Fugue: Subject and Answer

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The Subject
The "subject" of a fugue is its main theme. It is generally short--one or two measures--but may be longer (3-4 measures). While they are usually harmonically generic, based on I, V, and IV, they are distinctive in melodic contour and rhythmic articulation, making them memorable after one hearing, and easily recognizable.

1 measure{1}: A major, Ab major
2 measures: C major, C minor
3 measures: F# minor, A minor
4 measures: Bb major, G major

Jagged: B minor, C# major (compound melodic)
Chromatic: F minor, E minor
Smooth: C major, F# minor

Starting and Ending Notes
For reasons that will become apparent in the discussion below on the "Answer," the starting and ending notes of the subject are of great importance. Fugues in volume 1 of the the Well-tempered Clavier (WTC 1) begin on either scale degree 1 (67%) or 5 (33%), the two tonal anchors of a scale. No fugues begin on 3 (more below). The most common ending notes are 1 (33%), 3 (38%), and 5 (21%). Two subjects (8%) end on 7 (fugue nos. 10 and 15). Not surprisingly, the initial and final notes of fugue subjects are the chief degrees in a diatonic scale{2}.

The reasons for subjects beginning on scale degree 1 or 5, but not on 3, have to do with the interval at which the second voice enters with the so-called "answer." The answer reproduces the subject almost exactly, sometimes exactly, transposed a fifth higher--once again, a reinforcement of diatonic tonality. The subject of the C-major fugue, for instance, begins on C, the answer on G (m. 2). Similarly in the D-major fugue, the subject begins on D, the answer on A.

From what we have just said about the answer beginning a fifth higher than the subject (or fourth lower, which is essentially the same thing), it would follow that a subject that begins on scale degree 5 would lead to an answer that beings on 2, a fifth higher. However, that is not the case. Examine the beginning of the F-major fugue (no. 11). The subject begins on scale degree 5 ("middle" C), the answer a fourth higher, on scale degree 1 (F), not on 2 (G)! Similarly, the subject of the G-minor fugue (no. 16) begins on 5 (D), the answer a fourth higher, on scale degree 1 (G), not on 2 (A). Why? Why does the answer begin a fifth higher, on 5, when the subject begins on 1, but a fourth higher, on 1, when the subject begins on 5? Read on...

The Answer
As explained in the preceding section, the second voice to enter presents the answer, a repetition of the subject transposed up a fifth. The first note of the subject, however, and sometimes a few others as well, is transposed only a fourth higher, as we have just seen. After the first note, or first few, the remainder of the answer is an exact transposition up a fifth. Why?

The reason for this discrepancy has to do with harmony. At the end of the subject, especially one that ends on 1 or 3, the implied harmony is clearly tonic, as in the C-minor fugue (no. 2), C# major (no. 3), D major (no. 5), F# minor (no. 14), and many others. If the answer is to enter as the subject finishes, as it routeinly does, it must begin with a note that is consonant with tonic harmony, lest it enter jarringly on an unprepared dissonance. If the subject begins on scale degree 1, the answer can begin a fifth higher, on 5, which is consonant with the tonic harmony implied when the answer begins at the end of the subject. However, if the subject begins on 5, the answer cannot start a fifth higher, on 2, because 2 is dissonant with tonic harmony. Consequently, the answer is adjusted to begin on 1, a fourth higher, in order to begin on a consonance. An answer that has such an adjustment is designated a tonal answer, because it has been modified from its usual strict fifth transposition in order to confirm the tonality (tonic) by entering on a consonance, rather than conflict with it by entering on a dissonance. After this adjustment, the remaining notes of the answer are fifth transpositions of the subject, as can be seen, for example, in the F-major fugue (no. 11), or the G-minor fugue (no. 16). The appearance of scale degree 5 at or near the beginning of the subject is the signal that the answer must be tonally adjusted. If 5 does not appear at or near the beginning of the subject, no adjustment is necessary. The answer will be an exact transposition of the subject a fifth higher. In that case, we speak of a real answer.

Any subject that begins on scale degree 5, or features 5 prominently near the beginning, will result in a tonal answer, because 5 must be adjusted in the transposition to begin a fourth higher, on scale degree 1, rather than on 2. Following the adjustment, the notes of the answer are fifth transpositions of the subject. A real answer will occur when scale degree 5 does not appear prominently near the subject's beginning.

We can perhaps understand now why fugue subjects do not start on scale degree 3. The answer would have to begin on 7 (leading tone), a fifth higher than 3, and that is impossible because tonic harmony prevails as the answer begins, dovetailed as it is with the end of the subject.

1. All references are to volume 1 of Bach's Well-tempered Clavier.

2. Considering WTC 1 and 2 together, 60% of subjects begin on 1, 30% on 5, 5% on other degrees: one subject on 2, the other on 7). 29% of all the fugues end on 1, 50% on 3, 12.5% on 5, and 8% on 7.

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