323edo: Difference between revisions
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'''323edo''' is the [[EDO|equal division of the octave]] into 323 parts of 3.7152 [[cent]]s each. It [[ | The '''323 equal divisions of the octave''' ('''323edo''') is the [[EDO|equal division of the octave]] into 323 parts of 3.7152 [[cent]]s each. | ||
== Theory == | |||
It [[tempering out|tempers out]] the [[vulture comma]], {{monzo| 24 -21 4 }} and the [[luna comma]], {{monzo| 38 -2 -15 }}, in the [[5-limit]]; [[4375/4374]], 589824/588245 and [[703125/702464]] in the [[7-limit]], supporting 7-limit [[vulture]], [[lunatic]], [[enneadecal]], and [[gamera]]. In the 11-limit, the 323e val and the [[patent val]] are comparable in errors. 1375/1372, 5632/5625, [[14641/14580]], and [[19712/19683]] are tempered out in the patent val; [[540/539]], [[6250/6237]], 12005/11979, and [[16384/16335]] are tempered out in the 323e val. | |||
323 = 17 × 19, and shares the excellent approximations of [[25/24]] in [[17edo]] and of the [[28/27]] and the [[6/5]] in [[19edo]]. | |||
=== Prime harmonics === | |||
{{Primes in edo|323}} | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category:Theory]] | [[Category:Theory]] | ||
Revision as of 23:25, 26 October 2021
The 323 equal divisions of the octave (323edo) is the equal division of the octave into 323 parts of 3.7152 cents each.
Theory
It tempers out the vulture comma, [24 -21 4⟩ and the luna comma, [38 -2 -15⟩, in the 5-limit; 4375/4374, 589824/588245 and 703125/702464 in the 7-limit, supporting 7-limit vulture, lunatic, enneadecal, and gamera. In the 11-limit, the 323e val and the patent val are comparable in errors. 1375/1372, 5632/5625, 14641/14580, and 19712/19683 are tempered out in the patent val; 540/539, 6250/6237, 12005/11979, and 16384/16335 are tempered out in the 323e val.
323 = 17 × 19, and shares the excellent approximations of 25/24 in 17edo and of the 28/27 and the 6/5 in 19edo.
Prime harmonics
Script error: No such module "primes_in_edo".