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The paper that the notebook is based on goes in fascinating encyclopaedic detail, with the math and music theory to support the thesis. The claim in the paper i
by lioeters 4y ago
The paper that the notebook is based on goes in fascinating encyclopaedic detail, with the math and music theory to support the thesis. The claim in the paper is closer to yours, that some of the most popular rhyhms in music cultures around the world are Euclidean patterns.
> 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.
G. T. Toussaint, The Euclidean algorithm generates traditional musical rhythms, Proceedings of BRIDGES: Mathematical Connections in Art, Music, and Science - http://cgm.cs.mcgill.ca/~godfried/publications/banff-extended.pdf http://cgm.cs.mcgill.ca/~godfried/publications/banff-extende...
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The author published a book titled The Geometry of Musical Rhythm, one of whose chapters is based on the paper.
https://en.wikipedia.org/wiki/The_Geometry_of_Musical_Rhythm https://en.wikipedia.org/wiki/The_Geometry_of_Musical_Rhythm