328edo: Difference between revisions

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-The '''328 equal division''' divides the octave into 328 equal parts of 3.659 cents each. It tempers out the [[würschmidt comma]], 393216/390625, in the 5-limit and [[3136/3125]], 6144/6125 and [[2401/2400]] in the 7-limit, so that it supports [[würschmidt]] and [[hemiwuerschmidt]] temperaments, and provides the [[optimal patent val]] for 7-limit hemiwürschmidt.
+The '''328 equal divisions of the octave''' ('''328edo''') divides the octave into 328 [[equal]] parts of 3.659 [[cent]]s each.
+== Theory ==
+edo is [[enfactored]] in the 5-limit, with the same tuning as [[164edo]]. It tempers out [[2401/2400]], [[3136/3125]], and [[6144/6125]] in the 7-limit, [[9801/9800]], [[16384/16335]] and [[19712/19683]] in the 11-limit, [[676/675]], [[1001/1000]], [[1716/1715]] and [[2080/2079]] in the 13-limit, [[936/935]], [[1156/1155]] and [[2601/2600]] in the 17-limit, so that it supports [[würschmidt]] and [[hemiwürschmidt]], and provides the [[optimal patent val]] for 7-limit hemiwürschmidt, 11- and 13-limit [[semihemiwür]], and 13-limit [[semiporwell]].
+factors into 2<sup>3</sup> × 41, with subset edos 2, 4, 8, 41, 82, and 164.
+=== Prime harmonics ===
+{{Primes in edo|328}}
+[[Category:Equal divisions of the octave]]
 [[Category:Hemiwürschmidt]]
-[[Category:Würschmidt]]
+[[Category:Semiporwell]]