Fugue: Subject and Tonal Answer
In a tonal answer, scale degree 1 (SD1) in the subject is answered by SD5 in the answer and, conversely, SD5 in the subject is answered by SD1 in the answer.
Intervals of a subject that ranges at its beginning in the lower part of the scale (SD1-5) will appear contracted in the answer (in the range of SD5-8), e.g. leap of a fifth in the subject contracts to a leap of a fourth in the answer, a third to a second, a second to a unison. Conversely, intervals of a subject that ranges at its beginning in the upper part of the scale (SD5-8) will appear expanded in the answer (in the range of SD1-5), e.g. a leap of a fourth in the subject expands to a fifth in the answer, a unison to a second, a second to a third.
These intervallic contractions and expansions are accommodations to the hold of tonic harmony, which generally prevails at the close of the subject, as the answer starts.
The contractions and expansions in the answer last only until the prevailing tonic harmony shifts toward the dominant. As that shift occurs, the intervals of the subject are duplicated in the answer such that the answer is an exact transposition of the subject a fifth higher.
Example 1: WTC I, Fugue 2 (C minor)—expansion
The subject begins on SD5, signaling a tonal answer. The subject ranges at its beginning in the upper part of the C-minor scale (between SD5-8). The descending 4th leap in m. 1, from c2 to g1, expands in the answer to a descending fifth, from g2 to c2. Because of that expansion, the next interval of the subject, a rising minor second from g1 to ab1 (m. 1) also expands to become a rising minor third, c2 to eb2 (m. 3). The remaining notes of the answer are exact transpositions of the subject a fifth higher.
Example 2: WTC 1, Fugue 11 (F major)—expansion
The subject begins on SD5, signaling a tonal answer. The initial interval of the subject, a rising major second from c1 to d1, expands in the answer to a major third from f1 to a1 in mm. 4-5. The remaining notes of the answer are exact fifth transpositions of the subject.
Example 3: WTC 1, Fugue 17 (Ab major)—contraction
SD5 appears near the beginning of the subject (its second note), signaling a tonal answer. The ascending fifth at the subject’s opening, ab-eb1, contracts in the answer to an ascending fourth, eb-ab. That contraction causes a contraction of the subject’s descending minor third at its opening, eb1-c1 (second and third notes) to become a minor second, ab-g, in the answer (m. 2). The remaining notes of the answer are fifth transpositions of the subject.
Example 4: WTC 1, Fugue 24 (B minor)—contraction
This subject is one of the few modulating ones in volume 1
of the WTC. It modulates from B minor to F# minor. SD5 appearing as the first note of the
subject signals a tonal answer. The
answer to a modulating subject has the task of modulating back to tonic to
prepare for the third subject entry, which will be in tonic (see m. 9). The descending major third, f#1-d1, at the
opening of the subject—part of a descending arpeggiation of the tonic
triad—contracts in the answer to become a major second, b-a (m. 4). Further, the subject’s minor second, g1-f#1
(following the ascending minor-sixth leap from b to g1, m. 1) expands (!) to
become a minor third, d1-b (m. 4). Because
the answer must modulate back to tonic, the remaining intervals of the answer
are not fifth but rather fourth transpositions of the subject, which causes the
answer to modulate back to tonic. Had
the remaining intervals been fifth transpositions of the subject, the answer
would have modulated to the dominant of the dominant, i.e. to the
 In “real” answers, where SD5 does not occur prominently at or near the beginning of the subject, SD1 is answered by SD5, and SD5 by SD2. In WTC 1, real answers may be found in fugue numbers 1 (C), 4 (c#), 5 (D), 6 (d), 9 (E), 10 (e; the only two-voice fugue in WTC 1), 14 (f#), 15 (G), and 20 (a).
 Other modulatory subjects in WTC 1 are fugue number 7, in Eb major (which, however, modulates back to tonic before its close); and number 18, in G# minor.