Luna family - Revision history

FloraC: Oops

2026-06-23T04:12:01Z

Oops

← Older revision		Revision as of 04:12, 23 June 2026
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	=== Overview to extensions ===		=== Overview to extensions ===
	[[Hemimean clan #Hemithirds\|Hemithirds]] (25 & 31), a strong extension of [[didacus]] that tempers out [[1029/1024]] alongside [[3136/3125]], might be considered the main [[7-limit]] extension to luna of practical interest, as [[7/4]] is found at only 5 generators. However, luna ~~(118 & 323)~~ is an undoubted microtemperament of the [[5-limit]] in its own right, supported by systems like [[118edo]] and [[441edo]], and therefore merits consideration of other extensions to the 7-limit, which are documented on this page. Though of very high complexity, they continue the level of accuracy of 5-limit luna.		[[Hemimean clan #Hemithirds\|Hemithirds]] (25 & 31), a strong extension of [[didacus]] that tempers out [[1029/1024]] alongside [[3136/3125]], might be considered the main [[7-limit]] extension to luna of practical interest, as [[7/4]] is found at only 5 generators. However, luna is an undoubted microtemperament of the [[5-limit]] in its own right, supported by systems like [[118edo]] and [[441edo]], and therefore merits consideration of other extensions to the 7-limit, which are documented on this page. Though of very high complexity, they continue the level of accuracy of 5-limit luna.

	Weak extensions of luna include hemiluna (87 & 323), semiluna (118 & 292), and subneutral (31 & 441).		Weak extensions of luna include hemiluna (87 & 323), semiluna (118 & 292), and subneutral (31 & 441).

FloraC: Complete the list of extensions

2026-06-23T04:11:05Z

Complete the list of extensions

← Older revision		Revision as of 04:11, 23 June 2026
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	=== Overview to extensions ===		=== Overview to extensions ===
	[[Hemimean clan #Hemithirds\|Hemithirds]], a strong extension of [[didacus]] that tempers out [[1029/1024]] alongside [[3136/3125]], might be considered the main [[7-limit]] extension to luna of practical interest, as [[7/4]] is found at only 5 generators. However, luna is an undoubted microtemperament of the [[5-limit]] in its own right, supported by systems like [[118edo]] and [[441edo]], and therefore merits consideration of other extensions to the 7-limit, which are documented on this page. Though of very high complexity, they continue the level of accuracy of 5-limit luna.		[[Hemimean clan #Hemithirds\|Hemithirds]] (25 & 31), a strong extension of [[didacus]] that tempers out [[1029/1024]] alongside [[3136/3125]], might be considered the main [[7-limit]] extension to luna of practical interest, as [[7/4]] is found at only 5 generators. However, luna (118 & 323) is an undoubted microtemperament of the [[5-limit]] in its own right, supported by systems like [[118edo]] and [[441edo]], and therefore merits consideration of other extensions to the 7-limit, which are documented on this page. Though of very high complexity, they continue the level of accuracy of 5-limit luna.

			Weak extensions of luna include hemiluna (87 & 323), semiluna (118 & 292), and subneutral (31 & 441).

	Temperaments discussed elsewhere include:		Temperaments discussed elsewhere include:

FloraC: Move subneutral here and note its gen isn't really subneutral in quality

2026-06-23T04:05:48Z

Move subneutral here and note its gen isn't really subneutral in quality

@@ Line 31: / Line 31: @@
 Temperaments discussed elsewhere include:
 * [[Hemithirds]] (+3136/3125) → [[Hemimean clan #Hemithirds|Hemimean clan]]
 == Lunatic ==
@@ Line 116: / Line 117: @@
 Badness (Sintel): 2.24
 [[Category:Temperament families]]
 [[Category:Luna family| ]] <!-- main article -->
 [[Category:Rank 2]]

FloraC: /* Hemiluna */ - 11- and 13-limit (not necessarily canonical)

2026-06-23T03:59:56Z

Hemiluna: - 11- and 13-limit (not necessarily canonical)

← Older revision		Revision as of 03:59, 23 June 2026
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	[[Badness]] (Sintel): 4.54		[[Badness]] (Sintel): 4.54

