27 Jan '20

Euclidean rhythms in Extempore

As part of the new Extempore pattern language stuff I added a helper for generating euclidean rhythms. I wrote it (in a recursive style) in Scheme using the algorithm described in Godfried Toussaint’s paper (although it’s credited to Bjorklund).

As well as the obvious musical possibilities, one of the things I noticed when I was playing around that if one loops through euclidean rhythms of increasing “density” the visual representation exhibits some cool patterns as well. Here’s an example of the 17 different rhythms of length 16 (from 0 to 16 inclusive). We can print out the patterns using this loop (using 'X for the “hit” marker so that it looks more prominent in a log view).

(dotimes (i 17)
  (println (euclid i 16 'X)))

What gets printed to the log is:

(_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _)
(X _ _ _ _ _ _ _ _ _ _ _ _ _ _ _)
(X _ _ _ _ _ _ _ X _ _ _ _ _ _ _)
(X _ _ _ _ _ X _ _ _ _ X _ _ _ _)
(X _ _ _ X _ _ _ X _ _ _ X _ _ _)
(X _ _ _ X _ _ X _ _ X _ _ X _ _)
(X _ _ X _ X _ _ X _ _ X _ X _ _)
(X _ _ X _ X _ X _ X _ _ X _ X _)
(X _ X _ X _ X _ X _ X _ X _ X _)
(X _ X X _ X _ X _ X _ X X _ X _)
(X _ X X _ X _ X X _ X X _ X _ X)
(X _ X X X _ X X _ X X _ X X _ X)
(X _ X X X _ X X X _ X X X _ X X)
(X _ X X X X X _ X X X X _ X X X)
(X _ X X X X X X X _ X X X X X X)
(X _ X X X X X X X X X X X X X X)
(X X X X X X X X X X X X X X X X)

Look, there’s probably some super-cool mathematical explanation for why this looks like that. Stephen Wolfram, if you’re reading, drop me a line and tell me what it is. But I just thought it looked cool—I’m sure there are generative art possibilities here as well (they may have already been explored).