Fugue (Prout)/Chapter 5

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CHAPTER V.


THE COUNTERSUBJECT.


159. In our first chapter (§ 10), we defined a Countersubject as "a counterpoint which accompanies answer or subject systematically, though not of necessity invariably." We have now to consider the essentials of a good countersubject, and to endeavour to show when its introduction into a fugue is advisable.

160. The first and most important requisite for a countersubject is, that as it has to accompany either the subject or the answer in whatever part these may appear, it must be written in double counterpoint with the answer, as an accompaniment to which it is first heard. The double counterpoint is, in by far the largest number of cases, in the octave, but it is also sometimes in the tenth or twelfth. Sometimes a countersubject which has been used in the octave at first is subsequently employed in one of the other intervals. In Double Counterpoint will be seen in § 163 an example of a countersubject used both in the octave and in the tenth; and at § 175 of the same book a similar instance of the octave and the twelfth.

161. A most important point in writing a countersubject is individuality of melodic character, and contrast of rhythm as compared with the subject (Double Counterpoint, § 129). This will be best illustrated by examples, which we shall mostly take from Bach's 'Wohltemperirtes Clavier,' as being a work accessible to everybody.

162. In our first examples

J. S. Bach. Wohltemperirtes Clavier, Fugue 2.

\new ChoirStaff << \override Score.BarNumber #'break-visibility = #'#(#f #f #f)
  \new Staff \relative g'' { \key c \minor \time 4/4 \mark \markup \tiny { (\italic"a") } R1*2
    r8 g16 fis g8 c, ees g16 fis g8 a |
    d, g16 fis g8 a c,16 d ees4 d16 c | bes8 s }
  \new Staff \relative c'' { \key c \minor
    r8 c16 b c8 g aes c16 b c8 d | g, c16 b c8 d f,16 g aes4 g16 f |
    ees \[ c'^"CS" b a g f ees d c8 ees' d c |
    bes! a bes c fis, g a fis | g4 \] } >>


J. S. Bach. Wohltemperirtes Clavier, Fugue 37.

\new ChoirStaff << \override Score.BarNumber #'break-visibility = #'#(#f #f #f) \override Score.Rest #'style = #'classical
  \new Staff = "up" \relative b' { \key fis \major \time 2/2 \partial 2 \mark \markup \tiny { (\italic"b") } R2 R1*3
    r2 bis4.\trill ais16 bis | cis4 r gis ais |
    b4. ais16 gis fis8 eis fis gis |
    ais bis cis ais dis4 fis, | fis eis8 }
  \new Staff = "down" \relative e' { \clef bass \key fis \major
    \change Staff = "up" \stemDown eis4.\trill dis16 eis | fis4 r cis dis |
    e4. dis16 cis \change Staff = "down" \stemNeutral b8 ais b \change Staff = "up" cis |
    \stemDown dis eis! fis dis gis4 \change Staff = "down" \stemNeutral b, |
    b\mordent ais8 gis fis4 \[ fis'^"CS" |
    fis eis r e | e dis r dis8 eis | fis4 ais, bis2\trill | cis4 \] } >>

the countersubject (C S.) is mostly in longer notes than the subject, though at the beginning of (a) contrast is secured by accompanying the quavers of the subject by semiquavers. Let the student play the countersubjects by themselves, and notice how different they are from the subjects, and at the same time how thoroughly suited to them in character.

163. Our next illustration shows the opposite case—

J. S. Bach. Wohltemperirtes Clavier, Fugue 44.

\new ChoirStaff << \override Score.Rest #'style = #'classical \override Score.BarNumber #'break-visibility = #'#(#f #f #f)
  \new Staff \relative a' { \key a \minor \time 4/4 R1*2
    r4 \[ a^"A" g c | dis, r r8 a' fis b| g \] }
  \new Staff \relative e' { \clef bass \key a \minor
    r4 \[ e^"S" c f | gis, r4 r8 d'-! b-! e-! |
    c-! \] a-! fis-! dis'-! e, \[ e'32^"CS" d c b a8 c32 b a g |
    fis g a16 ~ a32 g fis e dis e fis16 ~ fis32 e d cis b8. c32 d
      d8.\trill c32 d | e8 \] } >>

Here the countersubject does not enter with the first note of the answer; but between it and the subject are a few notes of codetta (§ 62). This often happens; sometimes, as will be seen presently, only a part of the subject or answer is accompanied by the countersubject. In the above passage we see a subject in long notes accompanied by a countersubject of very short notes.

