Definition
The canon is strict imitation carried all the way through: the answer repeats the whole subject. Zarlino calls it fuga legata; from the seventeenth century the term canon indicates the rule itself that allows the second voice to be derived from the first.
Classification
| Type | Rule | Example |
|---|---|---|
| At the unison (rota, round) | same pitch, delayed entry | Fra Martino |
| At the octave | an octave below or above | The Art of Fugue, Canon alla ottava |
| At other intervals | at the second, third, fourth, fifth… | Goldberg Variations, a canon every three variations |
| By contrary motion (inversus) | inverted answer | Goldberg 12 and 15 |
| Retrograde (cancrizans) | answer read from right to left | The Musical Offering, Canon a 2 cancrizans |
| By augmentation or diminution | values doubled or halved | The Art of Fugue, canon per augmentationem in contrario motu |
| Perpetual (infinite) | the end connects back to the beginning | rounds, tavern canons |
| Spiral (per tonos) | each cycle modulates up a whole tone | The Musical Offering |
| Enigmatic | only one voice is written, with a riddle about the rule | canons by Bach and the Flemish composers |
| Mensuration | same notes, different speeds | Ockeghem, Missa prolationum |
| Accompanied | canon between two voices, other voices free | Goldberg, many canons with basso continuo |
The Goldberg Variations
Every third variation is a two-voice canon over a free bass, with a growing interval: variation 3 at the unison, 6 at the second, 9 at the third, 12 at the fourth (by contrary motion), 15 at the fifth (by contrary motion), 18 at the sixth, 21 at the seventh, 24 at the octave, 27 at the ninth (without bass). Variation 30 is a quodlibet.
Fra Martino: analysis of a canon at the unison
In C: C D E C | C D E C | E F G | E F G | G A G F E C | G A G F E C | C G C | C G C. The voices enter two bars apart. It works because every two-bar phrase is built on the notes of the C chord (with passing notes): any overlap produces C E G with passing tones. This is the principle of all perpetual canons on a single chord.
How to write a canon at the octave with a one-bar distance
- Write the first bar of the subject.
- Copy it an octave lower in bar 2 of the second voice.
- Write bar 2 of the subject as a counterpoint to the copy: it must be correct against the transposed bar 1.
- Copy bar 2 into bar 3 of the second voice and repeat.
- Close with a free coda or a cadence in which the answer ends with a long note.
Every new bar of the subject is a species exercise against the previous bar.
Verified example
Subject in half notes: C5 G4 | A4 B4 | C5 D5 | C5. Answer at the lower octave, entering after one bar: C4 G3 | A3 B3 | C4… The intervals that form are sixth, tenth, third, third, octave: all consonant, with no parallels.
Typical errors
- Subject too rich: beyond a certain point every added note creates problems.
- Forgetting the ending: a canon without a coda breaks off abruptly.
- Canons at intervals other than the octave without checking the accidentals.
Modern application
- Pop: the canon at the unison between voice and choir (same phrase offset by one bar) is a classic of finales; live it is done with a loop station.
- Minimalist music: Steve Reich and Arvo Pärt use mensuration canons and phasing canons: the voices repeat the same phrase at different speeds.
- Soundtracks: a canon by augmentation (the theme in the violins and the same theme in doubled values in the horns) gives grandeur without new material.
- Choirs: rounds are the quickest way to get an inexperienced group singing in several voices.
Related topics
Canon and imitation, imitation, counterpoint by contrary motion, Pachelbel progression, The Art of Fugue.