174edo: Difference between revisions

Fix section headings; add interval table
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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.


== Odd harmonics ==
=== Odd harmonics ===
{{Harmonics in equal|174}}
{{Harmonics in equal|174}}


== Subsets and supersets ==
=== Subsets and supersets ===
Since 174 factors into {{factorization|174}}, 174edo has subset edos {{EDOs| 2, 3, 6, 29, 58, and 87 }}.
Since 174 factors into primes as {{nowrap| 2 × 3 × 29 }}, 174edo has subset edos {{EDOs| 2, 3, 6, 29, 58, and 87 }}.


== Intervals ==
== Intervals ==
{{Interval table}}
{{Interval table}}