164. On its first appearance, in company with the answer, the countersubject should be in the same key as the answer. In the example last given the answer is in E minor, and the counter-subject is no less distinctly in the same key. Sometimes, however, as in our example to § 67, the key of the answer is not clearly defined by the countersubject until nearly the close.

165. It was said in the last chapter (§ 115) that the third voice in a fugue almost invariably entered with the subject. In the very common case in which the subject is in the key of the tonic throughout, the answer will be in the key of the dominant. In order to return speedily to the tonic key, and to allow the third voice to enter at once, we often find in such cases that at the end of the countersubject the leading note of the dominant key is flattened, becoming the subdominant of the tonic key.

J. S. Bach. Wohltemperirtes Clavier, Fugue 33.

 \new ChoirStaff << \override Score.BarNumber #'break-visibility = #'#(#f #f #f)
  \new Staff \relative e' { \key e \major \time 4/2 R1*6
    \[ e1^"S" fis2 a | s2 \] }
  \new Staff \relative b << \clef bass \key e \major
    \new Voice { \stemUp s1 s r1 \[ b^"A" | cis2 e dis cis |
      b2. \] \[ b4^"CS" a b cis dis | s2 \] }
    \new Voice { \stemDown \[ e,1_"S" fis2 a |
      gis fis e4 \] dis8 e dis4 \[ b_"CS" |
      e fis gis ais b8 fis b2 \] a4 ~ |
      a gis8 fis gis2 gis fis } >> >>

Here the subject ends in E; the answer and countersubject are in B. To enable the third voice to enter immediately, a return is made to the key of E at the end of the third bar, by contradicting the A sharp. Where this is not done, it is mostly necessary (as will be seen in the next chapter) to introduce a codetta before the entry of the third voice. The evasion of a full cadence in the dominant key by the device just explained is frequently called by its Italian name, inganno, i.e., "deception"—a deceptive cadence.

166. Sometimes the countersubject is constructed of material suggested by the subject itself, as in the following passage.

J. S. Bach. Wohltemperirtes Clavier, Fugue 18.

 \new ChoirStaff << \override Score.BarNumber #'break-visibility = #'#(#f #f #f) \override Score.Rest #'style = #'classical
  \new Staff \relative d' { \key gis \minor \time 4/4 R1*2
    r4 \[ dis^"A" bis8 cis16 dis e8 dis |
    cis fisis gis b, cis cis dis dis | gis,4 \] }
  \new Staff \relative g { \clef bass \key gis \minor
    r4 \[ gis4^"S" fisis8 gis16 a b8 a |
    gis cisis dis fis,! gis gis a a |
    dis, \] eis \[ fis4^"CS" ~ fis8 e16 fis gis8 fisis16 gis |
    a8 gis16 a b8 gis a r fisis r | gis[ \] fis!] } >>


Here the figure of the subject
{ \clef bass \override Score.TimeSignature #'stencil = ##f g16[ a] b8 }
furnishes the chief idea for the countersubject. More frequently, however, the countersubject contains an entirely fresh idea, as in the examples previously quoted.

167. It is in general desirable that the countersubject should contain some distinct melodic or rhythmic idea, which may be used later for codetta or episode. A particularly fine example of this will be seen in the twelfth fugue of the 'Wohltemperirtes Clavier.'

J. S. Bach. Wohltemperirtes Clavier, Fugue 12.

 \new ChoirStaff << \override Score.BarNumber #'break-visibility = #'#(#f #f #f) \override Score.Rest #'style = #'classical
  \new Staff \relative f' { \key f \minor \time 4/4 R1*3
    r4 \[ f^"A" aes g | fis b c f, | e ees d2 | c8 \] }
  \new Staff \relative c' { \clef bass \key f \minor
    r4 \[ c^"S" des c | b e f bes, | a aes g2 |
    f8[ \] \[ f16^"CS" g] aes8 aes16 bes c b, c d ees4 |
    r16 c d ees f4 r16 ees f g aes4 |
    r16 g e b c4 ~ c8 bes16 aes bes4\mordent | c8 \] } >>

Notice here the strongly marked contrast between the subject and the countersubject. This fugue contains altogether six episodes (bars 16–19, 22–27, 30–34, 37–40, 43–47, and 50–53), all of which are founded on the first six notes of the countersubject—

{ \override Score.TimeSignature #'stencil = ##f \clef bass f16[ g] a8[ a16 b] c'8 }

