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|53edo]], and is [[Saturation|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 [[Marvel_family#Spectacle|spectacle temperament]] and [[Semicomma_family#Borwell|borwell temperament]]. | 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|53edo]], and is [[Saturation|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 [[Marvel_family#Spectacle|spectacle temperament]] and [[Semicomma_family#Borwell|borwell temperament]]. | ||
The division is notable for the fact that it is related to the [[turkish_cent|turkish cent]], ot türk sent, which divides 106edo into 100 parts just as ordinary cents divides 12edo into 100 parts, thereby making it the [[Relative_cent|relative cent]] division for 106edo. | The division is notable for the fact that it is related to the [[turkish_cent|turkish cent]], ot türk sent, which divides 106edo into 100 parts just as ordinary cents divides 12edo into 100 parts, thereby making it the [[Relative_cent|relative cent]] division for 106edo. Conversely, it makes the [[Relative_cent|relative cent]] which most closely approximates dividing an exact 3/2, if you care about such a thing. | ||
Artists using 106 et: | Artists using 106 et: | ||
<ul><li>[[Dolores_Catherino|Dolores Catherino]] -- [http://dolorescatherino.com her website], [https://www.youtube.com/user/dolomuse YouTube profile: dolomuse]</li><li>[http://chrisvaisvil.com/still-life-in-106-notes-per-octave/ Still Life in 106 Notes Per Octave « Music & Techniques by Chris Vaisvil]</li></ul> [[Category:53edo]] | <ul><li>[[Dolores_Catherino|Dolores Catherino]] -- [http://dolorescatherino.com her website], [https://www.youtube.com/user/dolomuse YouTube profile: dolomuse]</li><li>[http://chrisvaisvil.com/still-life-in-106-notes-per-octave/ Still Life in 106 Notes Per Octave « Music & Techniques by Chris Vaisvil]</li></ul> | ||
[[Category:53edo]] | |||
[[Category:polychromatic]] | [[Category:polychromatic]] | ||
Revision as of 19:37, 5 March 2019
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, ot 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 relative cent which most closely approximates dividing an exact 3/2, if you care about such a thing.
Artists using 106 et: