323edo: Difference between revisions
Expansion |
Note that it's the OPV for 1573/1568 |
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== Theory == | == Theory == | ||
323et [[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. It provides the [[optimal patent val]] for the rank-5 temperament tempering out [[1573/1568]], the lambeth comma, as well as the 2.3.5.11 subgroup temperament tempering out 14641/14580, the semicanousma. | |||
323 = 17 × 19, and shares the excellent approximations of [[25/24]] in [[17edo]] and of the [[28/27]] and the [[6/5]] in [[19edo]]. | 323 = 17 × 19, and shares the excellent approximations of [[25/24]] in [[17edo]] and of the [[28/27]] and the [[6/5]] in [[19edo]]. | ||
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[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category: | [[Category:Deuteromere]] | ||
[[Category:Lambeth]] | |||
Revision as of 02:20, 6 January 2022
The 323 equal divisions of the octave (323edo) is the equal division of the octave into 323 parts of 3.7152 cents each.
Theory
323et 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. It provides the optimal patent val for the rank-5 temperament tempering out 1573/1568, the lambeth comma, as well as the 2.3.5.11 subgroup temperament tempering out 14641/14580, the semicanousma.
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".