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]]. ~~The~~ equal temperament [[tempering out|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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| {{monzo| 463 -292 }}

| {{mapping| 292 463 }}

| ~~−0~~.2476

| −0.2476

| 0.2475

| 6.02

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| {{monzo| 3 -18 11 }}, {{monzo| 38 -2 -15 }}

| {{mapping| 292 463 678 }}

| ~~−0~~.1633

| −0.1633

| 0.2346

| 5.71

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| 5120/5103, 390625/388962, 420175/419904

| {{mapping| 292 463 678 820 }}

| ~~−0~~.2148

| −0.2148

| 0.2219

| 5.40

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| 1375/1372, 5120/5103, 5632/5625, 14641/14580

| {{mapping| 292 463 678 820 1010 }}

| ~~−0~~.1353

| −0.1353

| 0.2544

| 6.19

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| 352/351, 625/624, 847/845, 1716/1715, 14641/14580

| {{mapping| 292 463 678 820 1010 1081 }}

| ~~−0~~.3480

| −0.3480

| 0.2736

| 6.66

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| 352/351, 625/624, 715/714, 847/845, 1225/1224, 2025/2023

| {{mapping| 292 463 678 820 1010 1081 1194 }}

| ~~−0~~.2376

| −0.2376

| 0.2696

| 6.56

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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 ~~it is~~ 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]]. The equal temperament [[tempering out|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 28: / Line 28: @@
 | {{monzo| 463 -292 }}
 | {{mapping| 292 463 }}
-| &minus;0.2476
+| −0.2476
 | 0.2475
 | 6.02
@@ Line 35: / Line 35: @@
 | {{monzo| 3 -18 11 }}, {{monzo| 38 -2 -15 }}
 | {{mapping| 292 463 678 }}
-| &minus;0.1633
+| −0.1633
 | 0.2346
 | 5.71
@@ Line 42: / Line 42: @@
 | 5120/5103, 390625/388962, 420175/419904
 | {{mapping| 292 463 678 820 }}
-| &minus;0.2148
+| −0.2148
 | 0.2219
 | 5.40
@@ Line 49: / Line 49: @@
 | 1375/1372, 5120/5103, 5632/5625, 14641/14580
 | {{mapping| 292 463 678 820 1010 }}
-| &minus;0.1353
+| −0.1353
 | 0.2544
 | 6.19
@@ Line 56: / Line 56: @@
 | 352/351, 625/624, 847/845, 1716/1715, 14641/14580
 | {{mapping| 292 463 678 820 1010 1081 }}
-| &minus;0.3480
+| −0.3480
 | 0.2736
 | 6.66
@@ Line 63: / Line 63: @@
 | 352/351, 625/624, 715/714, 847/845, 1225/1224, 2025/2023
 | {{mapping| 292 463 678 820 1010 1081 1194 }}
-| &minus;0.2376
+| −0.2376
 | 0.2696
 | 6.56
@@ 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 it is 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]]