Fugue: subject, real answer and tonal answer

The fugue in one sentence

The fugue is a contrapuntal composition in which a theme, the subject, enters successively in all the voices (usually 2–5) and is then developed in different keys. More than a fixed form it is a procedure: what is mandatory is the opening exposition with the alternating entries of subject and answer.

The subject

• Typical length: 1 to 4 bars.
• It has a recognizable profile: a characteristic opening (the "head") and a more flowing continuation (the "tail"), often with repeated notes, characteristic leaps or chromaticism.
• It defines the key: it usually starts on the tonic or the dominant and ends on the tonic, the third or the dominant.
• It may modulate to the dominant (modulating subject).
• A memorable example: the subject of the Fugue in C minor BWV 847 (The Well-Tempered Clavier I), two bars with repeated notes and leaps that make it almost speech-like.

The answer

The second voice enters with the subject transposed to the dominant (a fifth above or a fourth below): this is the answer. It has two varieties.

Real answer: exact transposition at the fifth. It is used when the subject does not emphasize the dominant at the beginning and does not modulate.

Tonal answer: some notes are modified in order to stay in the main key. The classical rules:

• A dominant appearing in the head of the subject (especially at the beginning) is answered with the tonic, and conversely the initial tonic with the dominant. In practice the subject's leap 1→5 becomes 5→1 in the answer (not 5→2).
• If the subject modulates to the dominant, the answer must modulate back to the tonic (not to the dominant of the dominant).
• The correction affects only the head or the point of modulation; the rest is transposed at the fifth.

Example in C major

Subject: C–G–A–G–F–E–D–C (begins with the leap tonic→dominant).

• Real answer: G–D–E–D–C–B–A–G → the second note D (second degree) sounds like an opening toward D, away from the tonal center.
• Tonal answer: G–C–D–C–B–A–G... that is, the leap 1→5 becomes 5→1 (G→C); the rest of the answer follows the transposition at the fifth. The result keeps the key of C anchored.

The exposition

1. Voice 1: subject in the tonic.
2. Voice 2: answer (at the dominant); meanwhile voice 1 plays the countersubject or a free counterpoint.
3. Possibly a codetta (short bridge) to return to the tonic.
4. Voice 3: subject in the tonic; voice 4: answer. And so on.
5. The exposition ends when all the voices have presented the theme; a counter-exposition may follow (a new series of entries, often in a different order).

Typical order of voices in a four-voice fugue: alto–soprano–bass–tenor or tenor–alto–soprano–bass; in BWV 847 (three voices) alto, soprano, bass.

Common mistakes

• Answering in a real way a subject that begins 5→1 or that modulates: the fugue slips toward the second degree.
• A subject that is too long or without profile: the later entries cannot be heard.
• Forgetting that the voice that has finished the subject must continue with something interesting (countersubject).

Exercise

1. Write three 2-bar subjects in A minor: one that starts from 1, one from 5, one that modulates to E minor.
2. For each one write the real answer and the tonal answer and play them over a tonic pedal: hear which one "stays home".
3. Build a three-voice exposition with the best subject, assigning a different sound to each voice (for example three channels of Piano V with different panning) to follow the entries.

Related topics

Fugue: countersubject and episodes, Fugue: stretto, pedal and devices, Fugue: formal plan, Canon and imitation, Invertible counterpoint.