A canon is a polyphonic work in which a single melodic line is followed strictly by one or more voices at a fixed time interval. From 'Row Your Boat' to Bach's Goldberg Variations to Steve Reich, canon is one of music's most durable structures.
What a Canon Is
A canon is a contrapuntal form in which a single voice — the dux (leader) — is imitated strictly by another voice — the comes (follower) — at a fixed time interval (the stretto interval) and often also at a fixed pitch interval. The dux begins; after a specified number of beats, the comes enters with the identical melody. Both continue simultaneously: the comes follows the dux exactly, while the dux has moved ahead to new material that must harmonise with the comes's restatement of the earlier material. A canon may have only two voices (the simplest case) or many — Tallis's Spem in alium, by contrast, is imitative rather than canonic, with 40 vocal lines organised into eight choirs of five voices each.
The compositional challenge of canon is severe: every note you write as the dux will become the comes material, and must harmonise with whatever the dux is playing at that point. Writing a canon is essentially writing invertible counterpoint at the temporal scale of the whole piece — every bar of the dux must work against itself delayed by the stretto interval. The composer is constantly looking ahead and looking back simultaneously, ensuring that what they are writing now will harmonise with what they wrote a few measures ago when it reappears in the comes voice.
Types of Canon
Canons are classified by the pitch interval and rhythmic transformation between dux and comes:
- Canon at the unison (or octave): the comes imitates at the same pitch level (or an octave displaced). This is the strictest and purest form. "Row, Row, Row Your Boat" and "Frère Jacques" are familiar examples.
- Canon at the fifth (or fourth): the comes imitates a fifth higher (or fourth lower), requiring modal transposition and careful attention to leading tones. This is the same interval relationship as a fugal answer.
- Canon at other intervals (second, third, sixth, seventh): each interval creates its own constraints on harmonic possibilities. Bach's Goldberg Variations include canons at every pitch interval from unison to ninth.
- Retrograde canon (crab canon, or canon cancrizans): the comes plays the dux melody backward. Bach's Musical Offering includes a famous crab canon.
- Inversion canon: the comes inverts every interval of the dux (what went up now goes down). The Art of Fugue contains multiple mirror canons of this type.
- Augmentation canon: the comes imitates at double the note values (twice as slow). The result is a canon in which the comes seems to lag dramatically behind the dux, with the harmonic relationships changing over a longer span.
- Diminution canon: the comes imitates at half the note values (twice as fast). The comes overtakes the dux mid-piece.
The Goldberg Variations as a Canonic Encyclopaedia
Bach's Goldberg Variations (BWV 988, 1741) include a canon at every third variation: Variation 3 is a canon at the unison; Variation 6 at the second; Variation 9 at the third; Variation 12 at the fourth; Variation 15 at the fifth; Variation 18 at the sixth; Variation 21 at the seventh; Variation 24 at the octave; and Variation 27 at the ninth — nine canons in total, each at a different pitch interval and each maintaining the same harmonic ground bass of the aria.
The Canone alla Seconda (Variation 6) is particularly beautiful and is a good study subject: the comes enters a second above the dux, one bar later, and the two voices weave together over the bass line. The challenge is enormous — each note must work simultaneously as part of the dux melody and as the future comes material, all within the harmonic constraints of the variation's bass. Bach makes it sound effortless.
Cadencing a Canon
One of the technical difficulties of canon is ending it. Since the comes follows the dux at a fixed delay, the comes is always behind by the stretto interval — when the dux finishes, the comes still has material to play. There are three standard solutions: (1) the dux stops, holding a final note, while the comes completes its imitation independently; (2) both voices arrive at a common cadential figure simultaneously, with the comes catching up through an asymmetric closing phrase; (3) the canon is "free at the end" — the strict imitation is abandoned in the final measures so that both voices can cadence together. Bach uses all three solutions in different canons.
Canon in Popular Music and Contemporary Composition
Canon is not exclusively a Baroque or Renaissance form. Pachelbel's Canon in D (c. 1680-1690) became one of the most recognisable pieces in Western music and introduced canon to popular culture; it is a three-voice canon at the unison over a repeating bass. The Beach Boys' "God Only Knows" uses canonic vocal layering. Steve Reich's minimalist compositions — Violin Phase (1967), Clapping Music (1972), Piano Phase (1967) — are canons at the rhythmic rather than the pitch level: the same pattern is imitated at slightly different time intervals, creating phasing patterns in which the resultant rhythm changes continuously.
Imogen Heap uses vocal layering techniques that amount to vocal canons in a contemporary pop context. Jacob Collier's vocal arrangements include strict canons at unusual intervals (such as a third or a sixth) layered with extended jazz harmony. Caroline Shaw's Partita for 8 Voices (2009-2011, Pulitzer Prize 2013) includes canonic passages drawing on Renaissance and Baroque techniques applied to a 21st-century musical language.
Writing a Simple Canon
To write a two-voice canon at the octave (the simplest type): decide on the stretto interval (typically 2-4 beats). Write the first 4 beats of the dux melody. Now the comes enters with those same 4 beats while the dux continues. Continue the dux for another 4 beats, ensuring that this new material harmonises with the comes's restatement of the original 4 beats. Then the comes restates these new 4 beats while the dux continues again. Continue this process throughout the piece. The challenge is that you cannot write the dux without thinking ahead about how each note will function as comes material later.
Sources and Further Reading
- Gauldin. A Practical Approach to 18th-Century Counterpoint. Waveland Press. Chapter on Canon.
- Kennan. Counterpoint. Prentice-Hall.
- Open Music Theory — Canon and Imitation (openmusictheory.net, CC BY-SA 4.0).
- IMSLP — All Bach Goldberg Variations canons, free score (imslp.org).