The context
After the species, Fux teaches imitation and fugue in the old vocal style, in two, three and four voices, using the six modes. It is a different type of fugue from Bach's tonal one: there is no plan of modulations, the entries stay on the finalis and its fifth, and the writing follows the rules of the species (in particular fifth species).
The division of the octave
Every authentic mode divides into a lower fifth and an upper fourth:
| Mode | Fifth | Fourth |
|---|---|---|
| Dorian | D–A | A–D |
| Phrygian | E–B | B–E |
| Lydian | F–C | C–F |
| Mixolydian | G–D | D–G |
| Aeolian | A–E | E–A |
| Ionian | C–G | G–C |
The principle of the modal answer is that what the subject sings in the fifth, the answer sings in the fourth, and vice versa. In this way subject and answer stay within the same modal octave and the mode does not change.
Example in D Dorian
- Subject: D4 A4 G4 F4 E4 D4 (descends from the fifth to the finalis).
- Modal answer: A4 D5 C5 B4 A4 (or with Bb4). The leap D–A (a fifth) becomes A–D (a fourth); the subject's descending fifth A–D becomes a descending fourth D–A in the answer, with one note fewer. The answer ends on the reciting tone (A) and leaves room for the third entry on the finalis.
- Third entry (in three voices): D again, an octave below or above the subject.
The Phrygian case
In Phrygian the fifth E–B touches B, which forms a tritone with F and is not the reciting tone (which is C). For this reason in Phrygian polyphony imitations often occur at the fourth (E–A) instead of the fifth, and modal theory admits irregular answers to preserve the character of the mode.
Fux's rules for fugue
- The entries alternate between the finalis and the fifth (or fourth) of the mode.
- The second voice enters when the first has finished the subject, or earlier (close fugue, already present in the vocal style).
- The voice that has finished continues in free counterpoint of fifth species; there is no fixed countersubject.
- After the exposition there may be new entries, even in stretto, and a cadence on the finalis.
- Intermediate cadences are made on the principal notes of the mode (finalis, fifth, sometimes third).
Why study it today
- It is the link between Renaissance imitation and tonal fugue: it explains why the tonal answer exists.
- It teaches you to write fugues with limited means: no modulations, only counterpoint.
- It prepares you for writing motets and ricercars.
Typical mistakes
- Answering the Dorian subject at the exact fifth (A E D C B A): the answer touches E and B as structural notes and the mode shifts toward an Aeolian on A.
- Treating the modal fugue as a tonal fugue with modulations to the dominant.
- Using accidentals not justified by musica ficta.
Modern application
- Scores for historical settings: a modal fugue in Dorian or Mixolydian, with a modal answer, gives a credible archaic sound without Baroque tonal effects.
- Choirs: fugatos in the old style for a cappella choir are among the easiest to sing: long note values, few accidentals, entries on the finalis and the fifth.
- Fantasy video game music: the shift from fifth to fourth in the answer keeps the melody within the same scale, which is useful for modal loops without tonal cadences.
Related topics
Church modes, tonal answer and mutation, imitation, mass and motet, history of fugue theory.