104edo: Difference between revisions

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== Theory ==

104edo has two different equally viable 5-limit [[val]]s, and both are useful. The flat major third val, {{val| 104 165 241 }} ([[patent val]]), tempers out [[3125/3072]], and ~~supports~~ [[magic]] temperament. The sharp major third val, {{val| 104 165 242 }} (104c val), tempers out [[2048/2025]] and supports [[diaschismic]] temperament.

104edo has two different equally viable 5-limit [[val]]s, and both are useful. The flat major third val, {{val| 104 165 241 }} ([[patent val]]), tempers out [[3125/3072]], and [[support]]s [[magic]] temperament. The sharp major third val, {{val| 104 165 242 }} (104c val), tempers out [[2048/2025]] and supports [[diaschismic]] temperament.

104edo with the flat third is especially notable as an excellent tuning for magic temperament, providing the [[optimal patent val]] for 11-limit magic and the 13-limit magic extension [[necromancy]]. In the 5-limit it tempers out the magic comma, 3125/3072; in the 7-limit, it tempers out [[225/224]], [[245/243]] and [[875/864]]; and in the 11-limit, [[100/99]], [[896/891]], [[385/384]] and [[540/539]]. It provides an excellent tuning also for the rank-3 temperaments pairing 100/99 with 225/224 ([[apollo]] temperament), 245/243 or 875/864, or the rank-4 temperament tempering out 100/99, for which it gives the optimal patent val.

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 == Theory ==
-edo has two different equally viable 5-limit [[val]]s, and both are useful. The flat major third val, {{val| 104 165 241 }} ([[patent val]]), tempers out [[3125/3072]], and supports [[magic]] temperament. The sharp major third val, {{val| 104 165 242 }} (104c val), tempers out [[2048/2025]] and supports [[diaschismic]] temperament.
+edo has two different equally viable 5-limit [[val]]s, and both are useful. The flat major third val, {{val| 104 165 241 }} ([[patent val]]), tempers out [[3125/3072]], and [[support]]s [[magic]] temperament. The sharp major third val, {{val| 104 165 242 }} (104c val), tempers out [[2048/2025]] and supports [[diaschismic]] temperament.
 edo with the flat third is especially notable as an excellent tuning for magic temperament, providing the [[optimal patent val]] for 11-limit magic and the 13-limit magic extension [[necromancy]]. In the 5-limit it tempers out the magic comma, 3125/3072; in the 7-limit, it tempers out [[225/224]], [[245/243]] and [[875/864]]; and in the 11-limit, [[100/99]], [[896/891]], [[385/384]] and [[540/539]]. It provides an excellent tuning also for the rank-3 temperaments pairing 100/99 with 225/224 ([[apollo]] temperament), 245/243 or 875/864, or the rank-4 temperament tempering out 100/99, for which it gives the optimal patent val.