410edo: Difference between revisions

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'''410edo''' is the [[EDO|equal division of the octave]] into 410 parts of 2.9268 ~~cents~~ each.

'''410edo''' is the [[EDO|equal division of the octave]] into 410 parts of 2.9268 [[cent]]s 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.

410edo is closely related to [[205edo]], but the [[patent val]] differs on the mappings for 7 and 13. It is contorted in the [[5-limit]], tempering out 1600000/1594323 ([[amity comma]]) and {{monzo| 38 -2 -15 }} (luna/hemithirds comma), as well as {{monzo| -29 -11 20 }} (gammic comma) and {{monzo| 47 -15 -10 }} (qintosec comma). Using the patent val, it tempers out 2401/2400 ([[breedsma]]), 4802000/4782969 ([[canousma]]), 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]], [[2080/2079]], [[4096/4095]], 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.

It provides the [[optimal patent val]] for the 11- and 13-limit rank-3 [[Canou family #Semicanou|semicanou temperament]], and the rank-4 temperament tempering out 14641/14580.

[[Category:Equal divisions of the octave]]

[[Category:Canou]]

[[Category:Semicanou]]

[[Category:Semicanousmic]]

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-'''410edo''' is the [[EDO|equal division of the octave]] into 410 parts of 2.9268 cents each.
+'''410edo''' is the [[EDO|equal division of the octave]] into 410 parts of 2.9268 [[cent]]s 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.
+edo is closely related to [[205edo]], but the [[patent val]] differs on the mappings for 7 and 13. It is contorted in the [[5-limit]], tempering out 1600000/1594323 ([[amity comma]]) and {{monzo| 38 -2 -15 }} (luna/hemithirds comma), as well as {{monzo| -29 -11 20 }} (gammic comma) and {{monzo| 47 -15 -10 }} (qintosec comma). Using the patent val, it tempers out 2401/2400 ([[breedsma]]), 4802000/4782969 ([[canousma]]), 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]], [[2080/2079]], [[4096/4095]], 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.
+It provides the [[optimal patent val]] for the 11- and 13-limit rank-3 [[Canou family #Semicanou|semicanou temperament]], and the rank-4 temperament tempering out 14641/14580.
 [[Category:Equal divisions of the octave]]
 [[Category:Canou]]
+[[Category:Semicanou]]
 [[Category:Semicanousmic]]