174edo: Difference between revisions

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'''174edo''' is the [[EDO|equal division of the octave]] into 174 parts of 6.8966 cents each. It is closely related to [[87edo]], but the patent vals differ on the mapping for 17 and some higher primes. It is [[contorted]] (or [[enfactored]]) 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.

[[~~Category:Equal divisions of~~ the ~~octave~~]]

== 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.

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 ===

=== Subsets and supersets ===

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

== Intervals ==

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-'''174edo''' is the [[EDO|equal division of the octave]] into 174 parts of 6.8966 cents each. It is closely related to [[87edo]], but the patent vals differ on the mapping for 17 and some higher primes. It is [[contorted]] (or [[enfactored]]) 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.
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Equal divisions of the octave]]
+== Theory ==
+edo 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 ===
+{{Harmonics in equal|174}}
+=== Subsets and supersets ===
+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}}