624edo: Difference between revisions
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== Theory == | == Theory == | ||
624edo is [[consistent]] to the [[27-odd-limit]]. | 624edo is [[consistent]] to the [[27-odd-limit]]. As an equal temperament, it [[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]], [[2646/2645]], 3520/3519, 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 2.3.5.11.13.17-[[subgroup]] [[restriction]] thereof. | It provides an excellent [[optimal patent val]] for the rank-6 temperament tempering out 936/935, as well as the rank-5 2.3.5.11.13.17-[[subgroup]] [[restriction]] thereof. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|624 | {{Harmonics in equal|624}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 624 factors into | Since 624 factors into 2<sup>4</sup> × 3 × 13, 624edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 156, and 312 }}. | ||
== Regular temperament properties == | == Regular temperament properties == | ||