164edo: Difference between revisions

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-The ''164 equal division'' divides the octave into 164 equal parts of 7.317 cents each. In the 5-limit it tempers out the [[würschmidt comma]], 393216/390625, and supplies the [[optimal patent val]] for the [[würschmidt]] temperament. In higher limits, also supplies the optimal patent val for the 7-limit, 1/41 octave period 41&amp;123 temperament, and the 13-limit the [[Gamelismic family #Portent|momentous]] temperament, the rank-3 temperament tempering out 196/195, 352/351, 385/384 and 441/440.
+{{Infobox ET
+| Prime factorization = 2<sup>2</sup> × 41
+| Step size = 7.31707¢
+| Fifth = 96\164 (702.44¢) (→ [[41edo|24\41]])
+| Semitones = 16:12 (117.07¢ : 87.80¢)
+| Consistency = 5
+}}
+{{EDO intro|164}}
-= 4 × 41, with divisors 2, 4, 41, 82
+== Theory ==
+In the 5-limit, 164edo tempers out the [[würschmidt comma]], 393216/390625, and supplies the [[optimal patent val]] for the [[würschmidt]] temperament. In higher limits, also supplies the optimal patent val for the 7-limit, 1/41 octave period 41&amp;123 temperament, and the 13-limit the [[Gamelismic family #Portent|momentous]] temperament, the rank-3 temperament tempering out 196/195, 352/351, 385/384 and 441/440.
+= 4 × 41, with divisors 2, 4, 41, 82.
 === Prime harmonics ===