456edo: Difference between revisions

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-'''456edo''' is the [[EDO|equal division of the octave]] into 456 parts of 2.63158 cents each. It is contorted in the 5-limit, tempering out 1600000/1594323 (amity comma) and 4294967296/4271484375 (escapade comma), as well as 6115295232/6103515625 (vishnuzma), 2199023255552/2179240250625 (undim comma), and 19073486328125/19042491875328 (enneadeca). In the 7-limit, it tempers out 10976/10935, 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[Hemimage temperaments|chromat temperament]].
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Equal divisions of the octave]]
+edo is [[enfactoring|enfactored]] in the 5-limit, with the same tuning as [[152edo]], defined by [[tempering out]] 1600000/1594323 ([[amity comma]]) and {{monzo| 32 -7 -9 }} ([[escapade comma]]), as well as {{monzo| 23 6 -14 }} ([[vishnuzma]]), {{monzo| 41 -20 -4 }} (undim comma), and {{monzo| -14 -19 19 }} ([[enneadeca]]). In the 7-limit, it tempers out [[10976/10935]], 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[chromat]] temperament.
+=== Odd harmonics ===
+{{Harmonics in equal|456}}
+=== Subsets and supersets ===
+Since 456 factors into {{factorization|456}}, 456edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, and 228 }}.
+[[Category:Chromat]]