User:BudjarnLambeth/Table of n-comma meantone generators - Revision history

BudjarnLambeth: /* Sharper than sharpest negative harmonic-defined meantone */

2025-11-13T23:15:47Z

Sharper than sharpest negative harmonic-defined meantone

← Older revision		Revision as of 23:15, 13 November 2025
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	\|-		\|-
	\|}		\|}

			== See also ==
			* [[User:BudjarnLambeth/Some tunings for Japanese scales]] (includes several meantone tunings)

	[[Category:Tables]]		[[Category:Tables]]
	[[Category:Meantone]]		[[Category:Meantone]]

ArrowHead294 at 14:29, 8 June 2025

2025-06-08T14:29:08Z

← Older revision		Revision as of 14:29, 8 June 2025
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	{{Editable user page}}		{{DISPLAYTITLE:User:BudjarnLambeth/Table of ''n''-comma meantone generators}}{{Editable user page}}

	Here are all [[meantone]] tunings that can be written in the form "n-comma meantone", where the syntonic comma ([[81/80]]) is being divided and n is a fraction between -1 and 1 with a denominator 22 or smaller.		Here are all [[meantone]] tunings that can be written in the form "n-comma meantone", where the syntonic comma ([[81/80]]) is being divided and n is a fraction between -1 and 1 with a denominator 22 or smaller.

ArrowHead294: Undid revision 198849 by ArrowHead294 (talk)

2025-06-06T13:32:43Z

Undid revision 198849 by ArrowHead294 (talk)

← Older revision		Revision as of 13:32, 6 June 2025
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	{{Editable user page~~}}{{DISPLAYTITLE:User:BudjarnLambeth/Table of ''n''-comma menatone generators~~}}		{{Editable user page}}

	Here are all [[meantone]] tunings that can be written in the form "n-comma meantone", where the syntonic comma ([[81/80]]) is being divided and n is a fraction between -1 and 1 with a denominator 22 or smaller.		Here are all [[meantone]] tunings that can be written in the form "n-comma meantone", where the syntonic comma ([[81/80]]) is being divided and n is a fraction between -1 and 1 with a denominator 22 or smaller.

ArrowHead294 at 13:32, 6 June 2025

2025-06-06T13:32:22Z

← Older revision		Revision as of 13:32, 6 June 2025
Line 1:		Line 1:
	{{Editable user page}}		{{Editable user page}}{{DISPLAYTITLE:User:BudjarnLambeth/Table of ''n''-comma menatone generators}}

	Here are all [[meantone]] tunings that can be written in the form "n-comma meantone", where the syntonic comma ([[81/80]]) is being divided and n is a fraction between -1 and 1 with a denominator 22 or smaller.		Here are all [[meantone]] tunings that can be written in the form "n-comma meantone", where the syntonic comma ([[81/80]]) is being divided and n is a fraction between -1 and 1 with a denominator 22 or smaller.

Moremajorthanmajor: /* Negative harmony theory-defined meantone (most often approached as superpyth) */

2025-01-14T03:17:07Z

Negative harmony theory-defined meantone (most often approached as superpyth)

← Older revision		Revision as of 03:17, 14 January 2025
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	\|About as sharp of [[Pythagorean tuning]] as [[31edo]] is flat.		\|About as sharp of [[Pythagorean tuning]] as [[31edo]] is flat.
	\|-		\|-
	\|[[~~Negative Quarter~~-comma meantone\|~~Negative Quarter~~-comma]]		\|[[-1/4-comma meantone\|-1/4-comma]]
	\|707.332		\|707.332
	\|		\|

Moremajorthanmajor: /* The table */

2025-01-14T02:54:27Z

The table

← Older revision		Revision as of 02:54, 14 January 2025
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	\|		\|
	\|-		\|-
	\|[[~~Golden ratio~~-comma meantone\|~~Golden ratio~~-comma]]		\|[[1/φ-comma meantone\|1/ϕ-comma]]
	\|688.663		\|688.663
	\|		\|
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	\|[[5/13-comma meantone\|5/13-comma]] \|\|693.683\|\|		\|[[5/13-comma meantone\|5/13-comma]] \|\|693.683\|\|
	\|-		\|-
	\|[[~~Split golden ratio~~-comma meantone\|~~Split golden ratio~~-comma]]		\|[[1/(φ+1)-comma meantone\|1/(ϕ+1)-comma]]
	\|693.740		\|693.740
	\|Close to [[64edo]].		\|Close to [[64edo]].
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	\|		\|
	\|-		\|-
	\|[[~~Negative split golden ratio~~-comma meantone\|~~Negative split golden ratio~~-comma]]		\|[[-1/(φ+1)-comma meantone\|-1/(ϕ+1)-comma]]
	\|710.170		\|710.170
	\|Close to [[11-limit]] superpyth POTE tuning.		\|Close to [[11-limit]] superpyth POTE tuning.
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	\|		\|
	\|-		\|-
	\|[[~~Negative golden ratio~~-comma meantone\|~~Negative golden ratio~~-comma]]		\|[[-1/φ-comma meantone\|-1/ϕ-comma]]
	\|715.247		\|715.247
	\|		\|

