The following problem is considered by Bjorklund, in connection with the operation of certain components (such as high voltage power supplies) of spallation neutron source (SNS) accelerators used in nuclear physics.
Construct a binary sequence of n bits with k one’s, such that the k one’s are distributed as evenly as possible among the zero’s. For example, if n = 16 and k = 4, the solution is [1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0]. The problem of primary interest is when k and n are relatively prime numbers, i.e., when k and n are evenly divisible only by 1.
This is an excerpt from the somewhat melodramatically titled paper, The Euclidean Algorithm Generates Traditional Musical Rhythms. In short, sequences generated by the equal spacing algorithm described resemble various traditional rhythms, or otherwise sound pretty good. Create Digital Music did a post on various musical applications of it recently, like this neat little sequencer in flash.
Being a SuperCollider chauvinist I was happy to see Fredrik Olofsson had already written a pattern class to generate these sequences. It didn’t support embedding of patterns within it (which is what I really wanted to play with) but after a quick email to the list he patched it. Thanks Fredrik.
Anyway, here is a quick demo, with code after the jump.