Saturday, January 17, 2009

Harmonic control again

Looking at Bach's canon #9 from the Fourteen Canons on the Goldberg Ground, I started to think about harmonic control again.

Bach takes the Goldberg bass line and, above it, writes a canon at the unison with a time interval of one 16th note. In order to accommodate the harmonies, the last 16th of the dux (leader) becomes extremely significant. This pitch will not only be the last note of the "present" harmony but a split second later it will be the first pitch of the "next" harmony in the comes (follower).

In my analysis of the contrapuntal techniques in this canon, you can see how Bach handled this. When the two adjacent chords have a tone in common, that tone is used as the last note of the dux (and first of the comes). When there is no common tone Bach must use either a non-harmonic tone or a rest -- both of which he does, one time each.

(click on the image to enlarge)

You may also want to look back to my discussion of Bach's F major Invention on
January 4 (The Gift of Plurisignificance) for other ideas about controlling the chord progressions in canons.

For my canon, I used this same technique. For a harmonic progression, I chose a complete diatonic circle of 5ths in D minor. (i - iv6 - VII - III6 - VI - ii┬║6/5 - V7 - i) Since diatonic chords a 5th apart have common tones, I simply chose that common tone to be the last note of the measure for the dux each time. My time interval is an 8th note.

This one was fun to write. I may do a few more of this kind before moving on to other ideas.

(click on the image to enlarge)

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