Imitation and canon

One of the oldest ways to make two voices sound both independent and related is this: one voice presents an idea, and another repeats it a little later while the first carries on. That is imitation.

Leader and follower

In imitation, a musical idea is stated by one voice, or group of voices, and repeated by another. The stating voice is called the dux, Latin for leader; the imitating one is the comes, follower (Blatter 2007, part 5, art. 4). Imitation is not restricted to polyphonic music, but by its very nature it creates a contrapuntal texture.

An imitation at the octave, two bars later. The leader:

Hear the passage

The follower, an octave lower:

Hear the passage

Two measurements describe an imitation: the pitch interval between the voices and the time interval between the entries. Here, an octave and two bars. The moment the imitation begins, on the first beat of the third bar, is the point of imitation (Blatter 2007, part 5, art. 4).

Imitation need not be strict. When the follower repeats the leader only in part, or with changes, it is free imitation (Blatter 2007, part 5, art. 4).

The canon

When one voice presents an extended melodic idea and another imitates all of it while the first continues, there is a canon. In a canon the pitch and rhythmic relationships between the voices are precisely defined, and the word means exactly that: a list of rules (Blatter 2007, part 5, art. 4).

Many old canons were not written out in full. Only the leader was notated, and the rule for producing the follower was given in words or in code. Sometimes the rule was a puzzle the performers had to solve, and the result was called a riddle canon (Blatter 2007, part 5, art. 4).

Kinds of canon

Canons are described by the time interval between entries, the pitch interval, and the rule that turns the leader into the follower (Blatter 2007, part 5, art. 4).

The round. The most familiar canon: one melody imitated, usually three or four times, at the unison or octave, with entries always the same distance apart. Once everyone has come in, the first voice can start again. That is why the round is called an infinite canon. Every round is a canon, but not every canon is a round (Blatter 2007, part 5, art. 4). "Frère Jacques" and "Row, Row, Row Your Boat" are rounds.

Canon at another interval. The follower begins a fifth, a third or another interval above or below the leader, regardless of octave (Blatter 2007, part 5, art. 4).

Mirror canon. The follower is the inversion of the leader: where one rises, the other falls (Blatter 2007, part 5, art. 4).

Crab canon, or cancrizans. The follower is the leader backwards, the retrograde. Sometimes the music is read by two players sitting opposite each other, each starting from their own side of the same sheet (Blatter 2007, part 5, art. 4).

Mensuration canon. The voices start together, but each has the notes in different durations, in a set proportion: one sings the melody in augmentation, another in the original values (Blatter 2007, part 5, art. 4).

Crab and mirror canons are finite canons, made to end rather than to start over (Blatter 2007, part 5, art. 4). All of them apply the techniques of melodic manipulation to counterpoint: transposition, inversion, retrograde, augmentation.

How to write a round

Blatter notes that rounds are fun to sing and fairly easy to compose, and gives the procedure (Blatter 2007, part 5, art. 4):

1. write the first line, the leader's music from the beginning up to the second voice's entry;
2. on a staff below, write a simple counterpoint that works with the first line;
3. on a third staff, write another line that works with the first two. You now have a three-part round;
4. for four parts, write a fourth line that works with the other three.

Joined one after another, the lines make the round's melody, and numbers over the staff show where each group comes in. The secret is the order: each new line is written to sound right with all the earlier ones, because that is exactly how it will sound once the groups overlap.

Invertible counterpoint

Bach's inventions, two-part keyboard pieces, and his sinfonias, in three parts, have been counterpoint models in teaching since the Baroque. The name comes from a property they all share: invertible counterpoint (Blatter 2007, part 5, art. 4).

Invertible counterpoint means that two lines written one above the other can later swap places, the lower one moving on top, and the counterpoint still works (Blatter 2007, part 5, art. 4). Two lines in thirds:

Hear the passage

The same lines swapped, the upper one an octave lower and the lower one an octave higher:

Hear the passage

Inverted at the octave, thirds become sixths, and sixths are still consonant. The care goes into fifths: a perfect fifth inverted becomes a perfect fourth, which in counterpoint is dissonant and has to be treated as such (Blatter 2007, part 5, art. 4). In the inventions two motives are presented, change hands and keys as the piece goes on, and invertible counterpoint is what makes that exchange possible.

What comes next

The form in which imitation reaches its highest degree of organisation is the fugue: a theme entering voice by voice, always answered, and developed with every technique of counterpoint.