	~~=== 11-limit ===~~
	~~Subgroup: 2.3.5.7.11~~

	~~Comma list: 5632/5625, 14641/14580, 131072/130977~~

	~~Mapping: {{mapping\| 1 -26 6 92 -37 \| 0 30 -4 -97 44 }}~~

	~~Optimal tunings:~~
	* WE: ~2 = 1200.0004{{c}}, ~189/100 = 1103.4136{{c}} (~200/189 = 96.5868{{c}})
	* CWE: ~2 = 1200.0000{{c}}, ~189/100 = 1103.4133{{c}} (~200/189 = 96.5867{{c}})

	~~{{Optimal ET sequence\|legend=0\| 87, 236, 323, 410 }}~~

	~~Badness (Sintel): 3.31~~

	~~=== 13-limit ===~~
	~~Subgroup: 2.3.5.7.11.13~~

	~~Comma list: 676/675, 1001/1000, 4096/4095, 14641/14580~~

	~~Mapping: {{mapping\| 1 -26 6 92 -37 -34 \| 0 30 -4 -97 44 41 }}~~

	~~Optimal tunings:~~
	* WE: ~2 = 1200.0257{{c}}, ~189/100 = 1103.4377{{c}} (~143/135 = 96.5880{{c}})
	* CWE: ~2 = 1200.0000{{c}}, ~189/100 = 1103.4133{{c}} (~143/135 = 96.5869{{c}})

	~~{{Optimal ET sequence\|legend=0\| 87, 236, 323, 410 }}~~

	~~Badness (Sintel): 1.91~~

	== Semiluna ==		== Semiluna ==

FloraC: Switch to Sintel's badness, WE & CWE tunings (2/2)

2026-06-23T03:57:47Z

Switch to Sintel's badness, WE & CWE tunings (2/2)

← Older revision		Revision as of 03:57, 23 June 2026
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	[[Comma list]]: 48828125/48771072, 67108864/66976875		[[Comma list]]: 48828125/48771072, 67108864/66976875

	{{Mapping\|legend=1\| 1 ~~4 2~~ -5 \| 0 -30 4 97 }}		{{Mapping\|legend=1\| 1 -26 6 92 \| 0 30 -4 -97 }}
	: mapping generators: ~2, ~~~200~~/~~189~~		: mapping generators: ~2, ~189/100

	[[Optimal tuning]] ([[~~POTE~~]]): ~2 = 1200.~~000~~{{c}}, ~200/189 = 96.~~591~~{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.9023{{c}}, ~189/100 = 1103.3197{{c}} (~200/189 = 96.5827{{c}})
			: [[error map]]: {{val\| -0.098 +0.175 -0.178 +0.180 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~189/100 = 1103.4097{{c}} (~200/189 = 96.5903{{c}})
			: error map: {{val\| 0.000 +0.336 +0.047 +0.432 }}

	{{Optimal ET sequence\|legend=1\| 87, 236, 323, 410, 733, 1056, 1789bd, 2845bdd }}		{{Optimal ET sequence\|legend=1\| 87, 236, 323, 410, 733, 1056, 1789bd, 2845bdd }}

	[[Badness]] (~~Smith~~): 0.~~179304~~		[[Badness]] (Sintel): 4.54

	=== 11-limit ===		=== 11-limit ===
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	Comma list: 5632/5625, 14641/14580, 131072/130977		Comma list: 5632/5625, 14641/14580, 131072/130977

	Mapping: {{mapping\| 1 ~~4 2~~ -~~5 7~~ \| 0 -30 4 97 -44 }}		Mapping: {{mapping\| 1 -26 6 92 -37 \| 0 30 -4 -97 44 }}

	Optimal ~~tuning~~ (~~POTE~~): ~2 = 1200.~~000~~{{c}}, ~200/189 = 96.~~587~~{{c}}		Optimal tunings:
			* WE: ~2 = 1200.0004{{c}}, ~189/100 = 1103.4136{{c}} (~200/189 = 96.5868{{c}})
			* CWE: ~2 = 1200.0000{{c}}, ~189/100 = 1103.4133{{c}} (~200/189 = 96.5867{{c}})

	{{Optimal ET sequence\|legend=0\| 87, 236, 323, 410 }}		{{Optimal ET sequence\|legend=0\| 87, 236, 323, 410 }}

	Badness (~~Smith~~): 0.~~100077~~		Badness (Sintel): 3.31

	=== 13-limit ===		=== 13-limit ===
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	Comma list: 676/675, 1001/1000, 4096/4095, 14641/14580		Comma list: 676/675, 1001/1000, 4096/4095, 14641/14580

