Wednesday, January 21, 2009


There is an odd little canon by J.S. Bach called Trias Harmonica (The Harmonic Triad) which was transmitted to us by F.W. Marpurg in his Abhandlung von der Fuge (1753).

In its written form, it has eight pitches -- a C major scale that ascends stepwise from C to G and back. The dotted rhythm makes it obvious that the Ds and Fs are simply passing tones. We are told that this is an "eight-part canon in contrary motion." Typical of a puzzle canon, this is all we get.

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Now to the nuts and bolts: A very little thought reveals the solution. There are eight beats to the theme and the chord tones are articulated on every other beat. If we add three entrances of simple canon at the time interval of a half note and, beginning on G, add the four contrary-motion voices on the even numbered beats, we get the full canon.

The result is a C major chord that is constantly in motion with passing tones occurring in unaccented positions between the beats.

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A work of genius? it is a clear demonstration of some basic principles of counterpoint and Bach's ability to condense his musical gestures.

I've chosen a different type of chord for my canon -- a four note chord of stacked perfect fourths. This is not an 18th century chord. Its most frequent use came in the twentieth century. You'll find this sonority in works by composers as diverse as Paul Hindemith, Charles Ives, Arnold Schönberg, and McCoy Tyner (that's right, the great jazz pianist -- 4th chords are common in some types of jazz and popular music too).

(Click on image to enlarge)

My example is structurally simpler than Bach's. I set mine in 9/8 time, two measures, with the chord tones falling on each of the six beats. The intervening notes are not traditional passing tones which would need to be approached and let by step. Rather, these tones are approached by step and left by leap, when ascending and the opposite when descending This enables me to have another chord of perfect fourths in the unaccented position. In this manner, I'm able to maintain a consistent harmonic language.

The solution is in six voices at the unison.
(Click on image to enlarge)

Ezra Pound once wrote "dichtung=condensare" ("poetry is to condense")

I'm certainly not saying that this canon is poetic. I'm just practicing my condensation.

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