# Experiment with roots of unity

This is an experiment with roots of unity in supercollider.
I took Eulers formula

exp(2piIk/n) = cos(2pik/n)+sin(2pi*k/n)*I

to sonify sums of roots of unity where the sums run through divisors of some numbers.

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That is a neat idea, to invert the harmonic series!

hjh

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I use the divisors of a number to be played in parallel, that is as a sum of roots of unity, and then in sequence. For instance. If the number to be played is 12, then we have:
divisors = [1,2,3,4,6,12]
I play in succesion the sum of roots of unity of:
,[1,2],[1,3],[1,.2,4],[1,2,3,6],[1,2,3,4,6,12]
So this creates a variation and a little bit of repetition. I hope that makes sense what I just wrote.
In the piece above, the numbers which get played this way are 1…13.

Nice! I use this divisor harmonics technique quite frequently as well. Erkki Kurenniemi is usually credited for coming up with the concept i guess. He wrote at least a couple of papers about it. Here’s one.

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