The problem
The answer repeats the subject a fifth higher (or a fourth lower), that is, in the key of the dominant. If the answer transposed every note exactly (real answer), a subject that touches the dominant right away would take the answer to scale degree 2, moving too far from the home key. The tonal answer corrects this: some notes are modified, and the point where the answer passes from the tonic area to the dominant area is called the mutation.
The basic rule
In the opening zone of the subject:
- the tonic of the subject is answered by the dominant;
- the dominant of the subject is answered by the tonic (not by scale degree 2).
After the point of mutation the answer continues exactly a fifth away, in the key of the dominant. In terms of the divided octave: the part of the subject that lies within the fifth 1–5 is answered in the fourth 5–8, and vice versa.
Examples
The Art of Fugue (D minor)
- Subject: D A F D C# D E F…
- Tonal answer: A D C A G# A B C…
The opening leap of a fifth D–A becomes the leap of a fourth A–D: the dominant A of the subject is answered by the tonic D. From there on the answer is at the fifth (F→C, D→A, C#→G#).
Teaching example in C major
- Subject: G4 C5 D5 E5 D5 C5 B4 C5 (begins on the dominant).
- Real answer (wrong in this case): D5 G5 A5 B5 A5 G5 F#5 G5. The opening D sounds like a functionless scale degree 2.
- Tonal answer: C5 G5 A5 B5 A5 G5 F#5 G5. The first note is mutated (the dominant G is answered by the tonic C); the opening leap of a fourth becomes a fifth.
When a tonal answer is needed
- The subject begins on the dominant.
- The subject touches the dominant in its first notes in a strong position (leap 1–5 or 5–1).
- The subject modulates to the dominant: the answer must modulate back, from the dominant to the tonic, otherwise it would end up on the dominant of the dominant.
If the subject moves by step around the tonic without emphasizing the dominant, the real answer is enough (example: Fugue in C major BWV 846 from The Well-Tempered Clavier I).
Where to put the mutation
- As early as possible, usually on the first note or the first two notes.
- At a point where the change does not distort the head: it is better to change a leap (fourth ↔ fifth) than a stepwise motion.
- If the subject modulates, the mutation falls at the point where the subject passes to the dominant, and the answer compensates in the opposite direction.
In the tradition
- Fux reasons in terms of the modes: the answer exchanges the species of fifth with the species of fourth of the mode (in Dorian, D–A becomes A–D).
- Marpurg codifies the distinction between real fugue and tonal fugue on the model of Bach.
- Padre Martini and the Italian school distinguish the fugue of the key (tonal) from the real fugue.
- Cherubini and Gedalge turn it into precise rules for the school fugue, with tables of cases.
Typical mistakes
- Using the real answer for a subject that begins on the dominant: the second entry sounds out of key.
- Mutating too many notes: the answer becomes a different theme.
- Mutating a note in the head so that it becomes unrecognizable (for example, turning a stepwise motion into a leap).
- Forgetting the compensation in a modulating subject.
Modern application
- Film and video game scores: when a theme passes from one section to another in imitation, the logic of the tonal answer keeps the second entry from sounding in another key: just answer the dominant with the tonic in the head of the motif.
- Pop: in instrumental answers to a vocal phrase (a riff answering the voice) the same device keeps the song anchored on the tonic.
- Choirs: in choral fugatos the tonal answer lets altos and basses stay in a comfortable register.
Related topics
Fugue: subject and answer, fugue in the modes, exposition, church modes, The Art of Fugue.