168. Not infrequently the countersubject accompanies only a part, and not the whole of the subject or answer.

J. S. Bach. Wohltemperirtes Clavier, Fugue 34.

\new ChoirStaff << \override Score.BarNumber #'break-visibility = #'#(#f #f #f) \override Score.Rest #'style = #'classical
  \new Staff \relative e' { \key e \minor \time 4/4 \partial 4
    \[ \tuplet 3/2 { r8^"S" e fis } |
    g4_! a16 g fis g a4_! b16 a g a | b4_! g_! e_! c' ~ |
    c b8. dis16 e4^! a, ~ | a g8. dis'16 e4^! fis, ~ |
    \tuplet 3/2 4 { fis8 g a g fis e dis c' b a g fis |
      g a b a g fis e \] e' d cis b ais } |
    \tuplet 3/2 { b d fis } gis4 \tuplet 3/2 { cis,8 e g } ais4 |
    \tuplet 3/2 { d,8 fis ais } b4 ~ \tuplet 3/2 4 { b8 a g fis e dis }
    \[ e2^"CS" d! | cis b | ais4 b cis2 ~ |
    cis4 \] e8. ais,16 b2 }
  \new Staff \relative b { \key e \minor r4 R1*5
    r2 r4 \[ \tuplet 3/2 { r8^"A" b cis } |
    d4_! e16 d cis d e4_! fis16 e d e | fis4_! d_! b_! g' ~ |
    g fis8. ais16 b4 e, ~ | e d8. ais'16 b4 cis, ~ |
    \tuplet 3/2 4 { cis8 d e d cis b ais g' fis e d cis |
      d e fis e d cis } b8 s s4 } >>

That the countersubject has only the limited extent here marked for it, is proved by the fact that the rest of the counterpoint does not systematically reappear later in the fugue as an accompaniment to the subject or answer (see § 298, where the whole fugue is given in score and analyzed).

169. In tonal fugues that modulate to the dominant, the entry of the countersubject is often deferred till after the modulation has taken place. This allows the countersubject to appear without alteration against either subject or answer.

J. S. Bach. Wohltemperirtes Clavier, Fugue 24.

 \new ChoirStaff << \override Score.BarNumber #'break-visibility = #'#(#f #f #f) \override Score.Rest #'style = #'classical
  \new Staff \relative f' { \key b \minor \time 4/4
    r8 \[ fis^"S" d b g'( fis) b( ais) |
    e( dis) c'( b) fis( eis) d'( cis) | bis cis a fis gis2\trill |
    fis8.[ \] eis16] fis gis a cis b gis a c \[ fis4^"CS" |
    e d cis b ~ |
    b8 ais b4 ~ b16 cis d e fis g b, ais | d2 \] }
  \new Staff \relative b { \key b \minor \clef bass R1*3
    r8 \[ b^"A" a fis d'( b) e( dis) |
    a( gis) f'( e) b( ais) g'( fis) |
    eis fis d b cis2 | b16 \] s16 s8 s4 } >>

This subject is quoted in some text-books as a particularly difficult one to answer. There is, however, no real difficulty here, if we remember our rule (§ 121), that the modulation must be regarded as taking place as soon as possible. Here it cannot be till after the fourth quaver, because G natural does not belong to the scale of F sharp minor; but from the fifth note of the subject all is regarded in its relation to F sharp minor, and answered exactly by the corresponding notes in relation to B minor, and the whole countersubject is distinctly in the latter key. Notice the curious, and doubtless accidental, resemblance of this countersubject to that of the fugue in E minor, quoted in § 168.

170. If, on the other hand, the countersubject begins before the modulation has taken place, it will often need modification similar to that of a tonal answer, according to whether it is accompanying the subject or the answer.

J. S. Bach. Wohltemperirtes Clavier, Fugue 7.

 \new ChoirStaff << \override Score.BarNumber #'break-visibility = #'#(#f #f #f) \override Score.Rest #'style = #'classical
  \new Staff \relative b' { \key ees \major \time 4/4 \mark \markup \tiny { (\italic"a") }
    \[ bes16^"S" g f g ees aes g aes c8 bes r a16 f |
    ees'8 d c4\trill bes16[ \] f' d bes] aes f' d aes |
    g8[ \[ aes'^"CS" g f] ees16 c d ees f4 ~ |
    f16 ees f g aes f bes, aes' g8 \] \bar "||" }
  \new Staff \relative e' { \key ees \major R1*2
    \[ ees16^"A" d c d bes ees d ees g8 f r d16 bes |
    aes'8 g f4\trill ees16 \] s } >>


