292edo: Difference between revisions

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== Theory ==

292edo is closely related to [[146edo]], but the [[patent val]]s differ on the mapping for [[3/1|3]]. It [[tempers out]] {{monzo| 3 -18 11 }} (quartonic comma) and {{monzo| 38 -2 -15 }} (luna/hemithirds comma) in the [[5-limit]]; 5120/5103 ([[5120/5103|hemifamity]]), 390625/388962 ([[dimcomp comma|dimcomp]]), 420175/419904 ([[wizma]]), and 4802000/4782969 ([[canousma]]) in the [[7-limit]]; 1375/1372, [[5632/5625]], [[6250/6237]], [[9801/9800]] and [[14641/14580]] in the [[11-limit]]; [[352/351]], [[625/624]], [[847/845]], [[1716/1715]], and [[2080/2079]] in the [[13-limit]].

292edo is closely related to [[146edo]], but the [[patent val]]s differ on the mapping for [[3/1|3]]. As an equal temperament, it [[tempering out|tempers out]] {{monzo| 3 -18 11 }} ([[quartonic comma]]) and {{monzo| 38 -2 -15 }} ([[luna comma|luna/hemithirds comma]]) in the [[5-limit]]; 5120/5103 ([[5120/5103|hemifamity]]), 390625/388962 ([[dimcomp comma|dimcomp]]), 420175/419904 ([[wizma]]), and 4802000/4782969 ([[canousma]]) in the [[7-limit]]; 1375/1372, [[5632/5625]], [[6250/6237]], [[9801/9800]] and [[14641/14580]] in the [[11-limit]]; [[352/351]], [[625/624]], [[847/845]], [[1716/1715]], and [[2080/2079]] in the [[13-limit]].

It provides the [[optimal patent val]] for the [[undim]] temperament in the 7-, 11-, and 13-limit, and notably [[support]]s [[~~Hemifamity~~ temperaments #Semiseptiquarter|semiseptiquarter]] and [[semiluna]].

It provides the [[optimal patent val]] for the [[undim]] temperament in the 7-, 11-, and 13-limit, and notably [[support]]s [[hemifamity temperaments #Semiseptiquarter|semiseptiquarter]] and [[semiluna]].

=== Prime harmonics ===

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=== Subsets and supersets ===

Since 292 factors into ~~{{factorization|292}}~~, 292edo has subset edos {{EDOs| 2, 4, 73, and 146 }}.

Since 292 factors into 2<sup>2</sup> × 73, 292edo has subset edos {{EDOs| 2, 4, 73, and 146 }}.

== Regular temperament properties ==

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| [[Undim]]

|}

<nowiki />* [[Normal ~~lists~~|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~|minimal form]] in parentheses if distinct

<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct

[[Category:~~Hemifamity~~]]

[[Category:Aberschismic]]

[[Category:Septiquarter]]

[[Category:Semiluna]]

[[Category:Undim]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro}}
+{{ED intro}}
 == Theory ==
-edo is closely related to [[146edo]], but the [[patent val]]s differ on the mapping for [[3/1|3]]. It [[tempers out]] {{monzo| 3 -18 11 }} (quartonic comma) and {{monzo| 38 -2 -15 }} (luna/hemithirds comma) in the [[5-limit]]; 5120/5103 ([[5120/5103|hemifamity]]), 390625/388962 ([[dimcomp comma|dimcomp]]), 420175/419904 ([[wizma]]), and 4802000/4782969 ([[canousma]]) in the [[7-limit]]; 1375/1372, [[5632/5625]], [[6250/6237]], [[9801/9800]] and [[14641/14580]] in the [[11-limit]]; [[352/351]], [[625/624]], [[847/845]], [[1716/1715]], and [[2080/2079]] in the [[13-limit]].
+edo is closely related to [[146edo]], but the [[patent val]]s differ on the mapping for [[3/1|3]]. As an equal temperament, it [[tempering out|tempers out]] {{monzo| 3 -18 11 }} ([[quartonic comma]]) and {{monzo| 38 -2 -15 }} ([[luna comma|luna/hemithirds comma]]) in the [[5-limit]]; 5120/5103 ([[5120/5103|hemifamity]]), 390625/388962 ([[dimcomp comma|dimcomp]]), 420175/419904 ([[wizma]]), and 4802000/4782969 ([[canousma]]) in the [[7-limit]]; 1375/1372, [[5632/5625]], [[6250/6237]], [[9801/9800]] and [[14641/14580]] in the [[11-limit]]; [[352/351]], [[625/624]], [[847/845]], [[1716/1715]], and [[2080/2079]] in the [[13-limit]].
-It provides the [[optimal patent val]] for the [[undim]] temperament in the 7-, 11-, and 13-limit, and notably [[support]]s [[Hemifamity temperaments #Semiseptiquarter|semiseptiquarter]] and [[semiluna]].
+It provides the [[optimal patent val]] for the [[undim]] temperament in the 7-, 11-, and 13-limit, and notably [[support]]s [[hemifamity temperaments #Semiseptiquarter|semiseptiquarter]] and [[semiluna]].
 === Prime harmonics ===
@@ Line 11: / Line 11: @@
 === Subsets and supersets ===
-Since 292 factors into {{factorization|292}}, 292edo has subset edos {{EDOs| 2, 4, 73, and 146 }}.
+Since 292 factors into 2<sup>2</sup> × 73, 292edo has subset edos {{EDOs| 2, 4, 73, and 146 }}.
 == Regular temperament properties ==
@@ Line 120: / Line 120: @@
 | [[Undim]]
 |}
-<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
+<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
-[[Category:Hemifamity]]
+[[Category:Aberschismic]]
 [[Category:Septiquarter]]
 [[Category:Semiluna]]
 [[Category:Undim]]