164edo: Difference between revisions
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== Theory == | == Theory == | ||
In the 5-limit, 164edo tempers out the [[würschmidt comma]], 393216/390625, and supplies the [[optimal patent val]] for the [[würschmidt]] temperament. In | In the 5-limit, 164edo tempers out the [[würschmidt comma]], 393216/390625, and the [[vulture comma]], {{monzo| 24 -21 4 }}. It supplies the [[optimal patent val]] for the [[würschmidt]] temperament. | ||
In the [[patent val]] {{val| 164 260 381 '''460''' '''567''' 607 }}, it tempers out [[196/195]], [[352/351]], [[385/384]], [[441/440]], [[676/675]], and supplies the optimal patent val for the 7-limit, 1/41 octave period 41&123 temperament, and the 13-limit [[Gamelismic family #Portent|momentous]] temperament, the rank-3 temperament tempering out 196/195, 352/351, 385/384 and 441/440. | |||
In the alternative val 164de {{val| 164 260 381 '''461''' '''568''' 607 }}, it tempers out [[243/242]], [[351/350]], [[364/363]], [[640/637]], [[676/675]], [[729/728]], and [[1575/1573]]. | |||
164 = 4 × 41, with divisors 2, 4, 41, 82. | 164 = 4 × 41, with divisors 2, 4, 41, 82. | ||
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| 275/256 | | 275/256 | ||
| [[Semivulture]] (164) | | [[Semivulture]] (164) | ||
|- | |||
| 2 | |||
| 25\164 | |||
| 182.93 | |||
| 10/9 | |||
| [[Unidecmic]] | |||
|- | |- | ||
| 4 | | 4 | ||