Moremajorthanmajor: /* The table */

2025-01-13T20:34:59Z

The table

← Older revision		Revision as of 20:34, 13 January 2025
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	\|		\|
	\|-		\|-
	\|[[5/8-comma meantone\|5/8-comma]] \|\|688.514\|\|Close to [[61edo]].		\|[[5/8-comma meantone\|5/8-comma]] \|\|688.514\|\|Close to [[61edo]] and [[43/32]].
	\|-		\|-
	\|[[13/21-comma meantone\|13/21-comma]]		\|[[13/21-comma meantone\|13/21-comma]]
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	\|[[-5/8-comma meantone\|-5/8-comma]]		\|[[-5/8-comma meantone\|-5/8-comma]]
	\|715.396		\|715.396
	\|Close to [[52edo]].		\|Close to [[52edo]] and 387/256.
	\|-		\|-
	\|[[-12/19-comma meantone\|-12/19-comma]]		\|[[-12/19-comma meantone\|-12/19-comma]]

BudjarnLambeth: Add superpyth CTE and POTE

2024-12-29T02:36:55Z

Add superpyth CTE and POTE

← Older revision		Revision as of 02:36, 29 December 2024
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	* Whether it saw historical (pre-1950) use		* Whether it saw historical (pre-1950) use
	* Whether it is close to (i.e. within 1/2 a degree of closing of) an [[edo]] smaller than 100		* Whether it is close to (i.e. within 1/2 a degree of closing of) an [[edo]] smaller than 100
	* Whether it is the closest on the table to the optimal [[CTE]] or [[POTE]] tuning of meantone in any ~~prime~~ limit ~~5, 7, 11 or 13~~		* Whether it is the closest on the table to the optimal [[CTE]] or [[POTE]] tuning of meantone or [[superpyth]] in any JI [[limit]]
	* Whether it approximates a very simple n-[[Pythagorean comma]] meantone		* Whether it approximates a very simple n-[[Pythagorean comma]] meantone
	* Whether it is about equally sharp of [[3/2]] as some other listed temperament is flat		* Whether it is about equally sharp of [[3/2]] as some other listed temperament is flat
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	\|[[-9/26-comma meantone\|-9/26-comma]]		\|[[-9/26-comma meantone\|-9/26-comma]]
	\|709.399		\|709.399
	\|		\|Close to [[2.3.7-limit]] superpyth [[POTE]] tuning.
	\|-		\|-
	\|[[-8/23-comma meantone\|-8/23-comma]]		\|[[-8/23-comma meantone\|-8/23-comma]]
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	\|[[-6/17-comma meantone\|-6/17-comma]]		\|[[-6/17-comma meantone\|-6/17-comma]]
	\|709.545		\|709.545
	\|		\|Close to [[11-limit]] superpyth [[CTE]] tuning.
	\|-		\|-
	\|[[-5/14-comma meantone\|-5/14-comma]]		\|[[-5/14-comma meantone\|-5/14-comma]]
	\|709.636		\|709.636
	\|Close to [[93edo]]		\|Close to [[93edo]]. Close to [[2.3.7-limit]] and [[7-limit]] superpyth CTE tunings.
	\|-		\|-
	\|[[-4/11-comma meantone\|-4/11-comma]]		\|[[-4/11-comma meantone\|-4/11-comma]]
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	\|[[-7/19-comma meantone\|-7/19-comma]]		\|[[-7/19-comma meantone\|-7/19-comma]]
	\|709.878		\|709.878
	\|		\|Close to [[13-limit]] superpyth CTE tuning.
	\|-		\|-
	\|[[-3/8-comma meantone\|-3/8-comma]]		\|[[-3/8-comma meantone\|-3/8-comma]]
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	\|[[Negative split golden ratio-comma meantone\|Negative split golden ratio-comma]]		\|[[Negative split golden ratio-comma meantone\|Negative split golden ratio-comma]]
	\|710.170		\|710.170
	\|		\|Close to [[11-limit]] superpyth POTE tuning.
	\|-		\|-
	\|[[-5/13-comma meantone\|-5/13-comma]]		\|[[-5/13-comma meantone\|-5/13-comma]]
	\|710.227		\|710.227
	\|Close to [[49edo]].		\|Close to [[49edo]]. Close to [[7-limit]] superpyth POTE tuning.
	\|-		\|-
	\|[[-7/18-comma meantone\|-7/18-comma]]		\|[[-7/18-comma meantone\|-7/18-comma]]
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	\|[[-2/5-comma meantone\|-2/5-comma]]		\|[[-2/5-comma meantone\|-2/5-comma]]
	\|710.558		\|710.558
	\|		\|Close to [[13-limit]] superpyth POTE tuning.
	\|-		\|-
	\|[[-9/22-comma meantone\|-9/22-comma]]		\|[[-9/22-comma meantone\|-9/22-comma]]

