubjects tendnot to be found in fugues in which "speci altr ick s" suc h as stre tto, augme nta tio n, andmelodic inversion are extens ive ly featured ,because the im pl em entat ion of th ese de­vices deprives the countersubjec t of the con­trapuntal space needed for its presentation,or else alte rs th e rhythmic or harmonic en­viro nment ofthe subjec t, mak ing surviva l ofthe countersubject impossible. Also, doublean d tripl e fugues almost never possess regu­lar countersubjects , because th e seco nd (andth ird) subjects th emselves fun ct ion , in ef­fect, as glo ri fie d regular countersub jec tswh en combi ne d with th e opening subject.One beautiful exce ption is th e Fugue in FMajor for organ (from th e Toccata and Fuguein F Major), a double fugue that does offer aregul ar coun ters ubject to its opening subjectfor all ins tances whe re it is no t combine dwith th e second su b jec t , th ough it th enyield s th e stage wh en the two main subjectsare combine d.

Since a regul ar countersubject is clearl ynot a universal requirement for successfulfugue writing, it may well be asked wh y ithas become such a hard-and-fast tradition toask for one on th e fugu e qu estions of th eGuild 's advanced ce rtifica ti on exam ina ­tions. Our response mu st surely be th at it isbecau se th is requirement test s , in admirablyshort space, the candidate's gras p and mas­tery of so man y fundamental contrapuntaland harmonic aspects of our tonal language.

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54 THE A MERICAN O RGANIST