	Mapping: {{mapping\| 1 ~~4 2~~ -~~5 7 7~~ \| 0 -30 4 97 -44 -41 }}		Mapping: {{mapping\| 1 -26 6 92 -37 -34 \| 0 30 -4 -97 44 41 }}

	Optimal ~~tuning~~ (~~POTE~~): ~2 = 1200.~~000~~{{c}}, ~143/135 = 96.~~586~~{{c}}		Optimal tunings:
			* WE: ~2 = 1200.0257{{c}}, ~189/100 = 1103.4377{{c}} (~143/135 = 96.5880{{c}})
			* CWE: ~2 = 1200.0000{{c}}, ~189/100 = 1103.4133{{c}} (~143/135 = 96.5869{{c}})

	{{Optimal ET sequence\|legend=0\| 87, 236, 323, 410 }}		{{Optimal ET sequence\|legend=0\| 87, 236, 323, 410 }}

	Badness (~~Smith~~): 0.~~046151~~		Badness (Sintel): 1.91

	== Semiluna ==		== Semiluna ==
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	[[Comma list]]: 4802000/4782969, 95703125/95551488		[[Comma list]]: 4802000/4782969, 95703125/95551488

	{{Mapping\|legend=1\| 2 ~~8 4 23~~ \| 0 -15 2 -54 }}		{{Mapping\|legend=1\| 2 -7 6 -31 \| 0 15 -2 54 }}
	: mapping generators: ~10125/7168, ~~~2187~~/~~1960~~		: mapping generators: ~10125/7168, ~4375/3456

	[[Optimal tuning]] ([[~~POTE~~]]): ~99/70 = 600.0000{{c}}, ~2187/1960 = 193.~~1725~~{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~10125/7168 = 600.0000{{c}}, ~4375/3456 = 406.8061{{c}} (~2187/1960 = 193.1624{{c}})
			: [[error map]]: {{val\| -0.063 +0.358 -0.115 -0.318 }}
			* [[CWE]]: ~10125/7168 = 600.0000{{c}}, ~4375/3456 = 406.8263{{c}} (~2187/1960 = 193.1737{{c}})
			: error map: {{val\| 0.000 +0.440 +0.034 -0.203 }}

	{{Optimal ET sequence\|legend=1\| 56d, 118, 292, 410 }}		{{Optimal ET sequence\|legend=1\| 56d, 118, 292, 410 }}

	[[Badness]] (~~Smith~~): 0.~~192167~~		[[Badness]] (Sintel): 4.86

	=== 11-limit ===		=== 11-limit ===
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	Comma list: 5632/5625, 9801/9800, 14641/14580		Comma list: 5632/5625, 9801/9800, 14641/14580

	Mapping: {{mapping\| 2 8 ~~4 23 14~~ \| 0 -15 2 -54 -22 }}		Mapping: {{mapping\| 2 -7 6 -31 -8 \| 0 15 -2 54 22 }}

	Optimal ~~tuning~~ (~~POTE~~): ~99/70 = 600.0000{{c}}, ~121/108 = 193.~~1732~~{{c}}		Optimal tunings:
			* WE: ~99/70 = 600.0093{{c}}, ~486/385 = 406.8331{{c}} (~121/108 = 193.1762{{c}})
			* CWE: ~99/70 = 600.0000{{c}}, ~486/385 = 406.8272{{c}} (~121/108 = 193.1728{{c}})

	{{Optimal ET sequence\|legend=0\| 56d, 118, 292, 410 }}		{{Optimal ET sequence\|legend=0\| 56d, 118, 292, 410 }}

	Badness (~~Smith~~): 0.~~067783~~		Badness (Sintel): 2.24

	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Luna family\| ]] <!-- main article -->		[[Category:Luna family\| ]] <!-- main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: Switch to Sintel's badness, WE & CWE tunings (1/)

2026-06-23T03:32:50Z

Switch to Sintel's badness, WE & CWE tunings (1/)

← Older revision		Revision as of 03:32, 23 June 2026
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	{{See also\| Luna and hemithirds }}		{{See also\| Luna and hemithirds }}

	Luna divides [[16/3]] into fifteen parts, two of which make [[5/4]]. It also divides [[9/8]] in five and [[3/2]] in three.		Luna divides [[16/3]] into fifteen parts, two of which make [[5/4]]. It has a [[ploidacot]] signature of 12-sheared 15-cot (or beta-seph). It also divides [[9/8]] in five and [[3/2]] in three. It is part of the [[syntonic–31 equivalence continuum]] with {{nowrap\| ''n'' {{=}} 15/2 }}.

