[seqfan] XronoMorph - Overlaid polygons and music

Charles Greathouse charles.greathouse at case.edu
Tue Jul 19 06:33:01 CEST 2016


I found an interesting article:
http://theconversation.com/how-a-little-mathematics-can-help-create-some-beautiful-music-61812

It discusses music generated from fairly simple mathematical structures:
(small) subsets of the vertices of a polygon. Each subset is displayed as a
polygon of a different color.

>From the article: "There are more than 17 trillion different rhythms, and
that is only counting rhythms with three levels where every beat occurs at
one of 16 distinct time locations (16 being a very common temporal
subdivision in music)."

I'm trying to figure out how this number is computed. I've tried a few
different ways but none are close enough. binomial(2^16, 3) is too big, but
reducing it by circular shift makes it a bit more than 1/16th the size
which is too small. Any ideas? (I assume that by "more than 17 trillion"
they mean between 17e12 and 18e12.)

Charles Greathouse
Case Western Reserve University


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