624edo: Difference between revisions
OPV for ainismic and ainic |
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== Theory == | == Theory == | ||
624edo is [[consistent]] to the [[27-odd-limit]]. The equal temperament [[tempering out|tempers out]] {{monzo| 23 6 -14 }} ([[vishnuzma]]) and {{monzo| -69 45 -1 }} ([[counterschisma]]) in the 5-limit; [[250047/250000]], 2460375/2458624, and 134217728/133984375 in the 7-limit; [[9801/9800]], 46656/46585, [[131072/130977]], and 151263/151250 in the 11-limit; [[1716/1715]], [[2080/2079]], [[4096/4095]], 34398/34375, and 39366/39325 in the 13-limit; [[936/935]], [[1701/1700]], [[2025/2023]], and [[2058/2057]] in the 17-limit; [[1521/1520]], 2376/2375, [[2432/2431]], and 3328/3325 in the 19-limit; 2024/2023, 2025/2024, and 3888/3887 in the 23-limit. | 624edo is [[consistent]] to the [[27-odd-limit]]. The equal temperament [[tempering out|tempers out]] {{monzo| 23 6 -14 }} ([[vishnuzma]]) and {{monzo| -69 45 -1 }} ([[counterschisma]]) in the 5-limit; [[250047/250000]], 2460375/2458624, and 134217728/133984375 in the 7-limit; [[9801/9800]], 46656/46585, [[131072/130977]], and 151263/151250 in the 11-limit; [[1716/1715]], [[2080/2079]], [[4096/4095]], 34398/34375, and 39366/39325 in the 13-limit; [[936/935]], [[1701/1700]], [[2025/2023]], and [[2058/2057]] in the 17-limit; [[1521/1520]], 2376/2375, [[2432/2431]], and 3328/3325 in the 19-limit; 2024/2023, 2025/2024, and 3888/3887 in the 23-limit. | ||
It provides an excellent [[optimal patent val]] for the rank-6 temperament tempering out 936/935, as well as the rank-5 2.3.5.11.13 [[subgroup]] [[restriction]] thereof. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | <nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | ||
[[Category:Ainismic]] | |||