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5
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	[[Comma list]]: 274877906944/274658203125		[[Comma list]]: 274877906944/274658203125

	{{Mapping\|legend=1\| 1 4 2 \| 0 -15 2 }}		{{Mapping\|legend=1\| 1 -11 4 \| 0 15 -2 }}
	: mapping generators: ~2, ~~~262144~~/~~234375~~		: mapping generators: ~2, ~234375/131072

	[[Optimal tuning]] ([[~~POTE~~]]): ~2 = 1200.~~000~~{{c}}, ~262144/234375 = 193.~~201~~{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.9803{{c}}, ~234375/131072 = 1006.7827{{c}} (~262144/234375 = 193.1976{{c}})
			: [[error map]]: {{val\| -0.020 +0.003 +0.042 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~234375/131072 = 1006.7987{{c}} (~262144/234375 = 193.2013{{c}})
			: error map: {{val\| 0.000 +0.025 +0.089 }}

	{{Optimal ET sequence\|legend=1\| 25, 31, 56, 87, 118, 323, 441, 559, 1000, 1559 }}		{{Optimal ET sequence\|legend=1\| 25, 31, 56, 87, 118, 323, 441, 559, 1000, 1559, 15031cc, 16590cc, …, 21267bccc }}

	[[Badness]] (~~Smith~~): 0.~~020576~~		[[Badness]] (Sintel): 0.483

	; Music		; Music
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	[[Comma list]]: 4375/4374, 274877906944/274658203125		[[Comma list]]: 4375/4374, 274877906944/274658203125

	{{Mapping\|legend=1\| 1 4 ~~2 21~~ \| 0 -15 2 -113 }}		{{Mapping\|legend=1\| 1 -11 4 -92 \| 0 15 -2 113 }}

	[[Optimal tuning]] ([[~~POTE~~]]): ~2 = 1200.~~000~~{{c}}, ~262144/234375 = 193.~~196~~{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.9687{{c}}, ~234375/131072 = 1006.7781{{c}} (~262144/234375 = 193.1906{{c}})
			: [[error map]]: {{val\| -0.031 +0.060 +0.005 -0.025 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~234375/131072 = 1006.8041{{c}} (~262144/234375 = 193.1959{{c}})
			: error map: {{val\| 0.000 +0.106 +0.078 +0.035 }}

	{{Optimal ET sequence\|legend=1\| 87d, 118, 323, 441, 1205, 1646 }}		{{Optimal ET sequence\|legend=1\| 87d, 118, 323, 441, 1205, 1646, 8671bc, 10317bcd, 11963bbcd }}

	[[Badness]] (~~Smith~~): 0.~~037966~~		[[Badness]] (Sintel): 0.961

	=== 11-limit ===		=== 11-limit ===
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	Comma list: 4375/4374, 12005/11979, 172032/171875		Comma list: 4375/4374, 12005/11979, 172032/171875

	Mapping: {{mapping\| 1 4 ~~2 21 14~~ \| 0 -15 2 -113 -140 }}		Mapping: {{mapping\| 1 -11 4 -92 -114 \| 0 15 -2 113 140 }}

	Optimal ~~tuning~~ (~~POTE~~): ~2 = 1200.000{{c}}, ~352/315 = 193.~~200~~{{c}}		Optimal tunings:
			* WE: ~2 = 1200.000{{c}}, ~315/176 = 1006.7823{{c}} (~352/315 = 193.1967{{c}})
			* CWE: ~2 = 1200.000{{c}}, ~315/176 = 1006.7998{{c}} (~352/315 = 193.2002{{c}})

	{{Optimal ET sequence\|legend=0\| 118, 323e, 441, 559, 1000e }}		{{Optimal ET sequence\|legend=0\| 118, 323e, 441, 559, 1000e }}

	Badness (~~Smith~~): 0.~~058588~~		Badness (Sintel): 1.94

	== Hemiluna ==		== Hemiluna ==

FloraC: Re-organize

2026-06-23T03:13:47Z

Re-organize

← Older revision		Revision as of 03:13, 23 June 2026
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	{{Technical data page}}		{{Technical data page}}
	The '''luna family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[luna comma]], 274877906944/274658203125, which has a monzo of {{monzo\| 38 -2 -15 }}. ~~It divides [[16/3]] into fifteen parts, two of which make [[5/4]]. It also divides [[9/8]] in five and [[3/2]] in three.~~		The '''luna family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[luna comma]], 274877906944/274658203125, which has a monzo of {{monzo\| 38 -2 -15 }}.

