410edo: Difference between revisions

Line 1:

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

The '''410 equal divisions of the octave''' ('''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]] 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). It tempers out 2401/2400 ([[breedsma]]), 4802000/4782969 ([[canousma]]), and 48828125/48771072 (neptunisma) 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]], [[4225/4224]] 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.

It provides the [[optimal patent val]] for the 11- and 13-limit semiluna, hemiluna, and floral temperament, the rank-3 [[semicanou]] temperament, and the rank-4 temperament tempering out 14641/14580.

=== Prime harmonics ===

[[Category:Equal divisions of the octave]]

@@ Line 1: / Line 1: @@
-'''410edo''' is the [[EDO|equal division of the octave]] into 410 parts of 2.9268 [[cent]]s each.
+The '''410 equal divisions of the octave''' ('''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]] 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). It tempers out 2401/2400 ([[breedsma]]), 4802000/4782969 ([[canousma]]), and 48828125/48771072 (neptunisma) 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]], [[4225/4224]] 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.
+It provides the [[optimal patent val]] for the 11- and 13-limit semiluna, hemiluna, and floral temperament, the rank-3 [[semicanou]] temperament, and the rank-4 temperament tempering out 14641/14580.
+=== Prime harmonics ===
+{{Primes in edo|410}}
 [[Category:Equal divisions of the octave]]