292edo - Revision history

FloraC: Text replacement - "Category:Hemifamity" to "Category:Aberschismic"

2026-06-06T12:39:16Z

Text replacement - "Category:Hemifamity" to "Category:Aberschismic"

← Older revision		Revision as of 12:39, 6 June 2026
Line 122:		Line 122:
	<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		<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:Septiquarter]]
	[[Category:Semiluna]]		[[Category:Semiluna]]
	[[Category:Undim]]		[[Category:Undim]]

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:33:08Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:33, 13 March 2026
Line 120:		Line 120:
	\| [[Undim]]		\| [[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:Hemifamity]]

ArrowHead294 at 22:40, 20 February 2025

2025-02-20T22:40:31Z

← Older revision		Revision as of 22:40, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T15:49:09Z

Theory: cleanup

← Older revision		Revision as of 15:49, 17 January 2025
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	== Theory ==		== 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 ===		=== Prime harmonics ===
Line 11:		Line 11:

	=== Subsets and supersets ===		=== 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 ==		== Regular temperament properties ==

ArrowHead294 at 14:06, 16 January 2025

2025-01-16T14:06:05Z

← Older revision		Revision as of 14:06, 16 January 2025
Line 3:		Line 3:

	== Theory ==		== 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]]. 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]].

	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]].
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	\| {{monzo\| 463 -292 }}		\| {{monzo\| 463 -292 }}
	\| {{mapping\| 292 463 }}		\| {{mapping\| 292 463 }}
	\| ~~−0~~.2476		\| −0.2476
	\| 0.2475		\| 0.2475
	\| 6.02		\| 6.02
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	\| {{monzo\| 3 -18 11 }}, {{monzo\| 38 -2 -15 }}		\| {{monzo\| 3 -18 11 }}, {{monzo\| 38 -2 -15 }}
	\| {{mapping\| 292 463 678 }}		\| {{mapping\| 292 463 678 }}
	\| ~~−0~~.1633		\| −0.1633
	\| 0.2346		\| 0.2346
	\| 5.71		\| 5.71
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	\| 5120/5103, 390625/388962, 420175/419904		\| 5120/5103, 390625/388962, 420175/419904
	\| {{mapping\| 292 463 678 820 }}		\| {{mapping\| 292 463 678 820 }}
	\| ~~−0~~.2148		\| −0.2148
	\| 0.2219		\| 0.2219
	\| 5.40		\| 5.40
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	\| 1375/1372, 5120/5103, 5632/5625, 14641/14580		\| 1375/1372, 5120/5103, 5632/5625, 14641/14580
	\| {{mapping\| 292 463 678 820 1010 }}		\| {{mapping\| 292 463 678 820 1010 }}
	\| ~~−0~~.1353		\| −0.1353
	\| 0.2544		\| 0.2544
	\| 6.19		\| 6.19
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	\| 352/351, 625/624, 847/845, 1716/1715, 14641/14580		\| 352/351, 625/624, 847/845, 1716/1715, 14641/14580
	\| {{mapping\| 292 463 678 820 1010 1081 }}		\| {{mapping\| 292 463 678 820 1010 1081 }}
	\| ~~−0~~.3480		\| −0.3480
	\| 0.2736		\| 0.2736
	\| 6.66		\| 6.66
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	\| 352/351, 625/624, 715/714, 847/845, 1225/1224, 2025/2023		\| 352/351, 625/624, 715/714, 847/845, 1225/1224, 2025/2023
	\| {{mapping\| 292 463 678 820 1010 1081 1194 }}		\| {{mapping\| 292 463 678 820 1010 1081 1194 }}
	\| ~~−0~~.2376		\| −0.2376
	\| 0.2696		\| 0.2696
	\| 6.56		\| 6.56
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	\| [[Undim]]		\| [[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 lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	[[Category:Hemifamity]]		[[Category:Hemifamity]]