\new ChoirStaff << \override Score.TimeSignature #'stencil = ##f
  \new Staff \relative d'' { \key ees \major \time 4/4 \mark \markup \tiny { (\italic"b") }
    s8 \[ des^"CS" c bes aes16 g aes bes c4 ~ |
    c16 bes c d ees c f, ees' d8 \] }
  \new Staff \relative b { \clef bass \key ees \major
    \[ bes16^"S" g f g ees aes g aes c8 bes r a16 f |
    ees'8 d c4\trill bes16 \] s } >>


At (a) the countersubject accompanies the answer; at (b) it accompanies the subject itself, and the third from C to E becomes a second from A to G. This is because the third in the answer, between F and D, was only a second (between B and A natural) in the subject. The change in the countersubject must be made, like that in the answer, at the point of modulation. Sometimes, also the countersubject is somewhat altered, even with a real answer, as in the fugue in E, referred to in § 165 (see the extract given later in § 269).

171. It may be as well to remind students that, as the countersubject is first heard against the answer only, it must not make with the answer any intervals which would not be allowed in free two-part counterpoint. The laws regulating the employment of these intervals will be found in Double Counterpoint, Chapter V.

172. Though, as a general rule, the countersubject makes its first appearance as an accompaniment to the answer in the exposition, we not infrequently meet with fugues in which its first appearance is deferred. The great fugue in C sharp minor (No. 4 of the 'Wohltemperirtes Clavier') is an example of this kind. We have already quoted the subject and answer in § 66. The counterpoint against the answer seen in that example accompanies also the entry of the third voice, but not those of the fourth and fifth, nor is it subsequently used at all. We cannot therefore consider it a countersubject. But at the 35th bar a genuine countersubject makes its appearance.

J. S. Bach. Wohltemperirtes Clavier, Fugue 4.

\new ChoirStaff <<
  \new Staff \relative d'' { \key cis \minor \time 4/4 \partial 2. \mark \markup \tiny { (\italic"a") }
    dis4^"CS" e fis | gis8 fis gis a gis fis e gis |
    fis e fis gis fis e dis fis | e s }
  \new Staff \relative c' { \clef tenor \key cis \minor
    s4 cis2^"S" | bis e | dis1 | cis1.*1/6 } >>

This countersubject accompanies every subsequent entry of the subject till the coda of the fugue. At the 49th bar a second countersubject is introduced—

\new ChoirStaff << \override Score.TimeSignature #'stencil = ##f \override Score.Rest #'style = #'classical
  \new Staff \relative f'' { \key cis \minor \time 4/4 \partial 8
    fis8^"S" | eis2 a | gis1 ~ | gis4 f8 }
  \new Staff \relative c' { \key cis \minor
    r8 r4 cis^"CS2." fis fis | fis eis8 dis eis2 | fis4 s8 } >>

Both countersubjects are worked together with the subject in triple counterpoint. Another fine example of two countersubjects introduced late in the fugue will be found in the 38th fugue (in F sharp minor) of the same work.

173. A remarkable example of a fugue with two regular countersubjects, both of which appear in the first exposition, is seen in No. 21 of the 'Wohltemperirtes Clavier.' We quote the commencement of the fugue, writing it in open score, that the separate parts may be more clearly followed—

J. S. Bach. Wohltemperirtes Clavier, Fugue 21.

\new ChoirStaff << \override Score.BarNumber #'break-visibility = #'#(#f #f #f) \override Score.Rest #'style = #'classical
  \new Staff \relative f' { \key bes \major \time 3/4
    r8 \[ f^"S" g f bes d, | c a'16 g bes a g f c'8 ees, |
    d bes'16 c a bes c d ees d c ees |
    d c bes c a bes c d ees d c ees |
    d8.[ \] c16]^\markup \tiny \italic "Codetta." bes a bes c d8[ \[ f]^"CS1." ~ |
    f bes, a bes e g ~ | g a,16 bes c8 c c c |
    c16 bes a bes c8 c c c | c4 \] r r16 \[ d^"CS2." bes d |
    ees8 r r4 r16 ees c ees | f8 r r a,16 bes c bes a c |
    bes4 r8 a16 bes c bes a c | bes8 \] s }
  \new Staff \relative b { \clef alto \key bes \major R2.*4
    r8 \[ bes^"A" d bes f' a, | g e'16 d f e d c g'8 bes, |
    a8 f'16 g e f g a bes a g bes | a g f g e f g a bes a g bes |
    a8.[ \] g16] f ees! d ees f8 \[ bes^"CS1." ~ |
    bes ees, d ees a c ~ | c d,16 ees f8 f f f |
    f16 ees d ees f8 f f f | f4 \] }
  \new Staff \relative f { \clef bass \key bes \major R2.*8
    r8 \[ f^"S" g f bes d, |
    c a'16 g bes a g f c'8 ees, |
    d bes'16 c a bes c d ees d c ees |
    d c bes c a bes c d ees d c ees | d8 \] s } >>

