Euclidean Rhythm

Tuesday, January 20, 2009 | |



I was watching a video from 25c3, a hacker convention in Berlin, and one of the speakers was talking about custom MIDI controllers which is interesting in itself but then he mentioned "Euclidean Rhythms"

Yea, my thoughts to, so I found the paper he was talking about it's here.

Here is the abstract from the paper:
"The Euclidean algorithm (which comes down to us from Euclid’s Elements) computes the greatest common divisor of two given integers. It is shown here that the structure of the Euclidean algorithm may be used to automatically generate, very efficiently, a large family of rhythms used as timelines (rhythmic ostinatos), in traditional world music. These rhythms, here dubbed Euclidean rhythms, have the property that their onset patterns are distributed as evenly as possible in a mathematically precise sense, and optimal manner. Euclidean rhythms are closely related to the family of Aksak rhythms studied by ethnomusicologists, and occur in a wide variety of other disciplines as well. For example they characterize algorithms for drawing digital straight lines in computer graphics, as well as algorithms for calculating leap years in calendar design. Euclidean rhythms also find application in nuclear physics accelerators and in computer science, and are closely related to several families of words and sequences of interest in the study of the combinatorics of words, such as mechanical words, Sturmian words, two-distance sequences, and Euclidean strings, to which the Euclidean rhythms are compared."

Wessen who was giving the speech has a blog post about it here, listening examples included.

and the video from 25c3 is here, Wessen's talk about Euclidean Rhythm starts about half way through.

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