BudjarnLambeth: WP:nocaps

2024-12-29T02:28:13Z

WP:nocaps

← Older revision		Revision as of 02:28, 29 December 2024
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	\|[[5/13-comma meantone\|5/13-comma]] \|\|693.683\|\|		\|[[5/13-comma meantone\|5/13-comma]] \|\|693.683\|\|
	\|-		\|-
	\|[[Split ~~Golden~~ ratio-comma meantone\|Split ~~Golden~~ ratio-comma]]		\|[[Split golden ratio-comma meantone\|Split golden ratio-comma]]
	\|693.740		\|693.740
	\|Close to [[64edo]].		\|Close to [[64edo]].
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	\|[[-4/15-comma meantone\|-4/15-comma]]		\|[[-4/15-comma meantone\|-4/15-comma]]
	\|707.690		\|707.690
	\|About as sharp of [[Pythagorean tuning]] as [[~~Golden~~ meantone]] is flat.		\|About as sharp of [[Pythagorean tuning]] as [[golden meantone]] is flat.
	\|-		\|-
	\|[[-7/26-comma meantone\|-7/26-comma]]		\|[[-7/26-comma meantone\|-7/26-comma]]
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	\|		\|
	\|-		\|-
	\|[[Negative ~~Split Golden~~ ratio-comma meantone\|Negative ~~Split Golden~~ ratio-comma]]		\|[[Negative split golden ratio-comma meantone\|Negative split golden ratio-comma]]
	\|710.170		\|710.170
	\|		\|
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	\|		\|
	\|-		\|-
	\|[[Negative ~~Golden~~ ratio-comma meantone\|Negative ~~Golden~~ ratio-comma]]		\|[[Negative golden ratio-comma meantone\|Negative golden ratio-comma]]
	\|715.247		\|715.247
	\|		\|

BudjarnLambeth: Add POTE tunings

2024-12-29T02:20:56Z

Add POTE tunings

← Older revision		Revision as of 02:20, 29 December 2024
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	* Whether it saw historical (pre-1950) use		* Whether it saw historical (pre-1950) use
	* Whether it is close to (i.e. within 1/2 a degree of closing of) an [[edo]] smaller than 100		* Whether it is close to (i.e. within 1/2 a degree of closing of) an [[edo]] smaller than 100
	* Whether it is the closest on the table to ~~an optimized tuning of meantone (e.g. 7-limit~~ [[CTE]])		* Whether it is the closest on the table to the optimal [[CTE]] or [[POTE]] tuning of meantone in any prime limit 5, 7, 11 or 13
	* Whether it approximates a very simple n-[[Pythagorean comma]] meantone		* Whether it approximates a very simple n-[[Pythagorean comma]] meantone
	* Whether it is about equally sharp of [[3/2]] as some other listed temperament is flat		* Whether it is about equally sharp of [[3/2]] as some other listed temperament is flat
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	\|[[7/26-comma meantone\|7/26-comma]] \|\|696.165\|\|Close to [[golden meantone]]. Historically significant (see [[historical temperaments]]).		\|[[7/26-comma meantone\|7/26-comma]] \|\|696.165\|\|Close to [[golden meantone]]. Historically significant (see [[historical temperaments]]).
	\|-		\|-
	\|[[4/15-comma meantone\|4/15-comma]] \|\|696.220\|\|		\|[[4/15-comma meantone\|4/15-comma]] \|\|696.220\|\|Close to [[5-limit]] meantone [[POTE]] tuning.
	\|-		\|-
	\|[[5/19-comma meantone\|5/19-comma]]		\|[[5/19-comma meantone\|5/19-comma]]
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	\|Close to [[81edo]].		\|Close to [[81edo]].
	\|-		\|-
	\|[[Quarter-comma meantone\|1/4-comma]] \|\|696.578\|\|Historically significant (see [[historical temperaments]]).		\|[[Quarter-comma meantone\|1/4-comma]] \|\|696.578\|\|Close to [[7-limit\|septimal]] and [[tridecimal]] meantone POTE tunings. Historically significant (see [[historical temperaments]]).
	\|-		\|-
	\|[[5/21-comma meantone\|5/21-comma]]		\|[[5/21-comma meantone\|5/21-comma]]
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	\|[[4/17-comma meantone\|4/17-comma]] \|\|696.895\|\|		\|[[4/17-comma meantone\|4/17-comma]] \|\|696.895\|\|
	\|-		\|-
	\|[[3/13-comma meantone\|3/13-comma]] \|\|696.992\|\|Close to [[7-limit\|septimal]] & [[tridecimal]] meantone [[CTE]] tunings.		\|[[3/13-comma meantone\|3/13-comma]] \|\|696.992\|\|Close to [[7-limit\|septimal]] & [[tridecimal]] meantone [[CTE]] tunings. Close to [[undecimal]] meantone POTE tuning.
	\|-		\|-
	\|[[5/22-comma meantone\|5/22-comma]]		\|[[5/22-comma meantone\|5/22-comma]]