Here the first countersubject accompanies the answer; when the third voice enters with the subject, the alto, which has just completed the answer, takes up the first countersubject, while the treble continues with a second countersubject. Every subsequent entry of the subject or answer down to the end of the fugue is accompanied by both the countersubjects.

174. A different method of employing two countersubjects will be seen in the 47th fugue (in B major) of the same work. The first appearance of the answer is accompanied by a countersubject.

J. S. Bach. Wohltemperirtes Clavier, Fugue 47.

\new ChoirStaff << \override Score.BarNumber #'break-visibility = #'#(#f #f #f)
  \new Staff \relative f { \clef tenor \time 2/2 \key b \major R1*4
    \[ fis2^"A" ais | dis b | gis eis' | fis4 \] }
  \new Staff \relative b, { \clef bass \key b \major
    \[ b2^"S" dis | gis e | cis ais' | b4 \] ais8 gis fis4 e |
    dis8 cis \[ e2^"CS1." dis8 cis |
    b fis' ais2 gis8 fis | eis b' dis2 cis8 b | ais4 \] } >>

This is regularly introduced against subject and answer throughout the whole of the exposition, after which it is heard no more. Its place is taken on the next entry of the subject by an entirely new countersubject, written in double counterpoint in the twelfth, and invariably inverted in that interval. We gave it as an illustration of this species of counterpoint in § 171 of Double Counterpoint, to which the student is referred. It is very rare to find two different countersubjects used, not simultaneously, but as here, successively.

175. Some theorists speak of a fugue with a regular countersubject as "a fugue with two subjects," or "a double fugue." It is best, however, not to apply this name to fugues such as those we have been speaking of, unless the countersubject, as is sometimes the case, does not appear in the first exposition, but has later an independent exposition of its own, and is not at first used as an accompaniment to the subject, with which it is not combined till its own separate exposition is completed. We shall treat of fugues of this kind, as well as of the other variety of double fugue, in which the second subject first appears not against the answer (as in the examples here given), but against the first subject, later in this volume (Chapter XI.).

176. It is by no means necessary that every fugue should have a regular countersubject. Of the forty-eight fugues in the 'Wohltemperirtes Clavier' there are seventeen which have none; and the question naturally arises, When it is desirable to write a countersubject to a fugue, and when can it be suitably dispensed with? It is impossible to lay down a hard and fast rule on the matter; but a careful examination of those fugues which have no countersubject shows that, in a large majority of cases, it is unnecessary, if the subject is intended to be elaborately combined with itself. The exact meaning of this will be better understood when we come to speak of the middle section of a fugue, and of stretto; but one or two illustrations will help to make the matter clearer. In fugues Nos. 1, 22, 26, 29, and 31, we find no countersubject, because the subject itself is so largely treated in stretto (§ 16) that a countersubject would only have been in the way. In fugues 8 and 20, the subject is treated by inversion and in canon, and in No. 27 extensive use is made of inversion and diminution. On the whole it may be said that, when there is no countersubject, we mostly find the more scientific devices of fugue writing applied to the subject itself. This, however, must not be taken for more than an attempt at generalization. There is no form of composition in which there is so much liberty of treatment and variety of detail as that of fugue.

177. The student should now compose countersubjects to all the fugue subjects given at the end of Chapter IV. He should try to write at least two or three, differing in character, to each subject. For this purpose he should write the subject on one staff, following it on a second by the answer, above or below which, according to its position, he should write his countersubject as the continuation of the subject. He may always introduce a short codetta, if necessary, between the end of the subject and the beginning of the countersubject, but it is best not to leave a rest between the two. The first voice should go on continuously to the end of the countersubject.[1]


  1. We occasionally find exceptions to this sound general principle, e.g., in Nos. 16 and 30 of the 'Forty-Eight' in both of which the entry of the countersubject is preceded by a rest, probably to call attention to it more strongly. We shall see later that a rest is generally advisable before the re-entry of the subject.