472edo: Difference between revisions

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== Theory ==

472edo ~~is [[consistent]] to the [[11-odd-limit]]. It~~ is [[Enfactoring|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]]. In the 7-limit, it tempers out [[2401/2400]], 2460375/2458624, and 30623756184/30517578125; in the 11-limit, [[9801/9800]], 46656/46585, 117649/117612, and 234375/234256, [[support]]ing the [[Breedsmic temperaments #Maviloid|maviloid]] temperament, the [[Schismatic family #Bisesqui|bisesqui temperament]], and the [[Schismatic family #Octant|octant temperament]]. Using the [[patent val]], it tempers out [[729/728]], [[1575/1573]], [[2200/2197]], [[4096/4095]], and 21168/21125 in the 13-limit, so it also supports the 13-limit octant.

472edo is [[Enfactoring|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]], but the approximation to higher harmonics are much improved. It is [[consistent]] to the [[11-odd-limit]]. In the 7-limit, the equal temperament tempers out [[2401/2400]], 2460375/2458624, and 30623756184/30517578125; in the 11-limit, [[9801/9800]], 46656/46585, 117649/117612, and 234375/234256, [[support]]ing the [[Breedsmic temperaments #Maviloid|maviloid]] temperament, the [[Schismatic family #Bisesqui|bisesqui temperament]], and the [[Schismatic family #Octant|octant temperament]]. Using the [[patent val]], it tempers out [[729/728]], [[1575/1573]], [[2200/2197]], [[4096/4095]], and 21168/21125 in the 13-limit, so it also supports the 13-limit octant.

472edo is a [[zeta peak integer edo]].

=== Prime harmonics ===

=== Subsets and supersets ===

Since 472 factors into 2<sup>3</sup> × 59, 472edo has subset edos {{EDOs| 2, 4, 8, 59, 118, and 236 }}.

== Regular temperament properties ==

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 == Theory ==
-edo is [[consistent]] to the [[11-odd-limit]]. It is [[Enfactoring|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]]. In the 7-limit, it tempers out [[2401/2400]], 2460375/2458624, and 30623756184/30517578125; in the 11-limit, [[9801/9800]], 46656/46585, 117649/117612, and 234375/234256, [[support]]ing the [[Breedsmic temperaments #Maviloid|maviloid]] temperament, the [[Schismatic family #Bisesqui|bisesqui temperament]], and the [[Schismatic family #Octant|octant temperament]]. Using the [[patent val]], it tempers out [[729/728]], [[1575/1573]], [[2200/2197]], [[4096/4095]], and 21168/21125 in the 13-limit, so it also supports the 13-limit octant.
+edo is [[Enfactoring|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]], but the approximation to higher harmonics are much improved. It is [[consistent]] to the [[11-odd-limit]]. In the 7-limit, the equal temperament tempers out [[2401/2400]], 2460375/2458624, and 30623756184/30517578125; in the 11-limit, [[9801/9800]], 46656/46585, 117649/117612, and 234375/234256, [[support]]ing the [[Breedsmic temperaments #Maviloid|maviloid]] temperament, the [[Schismatic family #Bisesqui|bisesqui temperament]], and the [[Schismatic family #Octant|octant temperament]]. Using the [[patent val]], it tempers out [[729/728]], [[1575/1573]], [[2200/2197]], [[4096/4095]], and 21168/21125 in the 13-limit, so it also supports the 13-limit octant.
 edo is a [[zeta peak integer edo]].
 === Prime harmonics ===
-{{Harmonics in equal|472|columns=11}}
+{{Harmonics in equal|472}}
+=== Subsets and supersets ===
+Since 472 factors into 2<sup>3</sup> × 59, 472edo has subset edos {{EDOs| 2, 4, 8, 59, 118, and 236 }}.
 == Regular temperament properties ==