ArrowHead294: Partial undo

2024-11-16T12:33:06Z

Partial undo

← Older revision		Revision as of 12:33, 16 November 2024
Line 14:		Line 14:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
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	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
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	\| 4/3		\| 4/3
	\| [[Undim]]		\| [[Undim]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	[[Category:Hemifamity]]		[[Category:Hemifamity]]

ArrowHead294 at 04:26, 16 November 2024

2024-11-16T04:26:51Z

← Older revision		Revision as of 04:26, 16 November 2024
Line 14:		Line 14:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|Comma List]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal<br>8ve Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{monzo\| 463 -292 }}		\| {{monzo\| 463 -292 }}
	\| {{mapping\| 292 463 }}		\| {{mapping\| 292 463 }}
	\| -0.2476		\| −0.2476
	\| 0.2475		\| 0.2475
	\| 6.02		\| 6.02
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	\| {{monzo\| 3 -18 11 }}, {{monzo\| 38 -2 -15 }}		\| {{monzo\| 3 -18 11 }}, {{monzo\| 38 -2 -15 }}
	\| {{mapping\| 292 463 678 }}		\| {{mapping\| 292 463 678 }}
	\| -0.1633		\| −0.1633
	\| 0.2346		\| 0.2346
	\| 5.71		\| 5.71
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	\| 5120/5103, 390625/388962, 420175/419904		\| 5120/5103, 390625/388962, 420175/419904
	\| {{mapping\| 292 463 678 820 }}		\| {{mapping\| 292 463 678 820 }}
	\| -0.2148		\| −0.2148
	\| 0.2219		\| 0.2219
	\| 5.40		\| 5.40
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	\| 1375/1372, 5120/5103, 5632/5625, 14641/14580		\| 1375/1372, 5120/5103, 5632/5625, 14641/14580
	\| {{mapping\| 292 463 678 820 1010 }}		\| {{mapping\| 292 463 678 820 1010 }}
	\| -0.1353		\| −0.1353
	\| 0.2544		\| 0.2544
	\| 6.19		\| 6.19
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	\| 352/351, 625/624, 847/845, 1716/1715, 14641/14580		\| 352/351, 625/624, 847/845, 1716/1715, 14641/14580
	\| {{mapping\| 292 463 678 820 1010 1081 }}		\| {{mapping\| 292 463 678 820 1010 1081 }}
	\| -0.3480		\| −0.3480
	\| 0.2736		\| 0.2736
	\| 6.66		\| 6.66
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	\| 352/351, 625/624, 715/714, 847/845, 1225/1224, 2025/2023		\| 352/351, 625/624, 715/714, 847/845, 1225/1224, 2025/2023
	\| {{mapping\| 292 463 678 820 1010 1081 1194 }}		\| {{mapping\| 292 463 678 820 1010 1081 1194 }}
	\| -0.2376		\| −0.2376
	\| 0.2696		\| 0.2696
	\| 6.56		\| 6.56
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	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
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	\| 4/3		\| 4/3
	\| [[Undim]]		\| [[Undim]]
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

	[[Category:Hemifamity]]		[[Category:Hemifamity]]

FloraC: Cleanup; +subsets and supersets

2024-03-04T09:10:17Z

Cleanup; +subsets and supersets

← Older revision		Revision as of 09:10, 4 March 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro~~\|292~~}}		{{EDO intro}}

	== Theory ==		== Theory ==
	292edo is closely related to [[146edo]], but the patent ~~vals~~ differ on the mapping for 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]]. 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]].