	~~Temperaments discussed elsewhere include:~~
	* ''[[Subneutral]]'' (+2401/2400) → [[Breedsmic temperaments #Subneutral\|Breedsmic temperaments]]
	* [[Hemithirds]] (+3136/3125) → [[Hemimean clan #Hemithirds\|Hemimean clan]]

	== Luna ==		== Luna ==
	{{See also\| Luna and hemithirds }}		{{See also\| Luna and hemithirds }}

	[[~~Hemimean clan #Hemithirds\|Hemithirds]], a strong extension of [[didacus]] that tempers out [[1029~~/~~1024]] alongside [[3136/3125~~]], ~~might be considered the main [[7-limit]] extension to luna~~ of ~~practical interest, as~~ [[7/4]] ~~is found at only 5 generators~~. ~~However, luna is an undoubted microtemperament of the~~ [[~~5-limit~~]] in ~~its own right, supported by systems like [[118edo]]~~ and [[~~441edo~~]]~~, and therefore merits consideration of other extensions to the 7-limit, which are documented on this page. Though of very high complexity, they continue the level of accuracy of 5-limit luna~~.		Luna divides [[16/3]] into fifteen parts, two of which make [[5/4]]. It also divides [[9/8]] in five and [[3/2]] in three.

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5
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	; Music		; Music
	* "Moongazing" from ''Lesser Groove'' (2020) – [https://xotla.bandcamp.com/track/moongazing-luna-25 Bandcamp] \| [https://www.youtube.com/watch?v=EWuVnLOcaRg YouTube] – atmospheric-electro, Luna[25] in 1000edo by [[Xotla]]		* "Moongazing" from ''Lesser Groove'' (2020) – [https://xotla.bandcamp.com/track/moongazing-luna-25 Bandcamp] \| [https://www.youtube.com/watch?v=EWuVnLOcaRg YouTube] – atmospheric-electro, Luna[25] in 1000edo by [[Xotla]]

			=== Overview to extensions ===
			[[Hemimean clan #Hemithirds\|Hemithirds]], a strong extension of [[didacus]] that tempers out [[1029/1024]] alongside [[3136/3125]], might be considered the main [[7-limit]] extension to luna of practical interest, as [[7/4]] is found at only 5 generators. However, luna is an undoubted microtemperament of the [[5-limit]] in its own right, supported by systems like [[118edo]] and [[441edo]], and therefore merits consideration of other extensions to the 7-limit, which are documented on this page. Though of very high complexity, they continue the level of accuracy of 5-limit luna.

			Temperaments discussed elsewhere include:
			* ''[[Subneutral]]'' (+2401/2400) → [[Breedsmic temperaments #Subneutral\|Breedsmic temperaments]]
			* [[Hemithirds]] (+3136/3125) → [[Hemimean clan #Hemithirds\|Hemimean clan]]

	== Lunatic ==		== Lunatic ==

FloraC: Units, misc. cleanup, - redundant category

2026-06-22T09:26:06Z

Units, misc. cleanup, - redundant category

← Older revision		Revision as of 09:26, 22 June 2026
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	{{Technical data page}}		{{Technical data page}}
	The '''luna family''' tempers out the [[luna comma]], 274877906944/274658203125, which has a monzo of {{monzo\| 38 -2 -15 }}. It divides [[16/3]] into fifteen parts, two of which make [[5/4]]. It also divides [[9/8]] in five and [[3/2]] in three.		The '''luna family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[luna comma]], 274877906944/274658203125, which has a monzo of {{monzo\| 38 -2 -15 }}. It divides [[16/3]] into fifteen parts, two of which make [[5/4]]. It also divides [[9/8]] in five and [[3/2]] in three.

