660edo: Difference between revisions

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660edo is [[enfactoring|enfactored]] in the 5-limit, with the same tuning as [[330edo]], tempering out the [[schisma]] and the 22nd-octave [[major arcana]] comma, {{monzo|-193 154 -22}}.

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Nonetheless, patent val does have some use. It tunes the [[undecimal dimcomp]] temperament and also provides the [[optimal patent val]] for the [[quadrant]] temperament in the 11-limit as well as the 13-limit. Furthermore, in 2.3.7 it is a [[septiruthenia]]n system, and the patent val mapping for 5 allows the tuning of [[ruthenium]] temperament.

Other mappings can be considered. Taking a different mapping for 5, the 660c val tunes [[qintosec]] and [[atomic]]. In the 7-limit, it tunes [[decoid]]. In addition, one can combine the mappings for five to produce a 2.3.25 subgroup interpretation. There, 660edo has less error than on either vals and it tempers out the [[kwazy]] comma, as well as the [[landscape comma]] in the 2.3.25.7 subgroup.

=== Odd harmonics ===

=== Subsets and supersets ===

Since 660 factors as {{Factorization|660}}, it has subset edos {{EDOs|1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330}}.

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|660}}
+{{ED intro}}
 edo is [[enfactoring|enfactored]] in the 5-limit, with the same tuning as [[330edo]], tempering out the [[schisma]] and the 22nd-octave [[major arcana]] comma, {{monzo|-193 154 -22}}.
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 Nonetheless, patent val does have some use. It tunes the [[undecimal dimcomp]] temperament and also provides the [[optimal patent val]] for the [[quadrant]] temperament in the 11-limit as well as the 13-limit. Furthermore, in 2.3.7 it is a [[septiruthenia]]n system, and the patent val mapping for 5 allows the tuning of [[ruthenium]] temperament.
+Other mappings can be considered. Taking a different mapping for 5, the 660c val tunes [[qintosec]] and [[atomic]]. In the 7-limit, it tunes [[decoid]]. In addition, one can combine the mappings for five to produce a 2.3.25 subgroup interpretation. There, 660edo has less error than on either vals and it tempers out the [[kwazy]] comma, as well as the [[landscape comma]] in the 2.3.25.7 subgroup.
 === Odd harmonics ===
 {{harmonics in equal|660}}
 === Subsets and supersets ===
 Since 660 factors as {{Factorization|660}}, it has subset edos {{EDOs|1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330}}.