328edo: Difference between revisions
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The '''328 equal | The '''328 equal divisions of the octave''' ('''328edo''') divides the octave into 328 [[equal]] parts of 3.659 [[cent]]s each. | ||
== Theory == | |||
328edo 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]]. | |||
328 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:Hemiwürschmidt]] | ||
[[Category: | [[Category:Semiporwell]] | ||
Revision as of 17:44, 10 October 2021
The 328 equal divisions of the octave (328edo) divides the octave into 328 equal parts of 3.659 cents each.
Theory
328edo 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.
328 factors into 23 × 41, with subset edos 2, 4, 8, 41, 82, and 164.
Prime harmonics
Script error: No such module "primes_in_edo".