106edo: Difference between revisions
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The 106 equal division divides the octave into 106 equal parts of 11.321 cents each. Since 106 = 2*53 it is closely related to [[53edo]], and is [[ | The '''106 equal division''' divides the octave into 106 equal parts of 11.321 cents each. Since 106 = 2*53 it is closely related to [[53edo]], and is [[Contorsion|contorted]] through the [[7-limit]], tempering out the same commas ([[32805/32768]], [[15625/15552]], 1600000/1594323, 2109375/2097152 in the [[5-limit]], 3125/3097, [[225/224]], 4000/3969, 1728/1715, 2430/2401, [[4375/4374]] in the 7-limit) as the patent val for 53edo. In the 11-limit it also tempers out [[243/242]], 3025/3024 and [[9801/9800]], so that it supports [[spectacle]] temperament and [[borwell]] temperament. | ||
The division is notable for the fact that it is related to the [[turkish cent]], or türk sent, which divides 106edo into 100 parts just as ordinary cents divides 12edo into 100 parts, thereby making it the [[relative cent]] division for 106edo. Conversely, it makes the Pythagorean [[relative cent]] (or pion, symbol π<sup>¢</sup>, π<sup>r¢</sup>), which most closely approximates equally dividing an exact 3/2, if you care about such a thing. | The division is notable for the fact that it is related to the [[turkish cent]], or türk sent, which divides 106edo into 100 parts just as ordinary cents divides 12edo into 100 parts, thereby making it the [[relative cent]] division for 106edo. Conversely, it makes the Pythagorean [[relative cent]] (or pion, symbol π<sup>¢</sup>, π<sup>r¢</sup>), which most closely approximates equally dividing an exact [[3/2]], if you care about such a thing. | ||
Artists using 106 et: | Artists using 106 et: | ||
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* [http://chrisvaisvil.com/still-life-in-106-notes-per-octave/ Still Life in 106 Notes Per Octave « Music & Techniques by Chris Vaisvil] | * [http://chrisvaisvil.com/still-life-in-106-notes-per-octave/ Still Life in 106 Notes Per Octave « Music & Techniques by Chris Vaisvil] | ||
[[Category:Edo]] | |||
[[Category:53edo]] | [[Category:53edo]] | ||
[[Category:Polychromatic]] | [[Category:Polychromatic]] | ||
Revision as of 16:43, 18 November 2020
The 106 equal division divides the octave into 106 equal parts of 11.321 cents each. Since 106 = 2*53 it is closely related to 53edo, and is contorted through the 7-limit, tempering out the same commas (32805/32768, 15625/15552, 1600000/1594323, 2109375/2097152 in the 5-limit, 3125/3097, 225/224, 4000/3969, 1728/1715, 2430/2401, 4375/4374 in the 7-limit) as the patent val for 53edo. In the 11-limit it also tempers out 243/242, 3025/3024 and 9801/9800, so that it supports spectacle temperament and borwell temperament.
The division is notable for the fact that it is related to the turkish cent, or türk sent, which divides 106edo into 100 parts just as ordinary cents divides 12edo into 100 parts, thereby making it the relative cent division for 106edo. Conversely, it makes the Pythagorean relative cent (or pion, symbol π¢, πr¢), which most closely approximates equally dividing an exact 3/2, if you care about such a thing.
Artists using 106 et: