The Euclidean Algorithm Generates Traditional Musical Rhythms

@inproceedings{Toussaint2005TheEA,
  title={The Euclidean Algorithm Generates Traditional Musical Rhythms},
  author={Godfried T. Toussaint},
  year={2005}
}
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… CONTINUE READING
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