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The '''Euclidean Rhythm''' in music was discovered by [[Godfried Toussaint]] in 2004 and is described in a 2005 paper "The [[Euclidean algorithm|Euclidean Algorithm]] Generates Traditional Musical Rhythms".<ref name="gtpdf">[http://cgm.cs.mcgill.ca/~godfried/publications/banff.pdf 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.</ref> The [[greatest common divisor]] of two numbers is used [[Rhythm|rhythmically]] giving the number of [[beat (music)|beats]] and silences, generating almost all of the most important [[World Music]] rhythms,<ref name="gtweb">[http://cgm.cs.mcgill.ca/~godfried/rhythm-and-mathematics.html Comparative Musicology - Musical Rhythm and Mathematics]</ref> (except [[India#Performing_Arts|Indian]]).<ref name="extv">The Euclidean Algorithm Generates Traditional Musical Rhythms, by Godfried Toussaint, [http://cgm.cs.mcgill.ca/~godfried/publications/banff-extended.pdf 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.</ref> |
The '''Euclidean Rhythm''' in music was discovered by [[Godfried Toussaint]] in 2004 and is described in a 2005 paper "The [[Euclidean algorithm|Euclidean Algorithm]] Generates Traditional Musical Rhythms".<ref name="gtpdf">[http://cgm.cs.mcgill.ca/~godfried/publications/banff.pdf 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.</ref> The [[greatest common divisor]] of two numbers is used [[Rhythm|rhythmically]] giving the number of [[beat (music)|beats]] and silences, generating almost all of the most important [[World Music]] rhythms,<ref name="gtweb">[http://cgm.cs.mcgill.ca/~godfried/rhythm-and-mathematics.html Comparative Musicology - Musical Rhythm and Mathematics]</ref> (except [[India#Performing_Arts|Indian]]).<ref name="extv">The Euclidean Algorithm Generates Traditional Musical Rhythms, by Godfried Toussaint, [http://cgm.cs.mcgill.ca/~godfried/publications/banff-extended.pdf 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.</ref> The beats in the resulting rhythms are as equidistant as possible; the same results can be obtained from the [[Bresenham]] algorithm. |
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==Open Source Hardware Projects== |
==Open Source Hardware Projects== |
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Revision as of 23:42, 15 July 2013
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.
Open Source Hardware Projects
Open-source music hardware projects that can generate Euclidean rhythms, include Mutable instruments' MIDIPal, RebelTech's Stoicheia and Ruin & Wesen's Minicommand
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]
References
- ^ 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.
- ^ Comparative Musicology - Musical Rhythm and Mathematics
- ^ 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.
- ^ Musical pitch and Euclid's algorithm
External links
- 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.
- Extended version of The Euclidean Algorithm Generates Traditional Musical Rhythms, by Godfried Toussaint, 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.
- Generating African rhythms using the euclidean algorithm by Ruin & Wesen
- Musical pitch and Euclid's algorithm by Benjamin Wardhaugh
- Links to videos about and a Flash app for experimenting with Euclidean rhythms
- A tutorial on The Euclidean Algorithm Generates Traditional Musical Rhythms by Derek Rivait