	Temperaments discussed elsewhere include:		Temperaments discussed elsewhere include:
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	== Luna ==		== Luna ==
	{{~~see~~ also\|Luna and hemithirds}}		{{See also\| Luna and hemithirds }}

	[[Hemimean clan #Hemithirds\|Hemithirds]], a strong extension of [[didacus]] that tempers out [[1029/1024]] alongside [[3136/3125]], might be considered the main [[7-limit]] extension to luna of practical interest, as [[7/4]] is found at only 5 generators. However, luna is an undoubted microtemperament of the [[5-limit]] in its own right, supported by systems like [[118edo]] and [[441edo]], and therefore merits consideration of other extensions to the 7-limit, which are documented on this page. Though of very high complexity, they continue the level of accuracy of 5-limit luna.		[[Hemimean clan #Hemithirds\|Hemithirds]], a strong extension of [[didacus]] that tempers out [[1029/1024]] alongside [[3136/3125]], might be considered the main [[7-limit]] extension to luna of practical interest, as [[7/4]] is found at only 5 generators. However, luna is an undoubted microtemperament of the [[5-limit]] in its own right, supported by systems like [[118edo]] and [[441edo]], and therefore merits consideration of other extensions to the 7-limit, which are documented on this page. Though of very high complexity, they continue the level of accuracy of 5-limit luna.
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	{{Mapping\|legend=1\| 1 4 2 \| 0 -15 2 }}		{{Mapping\|legend=1\| 1 4 2 \| 0 -15 2 }}
			: mapping generators: ~2, ~262144/234375

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~262144/234375 = 193.201		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~262144/234375 = 193.201{{c}}

	{{Optimal ET sequence\|legend=1\| 25, 31, 56, 87, 118, 323, 441, 559, 1000, 1559 }}		{{Optimal ET sequence\|legend=1\| 25, 31, 56, 87, 118, 323, 441, 559, 1000, 1559 }}

	[[Badness]]: 0.020576		[[Badness]] (Smith): 0.020576

	; Music		; Music
	* "Moongazing" from ''Lesser Groove'' (2020) [https://xotla.bandcamp.com/track/moongazing-luna-25 Bandcamp] \| [https://www.youtube.com/watch?v=EWuVnLOcaRg YouTube] – atmospheric-electro, ~~luna~~[25] in 1000edo by [[Xotla]]		* "Moongazing" from ''Lesser Groove'' (2020) – [https://xotla.bandcamp.com/track/moongazing-luna-25 Bandcamp] \| [https://www.youtube.com/watch?v=EWuVnLOcaRg YouTube] – atmospheric-electro, Luna[25] in 1000edo by [[Xotla]]

	== Lunatic ==		== Lunatic ==
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	{{Mapping\|legend=1\| 1 4 2 21 \| 0 -15 2 -113 }}		{{Mapping\|legend=1\| 1 4 2 21 \| 0 -15 2 -113 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~262144/234375 = 193.196		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~262144/234375 = 193.196{{c}}

	{{Optimal ET sequence\|legend=1\| 87d, 118, 323, 441, 1205, 1646 }}		{{Optimal ET sequence\|legend=1\| 87d, 118, 323, 441, 1205, 1646 }}

	[[Badness]]: 0.037966		[[Badness]] (Smith): 0.037966

	=== 11-limit ===		=== 11-limit ===
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	Mapping: {{mapping\| 1 4 2 21 14 \| 0 -15 2 -113 -140 }}		Mapping: {{mapping\| 1 4 2 21 14 \| 0 -15 2 -113 -140 }}

	Optimal tuning (POTE): ~2 = ~~1\1~~, ~352/315 = 193.200		Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~352/315 = 193.200{{c}}

	{{Optimal ET sequence\|legend=1\| 118, 323e, 441, 559, 1000e }}		{{Optimal ET sequence\|legend=0\| 118, 323e, 441, 559, 1000e }}

	Badness: 0.058588		Badness (Smith): 0.058588

	== Hemiluna ==		== Hemiluna ==
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	{{Mapping\|legend=1\| 1 4 2 -5 \| 0 -30 4 97 }}		{{Mapping\|legend=1\| 1 4 2 -5 \| 0 -30 4 97 }}

	: mapping generators: ~2, ~200/189		: mapping generators: ~2, ~200/189

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~200/189 = 96.591		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~200/189 = 96.591{{c}}

	{{Optimal ET sequence\|legend=1\| 87, 236, 323, 410, 733, 1056, 1789bd, 2845bdd }}		{{Optimal ET sequence\|legend=1\| 87, 236, 323, 410, 733, 1056, 1789bd, 2845bdd }}

