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Monday, June 14, 2004

Nesting Instinct

I started writing some 4-part counterpoint as an exercise. (See it here in a pdf file.) I stumbled across a contrapuntal technique I'm geeked about. The example shows the first two voices entering, with the tenor imitating the bass at a 30-beat interval. Now look carefully at the two sections outlined in the fourth measure: the bass is imitating the tenor at a 3-beat interval. This happens while the tenor is imitating the bass -- in other words, the counterpoint is nested. Now, I am under no illusion that I have invented this. But I don't recall anything like this being taught in any counterpoint text I've seen, and I don't recall noticing it in any music. OTOH it wouldn't always jump out at you where it did occur. I would love to know if other examples exist. Naturally there is no theoretical limit to the number of times the nesting occurs. In this case it was easy to do because the temporal intervals involved are different in scale, by a factor of 10 (30 versus 3). If the intervals were very close (say 6 versus 3), it might work but not be recognizable as such; it would probably start sounding like the same few notes repeated several times. I'd like to take a crack at several nested levels. No promises how soon I do it. I'd be pretty happy if I could just learn to write counterpoint as good as Dmitri Shostakovich.

1 Comments:

Blogger HuaiMao said...

Cool! You've discovered fractal counterpoint. Now calculate the Hausdorff-Besicovitch dimension of your exercise.

For extra credit, determine how adding Hocket to your exercise will render your exercise's melodic structure discontinuous. Can you still determine a harmonic metric using Lebesgue measure theory?

For discussion: Consider extending your counterpoint to the complex domain. Now consider a closed path in a 3-part invention - is it always a round?

12:18 PM  

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