Greenwoodmic temperaments - Revision history

Jdood: /* Secund */ Fixed a typo: "mapping generaators" --> "mapping generators"

2025-11-29T20:31:07Z

Secund: Fixed a typo: "mapping generaators" --> "mapping generators"

← Older revision		Revision as of 20:31, 29 November 2025
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	{{Mapping\|legend=1\| 1 1 3 2 \| 0 5 -6 7 }}		{{Mapping\|legend=1\| 1 1 3 2 \| 0 5 -6 7 }}

	: mapping ~~generaators~~: ~2, ~16/15		: mapping generators: ~2, ~16/15

	[[Optimal tuning]]s:		[[Optimal tuning]]s:

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

2025-11-27T12:31:26Z

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

← Older revision		Revision as of 12:31, 27 November 2025
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	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Greenwoodmic temperaments\| ]] <!-- main article -->		[[Category:Greenwoodmic temperaments\| ]] <!-- main article -->
	[[Category:Greenwoodmic\| ]] <!-- key article -->		[[Category:Greenwoodmic\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

Lériendil: Text replacement - "Category:Temperament collections" to "Category:Temperament collections Category:Pages with mostly numerical content"

2025-06-24T00:26:30Z

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

← Older revision		Revision as of 00:26, 24 June 2025
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	[[Category:Temperament collections]]		[[Category:Temperament collections]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Greenwoodmic temperaments\| ]] <!-- main article -->		[[Category:Greenwoodmic temperaments\| ]] <!-- main article -->
	[[Category:Greenwoodmic\| ]] <!-- key article -->		[[Category:Greenwoodmic\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

VectorGraphics at 05:17, 12 June 2025

2025-06-12T05:17:18Z

← Older revision		Revision as of 05:17, 12 June 2025
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	: mapping generaators: ~2, ~16/15		: mapping generaators: ~2, ~16/15

	~~{{Multival\|legend=1\| 5 -6 7 -21 -3 33 }}~~

	[[Optimal tuning]]s:		[[Optimal tuning]]s:

Lériendil: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"

2025-04-13T13:47:34Z

Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"

← Older revision		Revision as of 13:47, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	This is a collection of [[rank-2 temperament\|rank-2]] [[temperament]]s [[tempering out]] the [[greenwoodma]], 405/392 ({{monzo\| -3 4 1 -2 }}).		This is a collection of [[rank-2 temperament\|rank-2]] [[temperament]]s [[tempering out]] the [[greenwoodma]], 405/392 ({{monzo\| -3 4 1 -2 }}).

BudjarnLambeth: {{Technical data page}}

2025-04-13T05:36:30Z

{{Technical data page}}<br><br>

← Older revision		Revision as of 05:36, 13 April 2025
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			{{Technical data page}}<br><br>
	This is a collection of [[rank-2 temperament\|rank-2]] [[temperament]]s [[tempering out]] the [[greenwoodma]], 405/392 ({{monzo\| -3 4 1 -2 }}).		This is a collection of [[rank-2 temperament\|rank-2]] [[temperament]]s [[tempering out]] the [[greenwoodma]], 405/392 ({{monzo\| -3 4 1 -2 }}).

FloraC: Update

2025-01-06T12:22:27Z

Update

← Older revision		Revision as of 12:22, 6 January 2025
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	* ''[[Injera]]'' (+50/49 or 81/80) → [[Meantone family #Injera\|Meantone family]]		* ''[[Injera]]'' (+50/49 or 81/80) → [[Meantone family #Injera\|Meantone family]]
	* ''[[Schism]]'' (+64/63) → [[Archytas clan #Schism\|Archytas clan]]		* ''[[Schism]]'' (+64/63) → [[Archytas clan #Schism\|Archytas clan]]
	* ''[[Greenwood]]'' (+1323/1280) → [[Whitewood family #Greenwood\|~~Apotome~~ family]]		* ''[[Greenwood]]'' (+1323/1280) → [[Whitewood family #Greenwood\|Whitewood family]]