	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]].
Line 9:		Line 9:
	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|292}}		{{Harmonics in equal\|292}}

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

	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \| Subgroup		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br>8ve ~~stretch~~ (¢)		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	! colspan="2" \| Tuning ~~error~~		! colspan="2" \| Tuning Error
	\|-		\|-
	! [[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
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	\| 2.3		\| 2.3
	\| {{monzo\| 463 -292 }}		\| {{monzo\| 463 -292 }}
	\| [{{~~val~~\| 292 463 }}]		\| {{mapping\| 292 463 }}
	\| -0.2476		\| -0.2476
	\| 0.2475		\| 0.2475
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	\| 2.3.5		\| 2.3.5
	\| {{monzo\| 3 -18 11 }}, {{monzo\| 38 -2 -15 }}		\| {{monzo\| 3 -18 11 }}, {{monzo\| 38 -2 -15 }}
	\| [{{~~val~~\| 292 463 678 }}]		\| {{mapping\| 292 463 678 }}
	\| -0.1633		\| -0.1633
	\| 0.2346		\| 0.2346
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	\| 2.3.5.7		\| 2.3.5.7
	\| 5120/5103, 390625/388962, 420175/419904		\| 5120/5103, 390625/388962, 420175/419904
	\| [{{~~val~~\| 292 463 678 820 }}]		\| {{mapping\| 292 463 678 820 }}
	\| -0.2148		\| -0.2148
	\| 0.2219		\| 0.2219
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	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 1375/1372, 5120/5103, 5632/5625, 14641/14580		\| 1375/1372, 5120/5103, 5632/5625, 14641/14580
	\| [{{~~val~~\| 292 463 678 820 1010 }}]		\| {{mapping\| 292 463 678 820 1010 }}
	\| -0.1353		\| -0.1353
	\| 0.2544		\| 0.2544
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	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 352/351, 625/624, 847/845, 1716/1715, 14641/14580		\| 352/351, 625/624, 847/845, 1716/1715, 14641/14580
	\| [{{~~val~~\| 292 463 678 820 1010 1081 }}]		\| {{mapping\| 292 463 678 820 1010 1081 }}
	\| -0.3480		\| -0.3480
	\| 0.2736		\| 0.2736
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	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 352/351, 625/624, 715/714, 847/845, 1225/1224, 2025/2023		\| 352/351, 625/624, 715/714, 847/845, 1225/1224, 2025/2023
	\| [{{~~val~~\| 292 463 678 820 1010 1081 1194 }}]		\| {{mapping\| 292 463 678 820 1010 1081 1194 }}
	\| -0.2376		\| -0.2376
	\| 0.2696		\| 0.2696
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	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per ~~octave~~		! Periods<br>per 8ve
	! Generator~~<br>(reduced)~~		! Generator*
	! Cents~~<br>(reduced)~~		! Cents*
	! Associated<br>~~ratio~~		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\| [[Undim]]		\| [[Undim]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~
	[[Category:Hemifamity]]		[[Category:Hemifamity]]
	[[Category:Septiquarter]]		[[Category:Septiquarter]]
	[[Category:Semiluna]]		[[Category:Semiluna]]
	[[Category:Undim]]		[[Category:Undim]]

Plumtree: Infobox ET now computes most parameters automatically

2022-10-04T19:18:26Z

Infobox ET now computes most parameters automatically

← Older revision		Revision as of 19:18, 4 October 2022
Line 1:		Line 1:
	{{Infobox ET		{{Infobox ET}}
	~~\| Prime factorization = 2<sup>2</sup> × 73~~
	~~\| Step size = 4.10959¢~~
	~~\| Fifth = 171\292 (702.74¢)~~
	~~\| Semitones = 29:21 (119.18¢ : 86.30¢)~~
	~~\| Consistency = 9~~
	}}
	{{EDO intro\|292}}		{{EDO intro\|292}}

Fredg999 category edits: Sort key

2022-07-03T19:09:01Z

Sort key

← Older revision		Revision as of 19:09, 3 July 2022
Line 122:		Line 122:
	\|}		\|}

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
	[[Category:Hemifamity]]		[[Category:Hemifamity]]
	[[Category:Septiquarter]]		[[Category:Septiquarter]]
	[[Category:Semiluna]]		[[Category:Semiluna]]
	[[Category:Undim]]		[[Category:Undim]]