The Canon & The Round

Strict Two-Part Canons

A canon is the result of constant application of imitation between the voices.  If the following part (comes) is an exact transposition of the leading part (dux), it is a strict canon. There are two constant factors between the parts.  The first is size of the interval between the parts, and the second is the duration in time between them.

The most common and straightforward is a canon at the octave.  The duration between the parts is typically a measure or two, but that is variable from a single beat to several measures.  There are other more complex types of canons.  In a crab canon (cancrizans), or retrograde canon, the comes repeats the dux backwards.  In a canon in inversion the comes duplicates each interval of the dux with the direction of the interval reversed. In a canon in augmentation, the rhythmic values of the comes are proportionally longer that those of the dux.  In a canon in diminution, the rhythmic values of the comes are proportionally shorter that those of the dux.  In both cases, the proportion between the note values is typically doubled or halved.

Procedures for Writing a Strict Canon at the Octave

  1. Write the first part (dux), only as far as the distance between it and the second part (comes), a measure or two.
  2. Copy this much into the second part immediately at the octave.
  3. Write new counterpoint in the first part to accompany the notes entered in the second part, using primarily 3rds and 6ths between the voices. Follow the guidelines for tonal counterpoint, avoiding dissonances on strong beats and parallel 8ves and 5ths.
  4. Copy this new counterpoint into the second part.
  5. Repeat steps 3 and 4 (leap-frogging) until you have reached the end of the piece.
  6. Be mindful of the harmonic progressions you are implying with your choice of notes as you write each new counterpoint, and create strong forward movement. You may wish to modulate for tonal variety.
  7. Abandon the strict imitation at the end to create a strong final cadence.

As you compose the counterpoint you may need to edit the opening phrase if the scale degrees you chose do not yield a strong progression.  Analyze each measure harmonically with the goal of creating intentional movement between dominant and tonic functions at points of arrival.

Write the number of each interval between the pitches as you notate them to avoid undesirable dissonances.  The use of some non-chord tones will lend interest, such as accented passing tones and suspensions.

Even in a brief example, too much reliance on the same pitches and motives will yield a static result.  For this reason, a modulation or change of mode is a good way to introduce some variety, as is the incorporation of new rhythmic motives and some syncopation.  In general, short note values against longer ones and the use of rests will create a more interesting texture.

It is recommended that students use a keyboard to improvise musical ideas, composing with a pencil and paper to draft this assignment, rather than entering pitches directly into a computer.  Your creativity and aural imagination will be developed through this process.

Accompanied Canons and the Goldberg Variations

In an accompanied canon one or more voices are added in free counterpoint.  Each of the canons in Bach’s Aria mit dreissig Veranderungen, known as the Goldberg Variations, is an accompanied canon.  The 30 variations consist of ten groups of three pieces.  Each group includes a character piece, a toccata, and a canon.  The interval distance between the voices in each canon equals the number of the variation divided by three.  For example, Variation 9 is a canon at the 3rd, and variation 21 is a canon at the 7th.  The two upper voices are accompanied by a bass part in all but the canon at the 9th, Variation 27.  Variations 12 and 15 are canons in inversion.  The harmonic plan followed roughly by every variation is taken from the Aria, upon which it is all based.  Several of the canons from this masterpiece are included in the Materials.  Analysis of these pieces may lead to an increased appreciation for Bach’s ability to express beautiful melodic ideas within the confines of a strict canon.

The Round

A round is a type of canon that consists of a series of phrases.  Each part begins at a different point, but sings the same material at the octave or unison.  There are typically two, three, or four points of imitation.  The chord progressions are closely controlled so that each overlapping section matches the others harmonically.  It is also referred to as a perpetual canon, since it can be repeated endlessly.  Familiar examples of rounds are Row, Row, Row Your Boat and Freres Jaques. Another well-known round is Dona Nobis Pacem, attributed to Mozart.

Hansen:  Canon Example II   (PDF)

Bach:  Goldberg Variations, Aria   (PDF

Bach:  Goldberg Variations, Variation #6, Canon at the 2nd   (PDF)

Bach:  Goldberg Variations, Variation #12, Canon at the 4th (Inverted)   (PDF

Bach:  Goldberg Variations, Variation #18, Canon at the 6th   (PDF

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