174edo: Difference between revisions
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{{ED intro}} | {{ED intro}} | ||
== Theory == | |||
174edo is closely related to [[87edo]], but the [[patent val]]s differ on the mapping for [[17/1|17]] and some higher primes. It is [[contorted]] in the 13-limit, [[tempering out]] [[196/195]], [[245/243]], [[352/351]], [[364/363]], and [[625/624]]. Using the patent val, it tempers out [[289/288]] in the 17-limit; [[361/360]], [[476/475]], and 665/663 in the 19-limit; [[391/390]], [[392/391]], [[460/459]], [[529/528]], and [[760/759]] in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit. | 174edo is closely related to [[87edo]], but the [[patent val]]s differ on the mapping for [[17/1|17]] and some higher primes. It is [[contorted]] in the 13-limit, [[tempering out]] [[196/195]], [[245/243]], [[352/351]], [[364/363]], and [[625/624]]. Using the patent val, it tempers out [[289/288]] in the 17-limit; [[361/360]], [[476/475]], and 665/663 in the 19-limit; [[391/390]], [[392/391]], [[460/459]], [[529/528]], and [[760/759]] in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit. | ||
The 174b val flat fifth is a meantone fifth very close to the [[quarter-comma meantone]] fifth, being only 0.027 cents flat of it. | |||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 174 factors into {{ | Since 174 factors into primes as {{nowrap| 2 × 3 × 29 }}, 174edo has subset edos {{EDOs| 2, 3, 6, 29, 58, and 87 }}. | ||
== Intervals == | |||
{{Interval table}} | |||