Euclidean rhythm

The Euclidean rhythm in music was discovered by Godfried Toussaint in 2004 and is described in a 2005 paper "The Euclidean Algorithm Generates Traditional Musical Rhythms".[1] The greatest common divisor of two numbers is used rhythmically giving the number of beats and silences, generating almost all of the most important world music rhythms,[2] (except Indian).[3] The beats in the resulting rhythms are as equidistant as possible; the same results can be obtained from the Bresenham algorithm.

Other uses of Euclid's algorithm in music

In the 17th century Conrad Henfling writing to Leibniz about music theory and the tuning of musical instruments makes use of the Euclidean algorithm in his reasoning.[4]

gollark: https://discord.gg/8c2MvkqnqmWelcome, inevitable heavserver member!If you've ever wanted to join heavserver, then heavserver is the server for you!Heavserver is a Discord server with *various* things: an active and vibrant community of people who exist (with >92% confidence); several hundred bots with various useful features; frequently used and busy voice chats; advocacy permitted at any depth of recursion, as well as bitwise cyclic tag; a bridge to the APIONET IRC network, as well as many "telephone" bots; most integers (`floor(2π)` is not permitted).
gollark: If they had more memory, you could probably run a higher level spellcode interpreter on them.
gollark: CPUs would basically be "able to load multiple programs and run self modifying code", loosely defined.
gollark: I suppose if the summoning stones are ASICs, the magic circle things are FPGAs, and actual general purpose CPUs will probably come later.
gollark: Nullity.

See also

References
  1. The Euclidean algorithm generates traditional musical rhythms by G. T. Toussaint, Proceedings of BRIDGES: Mathematical Connections in Art, Music, and Science, Banff, Alberta, Canada, July 31 to August 3, 2005, pp. 47–56.
  2. Comparative Musicology – Musical Rhythm and Mathematics
  3. The Euclidean Algorithm Generates Traditional Musical Rhythms, by Godfried Toussaint, Extended version of the paper that appeared in the Proceedings of BRIDGES: Mathematical Connections in Art, Music and Science’’, Banff, Alberta, Canada, July 31–August 3, 2005, pp. 47–56.
  4. Musical pitch and Euclid's algorithm
  • G. T. Toussaint, The Euclidean algorithm generates traditional musical rhythms, Proceedings of BRIDGES: Mathematical Connections in Art, Music, and Science, Banff, Alberta, Canada, July 31 to August 3, 2005, pp. 47–56.
  • Phil Baljeu and Manuel Odendahl (Ruin & Wesen). "Generating African rhythms using the euclidean algorithm". Archived from the original on 2013-11-14.
  • Benjamin Wardhaugh (1 September 2006). "Music and Euclid's algorithm".
  • Links to videos about and a Flash app for experimenting with Euclidean rhythms
  • Euclidean rhythm demo — interactive browser-based tool for experimenting with Euclidean rhythms
  • A tutorial on The Euclidean Algorithm Generates Traditional Musical Rhythms by Derek Rivait
  • SoundHelix is a free software for algorithmic random music composition that supports Euclidean rhythms
  • Euclidian rhythms list - a list of all Euclidian rhythms E(i,2 to 32), indicating if they are Winograd-deep, Erdős-deep, Authentic Aksak, Quasi-Aksak or Pseudo-Aksak
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.