410edo: Difference between revisions
Created page with "'''410edo''' is the equal division of the octave into 410 parts of 2.9268 cents each. It is closely related to 205edo, but the patent vals differ on the mapping fo..." Tags: Mobile edit Mobile web edit |
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'''410edo''' is the [[EDO|equal division of the octave]] into 410 parts of 2.9268 cents each. It is closely related to [[205edo]], but the patent vals differ on the mapping for 7 and 13. It is contorted in the 5-limit, tempering out 1600000/1594323 (amity comma) and 274877906944/274658203125 (hemithirds comma), as well as 95367431640625/95105071448064 (gammic comma) and 140737488355328/140126044921875 (qintosec comma). Using the patent val, it tempers out 2401/2400, 4802000/4782969, and 48828125/48771072 in the 7-limit; 5632/5625, 9801/9800, 14641/14580, and 117649/117612 in the 11-limit; 676/675, 1001/1000, 1716/1715, 4096/4095, and 73205/73008 in the 13-limit. | '''410edo''' is the [[EDO|equal division of the octave]] into 410 parts of 2.9268 cents each. | ||
It is closely related to [[205edo]], but the patent vals differ on the mapping for 7 and 13. It is contorted in the [[5-limit]], tempering out 1600000/1594323 ([[amity comma]]) and 274877906944/274658203125 (luna/hemithirds comma), as well as 95367431640625/95105071448064 (gammic comma) and 140737488355328/140126044921875 (qintosec comma). Using the [[patent val]], it tempers out 2401/2400 ([[breedsma]]), 4802000/4782969 ([[canousma]]), and 48828125/48771072 in the [[7-limit]]; 5632/5625 (vishdel), 9801/9800 (kalisma), 14641/14580 ([[semicanousma]]), and 117649/117612 in the [[11-limit]]; 676/675 (island comma), 1001/1000 (sinbadma), 1716/1715 (lummic comma), 4096/4095 ([[schismina]]), and 73205/73008 in the 13-limit. | |||
It provides the [[optimal patent val]] for [[semicanousmic temperaments|semicanousmic]], the rank-4 temperament that tempers out 14641/14580, and for 11-limit [[Canou family #Semicanou|semicanou]], the rank-3 temperament that tempers out 9801/9800 and 14641/14580. | |||
[[Category:Edo]] | [[Category:Edo]] | ||
[[Category:Canou]] | |||
[[Category:Semicanousmic]] | |||
Revision as of 11:00, 3 October 2020
410edo is the equal division of the octave into 410 parts of 2.9268 cents each.
It is closely related to 205edo, but the patent vals differ on the mapping for 7 and 13. It is contorted in the 5-limit, tempering out 1600000/1594323 (amity comma) and 274877906944/274658203125 (luna/hemithirds comma), as well as 95367431640625/95105071448064 (gammic comma) and 140737488355328/140126044921875 (qintosec comma). Using the patent val, it tempers out 2401/2400 (breedsma), 4802000/4782969 (canousma), and 48828125/48771072 in the 7-limit; 5632/5625 (vishdel), 9801/9800 (kalisma), 14641/14580 (semicanousma), and 117649/117612 in the 11-limit; 676/675 (island comma), 1001/1000 (sinbadma), 1716/1715 (lummic comma), 4096/4095 (schismina), and 73205/73008 in the 13-limit.
It provides the optimal patent val for semicanousmic, the rank-4 temperament that tempers out 14641/14580, and for 11-limit semicanou, the rank-3 temperament that tempers out 9801/9800 and 14641/14580.