-T200 FUGUE

and finally supplanted by the earlier and more valid one of fugue as away of. writing, a particular contrapuntal approach. While we sometimesspeak of fugue as "one of the contrapuntal forms," the term "fugue form"actually has no exact meaning. This is not to say, though, that individualfugues are lacking in a formal plan, or that the ternary plan is not fre-quently encountered. The point is simply that there are various possibilitierin fugal architecture, so that it is impossible to single out any one of themas "fugue form." Probably the notion of a set three-part plan for fuguerarose because they usually contain:

l. an "exposition," in which the subject is announced in imitative fashionaccording to a traditional pattern;

2. a trcer portion, sometimes called a "development section," which gen-erally avoids the tonic key;

3. some reference to the subject, in the tonic key, near the end. This maybe anything from a portion of the subject to a series of complete and em.phatic statements, a full-fledged "recapitulation."

The ABA principle is obviously in evidence here in terms of key relation-ships and, to a greater or Iesser degree, in terms of the balancing of theexposition by a similar section near the end, But in determining the overallform of a fugue it is also important to take into account the proportionrof the various sections, and their relationship to each other as far atcontent is concerned. These may clearly indicate a binary (or some othernon-ternary) design, even though certain suggestions of the ABA feelingmay be present. We shall return to the matter of formal analysis later on,In the meantime some of the elements of fugal writing will be considereclin detail.

THE SUBJECT

Subjects vary considerably in length, some being as short as one measurcland others as long as eight or more measures. The principle involved here irthat a subject should be long enough to give the feeling of being an actunlline instead of a figure, but not so long that the listener will have difficultyin retaining it. The average length of the subjects in The Well-TemperodClauier is about two measures. The excerpts in Example I illustrate a shortand a relatively long subject, respectively.

Ex. la BACH: W.T.C., Book II, Fugue 9

201

lix. lb BACH: Fugue in C Major (Organ)

These two subjects (Example 1) represent two distinct types known intlrc eightdenth century as soggetto and, andamento, respecrir"ty. rrr" first is,[ short or medium length (no longer than about three measures), rela-tively simple, and sometimes similar, in its square-cut character, to thesrrbjects of the sixteenth-century ricercar. The second is longer, generallyrrrore flowing, and often made up of two ideas. In Bachis music, theundamento type occurs most often in his large organ fugues.

'I-o be interesting as w'ell as readily recognizabre when brought back, arrrbject should have some striking feature, melodic, rhythmic, oi both. Thesrrbjects shown in Example 2 all possess such features.lt,x.2a BACH: Fugue in E Minor (Organ)

lix. 2b PURCELL: Sonata No. 7. Canzonz

i

l'lx. 2c GOTTLIEB MUFFAT: Fugue in G Minor

l'lx. 2d HAYDN: Fifth Mass

I202

Ex. 2e

FUGUE

BACH: W-T.C., Book II, Fugue 6

For instance, in the first of these, the ever-widening interval between thealternating eighth notes (hence the name "Wedge Fugue") is highly distinc-tive and makes the subject easily recognizable, even without any unusualrhythmic features to distinguish it. In the beginning of the last subjectshown in Example 2, the interest centers in the triplet figure and its opposi'tion to the eighth-note rhythm that follows. Melodically, the descendingchromatic figure holds our attention. Notice the effective use of sequencein many of these subjects. The corroboration of an element creates amelodic pattern that the ear can grasp, and impresses the material morefirmly on the listener's mind.

It need hardly be added that a good subject u'ill have an interestingcurve, such as those discussed in Chapter 2. Related to this is the need fora climax point, preferably placed not too near the beginning.

Subjects should not use period construction; the latter is basicallv foreignto the character of fugue.

In this style, subjects most often begin on the tonic note, somewhat lessfrequently on the dominant note, and very rarely on the leading tone orsupertonic (always with that note as an anacrusis) . In any case, the tonicnote must be included near" the beginning so that the tonality will beclearly defined. The most successful subjects suggest a solid and interestingharmonic background. A subject may start either on or off the beat, afrequent arransement being a start after a short rest, as in Examples 20, 3,5,6, and 11.

Most fugue subjects do not exceed a range of one octave, and many,especially in four- and five-voice fugues, stay within an even smaller com-pass.

A subject that can be used in stretto fashion obviously presents specialpossibilities for interesting development.