	[[Badness]]: 0.179304		[[Badness]] (Smith): 0.179304

	=== 11-limit ===		=== 11-limit ===
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	Mapping: {{mapping\| 1 4 2 -5 7 \| 0 -30 4 97 -44 }}		Mapping: {{mapping\| 1 4 2 -5 7 \| 0 -30 4 97 -44 }}

	Optimal tuning (POTE): ~2 = ~~1\1~~, ~200/189 = 96.587		Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~200/189 = 96.587{{c}}

	{{Optimal ET sequence\|legend=1\| 87, 236, 323, 410 }}		{{Optimal ET sequence\|legend=0\| 87, 236, 323, 410 }}

	Badness: 0.100077		Badness (Smith): 0.100077

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 1 4 2 -5 7 7 \| 0 -30 4 97 -44 -41 }}		Mapping: {{mapping\| 1 4 2 -5 7 7 \| 0 -30 4 97 -44 -41 }}

	Optimal tuning (POTE): ~2 = ~~1\1~~, ~143/135 = 96.586		Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~143/135 = 96.586{{c}}

	{{Optimal ET sequence\|legend=1\| 87, 236, 323, 410 }}		{{Optimal ET sequence\|legend=0\| 87, 236, 323, 410 }}

	Badness: 0.046151		Badness (Smith): 0.046151

	== Semiluna ==		== Semiluna ==
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	{{Mapping\|legend=1\| 2 8 4 23 \| 0 -15 2 -54 }}		{{Mapping\|legend=1\| 2 8 4 23 \| 0 -15 2 -54 }}

	: mapping generators: ~10125/7168, ~2187/1960		: mapping generators: ~10125/7168, ~2187/1960

	[[Optimal tuning]] ([[POTE]]): ~99/70 = ~~1\2~~, ~2187/1960 = 193.1725		[[Optimal tuning]] ([[POTE]]): ~99/70 = 600.0000{{c}}, ~2187/1960 = 193.1725{{c}}

	{{Optimal ET sequence\|legend=1\| 56d, 118, 292, 410 }}		{{Optimal ET sequence\|legend=1\| 56d, 118, 292, 410 }}

	[[Badness]]: 0.192167		[[Badness]] (Smith): 0.192167

	=== 11-limit ===		=== 11-limit ===
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	Mapping: {{mapping\| 2 8 4 23 14 \| 0 -15 2 -54 -22 }}		Mapping: {{mapping\| 2 8 4 23 14 \| 0 -15 2 -54 -22 }}

	Optimal tuning (POTE): ~99/70 = ~~1\2~~, ~121/108 = 193.1732		Optimal tuning (POTE): ~99/70 = 600.0000{{c}}, ~121/108 = 193.1732{{c}}

	{{Optimal ET sequence\|legend=1\| 56d, 118, 292, 410 }}		{{Optimal ET sequence\|legend=0\| 56d, 118, 292, 410 }}

	Badness: 0.067783		Badness (Smith): 0.067783

	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Luna family\| ]] <!-- main article -->		[[Category:Luna family\| ]] <!-- main article -->
	~~[[Category:Luna\| ]] <!-- key article -->~~
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

2025-11-27T12:24:39Z

Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

← Older revision		Revision as of 12:24, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Luna family\| ]] <!-- main article -->		[[Category:Luna family\| ]] <!-- main article -->
	[[Category:Luna\| ]] <!-- key article -->		[[Category:Luna\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

Lériendil at 04:59, 17 July 2025

2025-07-17T04:59:44Z

← Older revision		Revision as of 04:59, 17 July 2025
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	{{Technical data page}}		{{Technical data page}}
	The '''luna family''' tempers out the [[~~hemithirds~~ comma]] ~~aka luna comma~~, 274877906944/274658203125, which has a monzo of {{monzo\| 38 -2 -15 }}. It divides [[16/3]] into fifteen parts, two of which make [[5/4]]. It also divides [[9/8]] in five and [[3/2]] in three.		The '''luna family''' tempers out the [[luna comma]], 274877906944/274658203125, which has a monzo of {{monzo\| 38 -2 -15 }}. It divides [[16/3]] into fifteen parts, two of which make [[5/4]]. It also divides [[9/8]] in five and [[3/2]] in three.

	Temperaments discussed elsewhere include:		Temperaments discussed elsewhere include: