410edo: Difference between revisions

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

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.

410edo is closely related to [[205edo]], but the [[patent val]] differs on the mappings for 7 and 13. It is [[contorted]] (or [[enfactored]]) 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 the 11- and 13-limit rank-3 [[Canou family #Semicanou|semicanou temperament]], and the rank-4 temperament tempering out 14641/14580.

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 '''410edo''' is the [[EDO|equal division of the octave]] into 410 parts of 2.9268 [[cent]]s each.
-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.
+edo is closely related to [[205edo]], but the [[patent val]] differs on the mappings for 7 and 13. It is [[contorted]] (or [[enfactored]]) 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 the 11- and 13-limit rank-3 [[Canou family #Semicanou|semicanou temperament]], and the rank-4 temperament tempering out 14641/14580.