	== Secund ==		== Secund ==

FloraC: Normalize mappings; +CTE and CWE tunings; +error maps;

2025-01-06T12:19:34Z

Normalize mappings; +CTE and CWE tunings; +error maps;

← Older revision		Revision as of 12:19, 6 January 2025
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	{{Mapping\|legend=1\| 1 1 3 2 \| 0 5 -6 7 }}		{{Mapping\|legend=1\| 1 1 3 2 \| 0 5 -6 7 }}

			: mapping generaators: ~2, ~16/15

	{{Multival\|legend=1\| 5 -6 7 -21 -3 33 }}		{{Multival\|legend=1\| 5 -6 7 -21 -3 33 }}

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
			* [[CTE]]: ~2 = 1200.000, ~16/15 = 138.454
			: [[error map]]: {{val\| 0.000 -9.684 -17.038 +0.353 }}
	* [[POTE]]: ~2 = 1200.000, ~16/15 = 137.958		* [[POTE]]: ~2 = 1200.000, ~16/15 = 137.958
			: error map: {{val\| 0.000 -12.167 -14.059 -3.123 }}

	{{Optimal ET sequence\|legend=1\| 9, 17, 26, 61bc, 87bcc }}		{{Optimal ET sequence\|legend=1\| 9, 17, 26, 61bc, 87bcc }}
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	Optimal tunings:		Optimal tunings:
			* CTE: ~2 = 1200.000, ~12/11 = 138.420
	* POTE: ~2 = 1200.000, ~12/11 = 137.900		* POTE: ~2 = 1200.000, ~12/11 = 137.900

	{{Optimal ET sequence\|legend=0\| 9, 17, 26, 61bc~~, 87bcc~~ }}		{{Optimal ET sequence\|legend=0\| 9, 17, 26, 61bc }}

	Badness (Smith): 0.042562		Badness (Smith): 0.042562
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	Optimal tunings:		Optimal tunings:
			* CTE: ~2 = 1200.000, ~12/11 = 137.455
	* POTE: ~2 = 1200.000, ~12/11 = 136.937		* POTE: ~2 = 1200.000, ~12/11 = 136.937

	{{Optimal ET sequence\|legend=0\| 9~~, 26f~~, 35 }}		{{Optimal ET sequence\|legend=0\| 9, 35 }}

	Badness (Smith): 0.049684		Badness (Smith): 0.049684
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	Optimal tunings:		Optimal tunings:
	* POTE: ~2 = 1200.000, ~12~~/11~~ = 137.917		* CTE: ~2 = 1200.000, ~13/12 = 138.583
			* POTE: ~2 = 1200.000, ~13/12 = 137.917

	{{Optimal ET sequence\|legend=0\| 9, 17, 26, 61bcf~~, 87bccf~~ }}		{{Optimal ET sequence\|legend=0\| 9, 17, 26, 61bcf }}

	Badness (Smith): 0.026212		Badness (Smith): 0.026212
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	[[Comma list]]: 405/392, 35721/32768		[[Comma list]]: 405/392, 35721/32768

	{{Mapping\|legend=1\| 2 ~~2 16 9~~ \| 0 1 -10 -3 }}		{{Mapping\|legend=1\| 2 0 36 15 \| 0 1 -10 -3 }}

			: mapping generators: ~189/128, ~3

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~189/128 = 600.000, ~3/2 = 681.532		* [[CTE]]: ~189/128 = 600.000, ~3/2 = 681.532 (~64/63 = 81.532)
			: [[error map]]: {{val\| 0.000 -20.423 -1.629 -13.421 }}
			* [[CWE]]: ~189/128 = 600.000, ~3/2 = 682.650 (~64/63 = 82.650)
			: error map: {{val\| 0.000 -19.305 -12.811 -16.775 }}

	~~[[Support]]ing [[ET]]s:~~ {{~~EDOs~~\| 14c~~, 30b~~, 44bd, 58bcd~~, 72bbccdd~~ }}		{{Optimal ET sequence\|legend=1\| 14c, 44bd, 58bcd }}

	[[Badness]] (Dirichlet): 8.420		[[Badness]]:
			* Smith: 0.333
			* Dirichlet: 8.420

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

	Comma list: 45/44, 99/98, ~~43659~~/~~40960~~		Comma list: 45/44, 99/98, 35721/32768

	Mapping: {{mapping\| 2 ~~2 16 9 16~~ \| 0 1 -10 -3 -8}}		Mapping: {{mapping\| 2 0 36 15 32 \| 0 1 -10 -3 -8 }}

	Optimal tunings:		Optimal tunings:
	* CTE: ~189/128 = 600.000, ~3/2 = 681.438		* CTE: ~189/128 = 600.000, ~3/2 = 681.438 (~64/63 = 81.438)
			* CWE: ~189/128 = 600.000, ~3/2 = 682.724 (~64/63 = 82.724)

	~~Supporting ETs:~~ {{~~EDOs~~\| 14c~~, 30b~~, 44bd, 58bcde, 72bbccddee }}		{{Optimal ET sequence\|legend=0\| 14c, 44bd, 58bcde, 72bbccddee }}

	Badness (Dirichlet): 4.148		Badness:
			* Smith: 0.125
			* Dirichlet: 4.148

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

	Comma list: 45/44~~, 27/26~~, 99/98, 35721/32768		Comma list: 27/26, 45/44, 99/98, 35721/32768

	Mapping: {{mapping\| 2 2 ~~16 9 16 4~~ \| 0 1 -10 -3 -8 3 }}		Mapping: {{mapping\| 2 0 36 15 32 -2 \| 0 1 -10 -3 -8 3 }}

	Optimal tunings:		Optimal tunings:
	* CTE: ~~~189~~/~~128~~ = 600.000, ~3/2 = 681.406		* CTE: ~91/64 = 600.000, ~3/2 = 681.406 (~64/63 = 81.406)
			* CWE: ~91/64 = 600.000, ~3/2 = 682.168 (~64/63 = 82.168)

	~~Supporting ETs:~~ {{~~EDOs~~\| 14c, 30b }}		{{Optimal ET sequence\|legend=0\| 14c, 30b }}

	Badness (Dirichlet): 4.377		Badness:
			* Smith: 0.106
			* Dirichlet: 4.377

	[[Category:Temperament collections]]		[[Category:Temperament collections]]

FloraC: Spell 1\1 etc. in decimal; note the badness metric being used; misc. cleanup

2025-01-06T11:39:05Z

Spell 1\1 etc. in decimal; note the badness metric being used; misc. cleanup

← Older revision		Revision as of 11:39, 6 January 2025
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	This is a collection of [[~~Rank~~-2 temperament\|rank-2]] [[temperament]]s [[tempering out]] the greenwoodma, {{monzo\| -3 4 1 -2 }} ~~= [[405/392]]~~.		This is a collection of [[rank-2 temperament\|rank-2]] [[temperament]]s [[tempering out]] the [[greenwoodma]], 405/392 ({{monzo\| -3 4 1 -2 }}).

	Temperaments discussed elsewhere are		Temperaments discussed elsewhere are
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	{{Multival\|legend=1\| 5 -6 7 -21 -3 33 }}		{{Multival\|legend=1\| 5 -6 7 -21 -3 33 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~16/15 = 137.958		[[Optimal tuning]]s:
			* [[POTE]]: ~2 = 1200.000, ~16/15 = 137.958

	{{Optimal ET sequence\|legend=1\| 9, 17, 26, 61bc, 87bcc }}		{{Optimal ET sequence\|legend=1\| 9, 17, 26, 61bc, 87bcc }}

	[[Badness]]: 0.089840		[[Badness]] (Smith): 0.089840

	=== 11-limit ===		=== 11-limit ===
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	Mapping: {{mapping\| 1 1 3 2 3 \| 0 5 -6 7 4 }}		Mapping: {{mapping\| 1 1 3 2 3 \| 0 5 -6 7 4 }}

	Optimal ~~tuning (~~POTE): ~2 = ~~1\1~~, ~12/11 = 137.900		Optimal tunings:
			* POTE: ~2 = 1200.000, ~12/11 = 137.900

	~~Optimal ET sequence:~~ {{Optimal ET sequence\| 9, 17, 26, 61bc, 87bcc }}		{{Optimal ET sequence\|legend=0\| 9, 17, 26, 61bc, 87bcc }}

	Badness: 0.042562		Badness (Smith): 0.042562

	==== 13-limit ====		==== 13-limit ====
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	Mapping: {{mapping\| 1 1 3 2 3 2 \| 0 5 -6 7 4 15 }}		Mapping: {{mapping\| 1 1 3 2 3 2 \| 0 5 -6 7 4 15 }}

	Optimal ~~tuning (~~POTE): ~2 = ~~1\1~~, ~12/11 = 136.937		Optimal tunings:
			* POTE: ~2 = 1200.000, ~12/11 = 136.937

	~~Optimal ET sequence:~~ {{Optimal ET sequence\| 9, 26f, 35 }}		{{Optimal ET sequence\|legend=0\| 9, 26f, 35 }}

	Badness: 0.049684		Badness (Smith): 0.049684

	==== Secundly ====		==== Secundly ====
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	Mapping: {{mapping\| 1 1 3 2 3 3 \| 0 5 -6 7 4 6 }}		Mapping: {{mapping\| 1 1 3 2 3 3 \| 0 5 -6 7 4 6 }}

	Optimal ~~tuning (~~POTE): ~2 = ~~1\1~~, ~12/11 = 137.917		Optimal tunings:
			* POTE: ~2 = 1200.000, ~12/11 = 137.917

	~~Optimal ET sequence:~~ {{Optimal ET sequence\| 9, 17, 26, 61bcf, 87bccf }}		{{Optimal ET sequence\|legend=0\| 9, 17, 26, 61bcf, 87bccf }}

	Badness: 0.026212		Badness (Smith): 0.026212

	== Semishallowtone ==		== Semishallowtone ==
	{{See also\|Shallowtone}}		{{See also\| Shallowtone }}

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

	[[Comma list]]: 405/392, 35721/32768		[[Comma list]]: 405/392, 35721/32768

	{{Mapping\|legend=1\| 2 2 16 9\|0 1 -10 -3}}		{{Mapping\|legend=1\| 2 2 16 9 \| 0 1 -10 -3 }}

	[[Optimal tuning]] ([[CTE]]): ~189/128 = ~~1\2~~, ~3/2 = 681.532		[[Optimal tuning]]s:
			* [[CTE]]: ~189/128 = 600.000, ~3/2 = 681.532

	[[Support]]ing [[ET]]s: {{EDOs\|14c, 30b, 44bd, 58bcd, 72bbccdd}}		[[Support]]ing [[ET]]s: {{EDOs\| 14c, 30b, 44bd, 58bcd, 72bbccdd }}

	~~Dirichlet~~ [[~~badness~~]]: 8.420		[[Badness]] (Dirichlet): 8.420

	=== 11-limit ===		=== 11-limit ===
	[[Subgroup]]: 2.3.5.7.11		Subgroup: 2.3.5.7.11

	[[Comma list]]: 45/44, 99/98, 43659/40960		Comma list: 45/44, 99/98, 43659/40960

	{{~~Mapping\|legend=1~~\| 2 2 16 9 16\|0 1 -10 -3 -8}}		Mapping: {{mapping\| 2 2 16 9 16 \| 0 1 -10 -3 -8}}

	[[Optimal ~~tuning]] ([[~~CTE~~]])~~: ~189/128 = ~~1\2~~, ~3/2 = 681.438		Optimal tunings:
			* CTE: ~189/128 = 600.000, ~3/2 = 681.438

	~~[[Support]]ing [[ET]]s~~: {{EDOs\|14c, 30b, 44bd, 58bcde, 72bbccddee}}		Supporting ETs: {{EDOs\| 14c, 30b, 44bd, 58bcde, 72bbccddee }}

	Dirichlet ~~[[badness]]~~: 4.148		Badness (Dirichlet): 4.148

	=== 13-limit ===		=== 13-limit ===
	[[Subgroup]]: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

	[[Comma list]]: 45/44, 27/26, 99/98, 35721/32768		Comma list: 45/44, 27/26, 99/98, 35721/32768

	{{~~Mapping\|legend=1~~\| 2 2 16 9 16 4\|0 1 -10 -3 -8 3}}		Mapping: {{mapping\| 2 2 16 9 16 4 \| 0 1 -10 -3 -8 3 }}

	[[Optimal ~~tuning]] ([[~~CTE~~]])~~: ~189/128 = ~~1\2~~, ~3/2 = 681.406		Optimal tunings:
			* CTE: ~189/128 = 600.000, ~3/2 = 681.406

	~~[[Support]]ing [[ET]]s~~: {{EDOs\|14c, 30b}}		Supporting ETs: {{EDOs\| 14c, 30b }}

	Dirichlet ~~[[badness]]~~: 4.377		Badness (Dirichlet): 4.377

	[[Category:Temperament collections]]		[[Category:Temperament collections]]

ArrowHead294 at 11:48, 5 January 2025

2025-01-05T11:48:42Z

← Older revision		Revision as of 11:48, 5 January 2025
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	* ''[[Sidi]]'' (+25/24) → [[Dicot family #Sidi\|Dicot family]]		* ''[[Sidi]]'' (+25/24) → [[Dicot family #Sidi\|Dicot family]]
	* ''[[August]]'' (+36/35) → [[Augmented family #August\|Augmented family]]		* ''[[August]]'' (+36/35) → [[Augmented family #August\|Augmented family]]
	* ''[[Superpelog]]'' (+49/48) → [[~~Slendro~~ clan #Superpelog\|~~Slendro~~ clan]]		* ''[[Superpelog]]'' (+49/48) → [[Semaphoresmic clan #Superpelog\|Semaphoresmic clan]]
	* ''[[Injera]]'' (+50/49 or 81/80) → [[Meantone family #Injera\|Meantone family]]		* ''[[Injera]]'' (+50/49 or 81/80) → [[Meantone family #Injera\|Meantone family]]
	* ''[[Schism]]'' (+64/63) → [[Archytas clan #Schism\|Archytas clan]]		* ''[[Schism]]'' (+64/63) → [[Archytas clan #Schism\|Archytas clan]]

← Older revision		Revision as of 11:48, 5 January 2025
Line 4:		Line 4:
	* ''[[Sidi]]'' (+25/24) → [[Dicot family #Sidi\|Dicot family]]		* ''[[Sidi]]'' (+25/24) → [[Dicot family #Sidi\|Dicot family]]
	* ''[[August]]'' (+36/35) → [[Augmented family #August\|Augmented family]]		* ''[[August]]'' (+36/35) → [[Augmented family #August\|Augmented family]]
	* ''[[Superpelog]]'' (+49/48) → [[~~Slendro~~ clan #Superpelog\|~~Slendro~~ clan]]		* ''[[Superpelog]]'' (+49/48) → [[Semaphoresmic clan #Superpelog\|Semaphoresmic clan]]
	* ''[[Injera]]'' (+50/49 or 81/80) → [[Meantone family #Injera\|Meantone family]]		* ''[[Injera]]'' (+50/49 or 81/80) → [[Meantone family #Injera\|Meantone family]]
	* ''[[Schism]]'' (+64/63) → [[Archytas clan #Schism\|Archytas clan]]		* ''[[Schism]]'' (+64/63) → [[Archytas clan #Schism\|Archytas clan]]