THIS ARTICLE is designed to be a sequel tomy essay, “The Fugal Answer,” foundin the April 2006 issue of TAO. Refer

back to that article for definitions of, and dis-cussions 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 stan-dard text on fugal composition. I will, how-ever, 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 be-ginning 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-

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

A “countersubject” is, as the word sug-gests, 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 in-troduced during the second statement of thesubject (i.e., the answer), it reappears duringall subsequent subject entries in the exposi-tion section of the fugue, and during a clearmajority of later statements (not necessarilyevery statement) of the subject. It acts, in ef-fect, 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 pre-sent 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 countersub-ject while Voice 4 states the subject; etc.

A regular countersubject, in order to be alaw-abiding element in the polyphonic fab-ric, must obey all traditional rules of coun-terpoint (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 es-chewed, dissonances properly prepared andresolved according to late-Baroque guide-lines, and the total range covered by themelody should be modest, generally not ex-ceeding a twelfth. To enjoy a profile suffi-ciently independent of the fugue subject, thecountersubject should offer significant con-trast to the subject in matters such asrhythms featured, pitch contour, andmelodic interval content. More often thannot, it should run in contrary or oblique mo-tion relative to the subject. While not neces-sarily as distinctive or memorable a melodic

52 THE AMERICAN ORGANIST

REGULAR COUNTERSUBJECTS IN FUGUEWalter Hilse, FAGO

conception as the subject, it should nonethe-less be easily recognizable. In addition,since, during the course of the fugue, the reg-ular countersubject will inevitably have oc-casion to appear both above and below thesubject, it must obey the traditional laws ofdouble (“invertible”) counterpoint, in orderto behave acceptably in both vertical ar-rangements. Thirds, sixths, octaves, unisons,and their octave compounds may be em-ployed 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 re-solved as if they were dissonances, sincetheir inversions are fourths— dissonances in18th-century language. (Please note: I am re-

stricting my discussion to double counter-point at the octave, which is only one,though by far the most common, of three tra-ditional 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 ap-pearances poses no problem. It will simplybe an exact transposition of its original form:

See Example 1a and 1b

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

dominant key area at that point. The next ap-pearance of the regular countersubject will,however, be back in the tonic key, during thetime the third voice has its crack at the sub-ject. Thus, the second presentation of the reg-ular 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 adjust-ment (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 coun-tersubject in Example 1 above.) In the patternof recurrence, the most important aspect ofthe relationship between the two voices is

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apparently not how they begin but rathertheir interaction as the cadence at the end ofthe subject is approached. Since most initialtonal adjustments involve only the first orsecond note of the subject, these adjustmentsare therefore often completed before thecountersubject begins. Consider, for exam-ple, the second and third entries in the Fuguein C-sharp Major, Book I:

See Example 2

In other cases of initial tonal adjustments,Bach finds it possible to preserve an exacttransposition of the regular countersubjecteven though there is an overlap between thebeginning of the countersubject (i.e., its pat-tern of recurrence) and the initial tonal ad-justment: this can happen if a note in thecountersubject on an important part of a beatfunctions as a consonance in the first ap-pearance of the countersubject, then as aproperly behaving dissonance in the next ap-pearance (or vice versa). Consider, in the fol-lowing example, the 16th note appearing inthe countersubject against the fourth note ofthe subject:

See Example 3a and 3b

It is a sixth in its first appearance, but aninth (accented passing tone) in the next.

If the fugue subject modulates to the dom-inant key, then things tend to be a bit more

complicated. The regular countersubjectusually must undergo a tonal adjustmentcorresponding to the terminal tonal adjust-ment found in the answer. (An exception oc-curs when the terminal adjustment is veryearly in the subject—e.g., in the Fugue in G-sharp Minor, Well-tempered Clavier, BookI—in which case the situation is similar to aquickly executed initial adjustment.) Fittedto the tonal-answer form of the subject in itsfirst appearance, the regular countersubjectmust now be fitted to the original form of thesubject. To accomplish this, one must lookfor a “splice-point” in the countersubject co-inciding (or almost coinciding) with thesplice-point in the answer. At the splice-point you have chosen, begin to state all sub-sequent pitches one scale-step higher thanthey would have been in an exact transposi-tion, in order to wind up in the dominant key(as the subject does in its third entry) ratherthan the subdominant:

See Example 4a and 4b

Regular countersubjects are not found inall fugues—in fact, among the 48 fugues ofthe two books of the Well-tempered Clavier,over 20 (i.e., close to 50%) do not have them.While an attractive regular countersubject isoften a major asset for a fugue, the absence ofone is not necessarily a shortcoming, and in-deed, some of Bach’s most masterly fuguesdo not have them.

In particular, regular countersubjects tendnot to be found in fugues in which “specialtricks” such as stretto, augmentation, andmelodic inversion are extensively featured,because the implementation of these de-vices deprives the countersubject of the con-trapuntal space needed for its presentation,or else alters the rhythmic or harmonic en-vironment of the subject, making survival ofthe countersubject impossible. Also, doubleand triple fugues almost never possess regu-lar countersubjects, because the second (andthird) subjects themselves function, in ef-fect, as glorified regular countersubjectswhen combined with the opening subject.One beautiful exception is the Fugue in FMajor for organ (from the Toccata and Fuguein F Major), a double fugue that does offer aregular countersubject to its opening subjectfor all instances where it is not combinedwith the second subject, though it thenyields the stage when the two main subjectsare combined.

Since a regular countersubject is clearlynot a universal requirement for successfulfugue writing, it may well be asked why ithas become such a hard-and-fast tradition toask for one on the fugue questions of theGuild’s advanced certification examina-tions. Our response must surely be that it isbecause this requirement tests, in admirablyshort space, the candidate’s grasp and mas-tery of so many fundamental contrapuntaland harmonic aspects of our tonal language.

54 THE AMERICAN ORGANIST