A question often posed by students is, "What is the difference betweena fugue subject and an invention motive?" Given the wide,variation inlength and character exhibited both by fugue subjects and by inventiorrmotives, it is difficult (and dangerous) to attempt comparisons between thrrtwo. Concerning length, about all that can be said is that a good many sub'jects exceed four measures, while none of Bach's Invention motives do (the

r;rrcrrti 203canonic inventions excluded) . Concerning clrttrtrttt !', ll ir rlrrkrrrlrtr:

204

Ex. 3

FUGUE

The subject, in C minor, starts on the tonic note in the middle voice lllr'lan eighth rest, and extends through the first sixteenth note in the tlrirrlmeasure. Certain points concerning the construction of this subject rr'r'r,mentioned earlier on page 7. The answer in the top voice, bt'qirrnirrron the second eighth note of the third mcasure, is tonal as rrriqlrt lrt'r'rpected, in vieu, of the dominant note, (1, ncrrr tlrc start o[ tlr

206 FUcuEIn three-voice fugues the pattern of keys in the exposition is always tonic,

dominant, tonic (subject, answer, subject), The voices may enter in variousorders, an order of entry being considered "regular" if an even-numberedvoice is answered by an odd-numbered voice or vice versa. (This willautomatically take place if the first two voices are adjacent.) The followingtable shows the relative frequency of different orders of entry in the 26three-voice fugues contained in both books of The Well-Tempered Claaier,(The voices are numbered from the top down.)

Order of entry12321332r312

Number oftimes used

t2r0)

2

Notice that the order 231, though regular, does not appear, while two fuguesmake use of the irregular order 312, in which the first two voices are notadjacent. The order of entry in Example 3 was 213.

The plan of the three-voice fugue exposition is as follows, the order 123having been arbitrarily chosen.

Ex. 4

Tonic key Dominant key Tonic keyFree or CS. trS. CS. I or free OPtional

A. bridge CS. I or free,

s.

It should perhaps be mentioned that when an exposition is extendedbeyond the normal proportions shown here, either by the addition of anannouncement or by sequential extension, the cadence at the end of itoften occurs in a key other than the tonic. Fugues 6 and 8 in the firstbook of The Well-Tempered Clauier are among those that demonstratethis possibility.

FOUR.VOICE COUNTERPOINT

The inclusion in this book of a separate chapter on four-voice counter-point (to parallel those on two- and three-voice counterPoint) was not felt

FUGUE 207to be necessary, since most of the material on three-part writing can beextended to apply to the four-voice texture. Then, too, the latter is normallythe basis for the study of harmony and is consequently familiar to moststudents. of course the contrapuntal approach puts far greater emphasison the linear aspect, although that element is obviously present to somedegree even in chord successions that are well constructed; ihe dividing linebetween four-part harmony and four-part counterpoint is not ul*Iys asharply defined one.

The presence of four voices allows for the simultaneous sounding of allfour notes of a seventh chord; in triads, one note must be doubled. Aithoughlinear considerations should govern doubling to a large extent, an effortshould be made to avoid giving special prominence to chord members notordinarily stressed-for example, a chromatically altered tone, or the thirdof a primary triad.

Rhythmic activity may be more or less evenly distributed among thevoices, or certain ones may play a more active role than others. Two voicesmay be paired rhythmically against the two others moving in a differentdesign; and so on.

In general, at least one of the voices in a four-voice contrapuntal fabricis likely to be somewhat subordinate in importance at any given point, sincethe ear would have difficulty in following four lines of equal rigrrifi.urr."and complexity for any extended period. The music is most olt"., .orr-structed in such a way that the listener's attention is focused first on oneline, with its supporting counterpoints, then on another such combination.

In most four-voice contrapuntal works, all four voices are not involvedcontinuously. one or two drop out from time to time (this is particularlylikely to happen in episodes) so that variety of texture is introduced. Evenshort rests have two further advantages: they help to define the segmentsof musical thought, and they make the voices that have rested morelellinglvhen they re-enter.

The chief problem in four-voice counterpoint is that of maintaining agood balance between harmonic definition and linear integrity. while thefirst becomes easier with four voices, care must be taken that the seconddoes not suffer in the process.

THE FOUR.VOICE FUGUE EXPOSITION

As might be expected, the exposition in a four-voice fugue simpry carriesone step further the pattern lve observed in three-voice fugues. The excerptshown here is a fairly typical example.

208 FUcUEEx. 5 BACH: W.T.C., Book I, Fugue 23

Although no bridge is present here betrveen the second and third:rrrnouncements of the subject, such passages are frequent in four-voice fugtt,'tas they are in the three-voice variety (see Example 10, page 226).

Once again we can observe the use of tonal imitation, in the thir

210 FUGUE

In Example 5, as in most four-voice fugue expositions, the pattern ofkey relationships is tonic, dominant, tonic, dominant. However, anotherpattern is possible and is seen occasionally: tonic, dominant, dominant,tonic. Example 6 illustrates this arrangement, which is clearly responsiblefor the irregular order of entry (2134) involved there. This is the onlyfugue of "the 48" that uses the I V V I key plan.Ex. 6 BACH: W.T.C., Book I, Fugue 1

The majority of four-voice fugues make use of one or more countersub.jects. The fugue in Example 5, for instance, has a countersubject, startingwith descending sixteenth notes, that first appears in the tenor line in tlrtthird measure, and is taken by the alto against the third announcement ofthe subject, and by the soprano against the fourth announcement. Althoughthe whole of this melodic line does not recur frequently in the courrrof the fugue, the beginning of it does, and this fact plus the repeated use ofthe line intact in the exposition and its reappearance at the encl, stx.rrrsufficient justification for calling it a countersubject.

FUGUE 2II

Second countersubjects are infrequent, and the use of a third counter-subject in a four-voice fugue is extremely rare. In the first place, that voiceis usually present, in the exposition, during only one announcement of thesubject. Consequently, one of the criteria for determining whether it is acountersubject, namely its reappearance with the subject in the exposition,is missing. The term "third countersubject" is probably appropriate only inrare cases where the material returns frequently in later portions of thefugue.

As mentioned earlier, not all fugues make use of a countersubject. Thebeginning of one that does not is shown in Example 7.

Ex. 7 BACH: W.T.C., Book I, Fugue 5

The absence of a countersubject here is offset by the arresting character ofthe subject itself, as well as by its shortness.

Other fugues in the first book of The Well-Tempered Clauier that donot use a countersubject are numbers l, B, L7, and 22. A further illustra-tion from the twelfth fugue in the second book can be seen in Example 10.

Example 8 shows the general plan of the exposition in a four-voice fugue.In it, the order of entry 3214 happened to be chosen from the numerous

212 FUGUEpossibilities. Where a .first countersubject or free material could be used,"CS. I" is listed first, inasmuch as a countersubject is encountered moreoften than free material at that point. On the other hand, second and thirdcountersubjects are /ess usual than free material. "Free" is therefore listedfirst when one or the other could be involved.

Ex. 8S. CS- I or free

A. Optional CS. I or free Free or CS. IIS. CS. I or free bridge

ruouli 213what Tovey has called "vexatious minutiae.,, The irnporttnt tlrlnxi rrrtlurr,is to glean from a study of fugue the broad underlying princilrrr.r ,f trutmusical structure. In the particular case at hand, the 1..y ro.t that wesometimes have difficulty determining exactly where the subject ends shouldtell us that in good fugue writing the subject generally flows smoothly intothe countersubject, the two often forming a continuous line.

As in three-part inventions, the end of the subject proper is sometimesfollowed by a link that keeps the rhythm going and leads smoothly to thefirst note of the countersubject or free material. The fugue which followscontains a good example.

Ex. l0 BACH: |,Y.T.C., Book II, Fugue t2Free or CS.[ Free or CS. III

THE SUBJECT AS RELATED TO THE MATERIALTHAT FOLLOWS IT

In most fugues the point at which the subject ends and the counter-subject or free material begins is quite clear. It may be marked by atleast a mild cadential feeling (though there is generally no pause in therhythmic motion) or by some new melodic or rhythmic element. Example5 illustrates both these features. However, in cases where neither of theseguideposts is present, the beginning of the countersubject may be difficultif not impossible to fix exactly. Consider this fugue, for example:Ex. 9 BACH: |,Y.T.C., Book I, Fugue 9

Here the first statement of the subject could be heard as extending throughthe G-sharp on the second beat of the second measure, or through the Ilwhich is also the fint note of the answer---or even through the E on thcthird beat.

The fact that this and certain other points in connection with fugurrcannot always be pinned down with a hard-and-fast analysis should not brra rnatter of concern to us. A great deal of time can be wasted in debatirrg

a3

Link

214 FUGUEHere the subject proper seems to end with the A-flat at the beginning ofthe fourth full measure, the rest of the notes in that measure being link-tones of lesser importance.

As mentioned earlier, there is no countersubject in this fugue.This example provides a further illustration of a bridge (measures 9-11)

between the second and third announcements of the subject.

THE SUBJECT AS RELATED TO TIIE ANSWER;THE STRETTO FUGUE

From the examples given so far it can be seen that in the two most usualarrangements the answer begins either immediately following the last noteof the subject or along with that note. Only rarely is it appropriate toanalyze the answer as overlapping the subject by more than one or twonotes. Yet that analysis seems necessary in fugues such as the one quotedin Example 11, where the ear receives a definite impression that the answerhas begun before the subject has been completed.

Ex. ll BACH: W.T.C., Book II, Fugue 3A.

q

begin in this fashionS,, con. mot.

are sornetimes referred to as "strettoFugues thatfugues."

SPECIAL DEVICES AS USED IN THE EXPOSITION

Augmentation, diminution, and contrary motion, like stretto, appear onlyrarely in the exposition of fugues. In Example 11 the third announcementof the subject is in contrary motion. The same principle is carried evenfurther in Example 12, where all the announcements after the initial oneare in contrary motion. Such a fugue is known as a "counterfugue"(Gegenfuge in German) . Example 12 also illustrates the use of other devices

FUcUE 215in an exposition. The first statement of the subject is in diminution, ascompared with the original form used earlier in the The Art ot' Fugue, andthe same is true of the announcement beginning in measure 3. The lastannouncement, measure 5 in the bottom voice, uses augmentation; there iseven a hint of double diminution in the last measure (top voice) ; andstretto is present throughout.

Ex. 12 BACH: The Art ol Fugue, No. 7

Dim.

(Double dim- )