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-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
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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:
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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
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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.
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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
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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
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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
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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- )