116edo - Revision history

ArrowHead294 at 19:24, 20 February 2025

2025-02-20T19:24:09Z

← Older revision		Revision as of 19:24, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	116edo is only [[consistent]] to the [[5-odd-limit]], and is not quite accurate for its size. It can be viewed as splitting [[58edo]]'s step in two, and the [[enfactoring\|enfactored]] 116cef [[val]] comes out on top accuracy in the 7-, 11-, and 13-limit. In the 5-limit, however, the [[patent val]] {{val\| 116 184 '''269''' }} beats the enfactored 116c val {{val\| 116 184 '''270''' }} by a thin margin, and it [[Tempering out\|tempers out]] 20000/19683 ([[tetracot comma]]) and 2197265625/2147483648 (wizard comma).		116edo is only [[consistent]] to the [[5-odd-limit]], and is not quite accurate for its size. It can be viewed as splitting [[58edo]]'s step in two, and the [[enfactoring\|enfactored]] 116cef [[val]] comes out on top accuracy in the 7-, 11-, and 13-limit. In the 5-limit, however, the [[patent val]] {{val\| 116 184 '''269''' }} beats the enfactored 116c val {{val\| 116 184 '''270''' }} by a thin margin, and it [[Tempering out\|tempers out]] 20000/19683 ([[tetracot comma]]) and 2197265625/2147483648 (wizard comma).

ArrowHead294 at 19:14, 20 February 2025

2025-02-20T19:14:22Z

← Older revision		Revision as of 19:14, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro~~\|116~~}}		{{EDO intro}}

	116edo is only [[consistent]] to the [[5-odd-limit]], and is not quite accurate for its size. It can be viewed as splitting [[58edo]]'s step in two, and the [[enfactoring\|enfactored]] 116cef [[val]] comes out on top accuracy in the 7-, 11-, and 13-limit. In the 5-limit, however, the [[patent val]] {{val\| 116 184 '''269''' }} beats the enfactored 116c val {{val\| 116 184 '''270''' }} by a thin margin, and it [[Tempering out\|tempers out]] 20000/19683 ([[tetracot comma]]) and 2197265625/2147483648 (wizard comma).		116edo is only [[consistent]] to the [[5-odd-limit]], and is not quite accurate for its size. It can be viewed as splitting [[58edo]]'s step in two, and the [[enfactoring\|enfactored]] 116cef [[val]] comes out on top accuracy in the 7-, 11-, and 13-limit. In the 5-limit, however, the [[patent val]] {{val\| 116 184 '''269''' }} beats the enfactored 116c val {{val\| 116 184 '''270''' }} by a thin margin, and it [[Tempering out\|tempers out]] 20000/19683 ([[tetracot comma]]) and 2197265625/2147483648 (wizard comma).
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 116 factors into ~~2<sup>2</sup> × 29~~, 116edo has subset edos {{EDOs\| 2, 4, 29, and 58 }}. [[232edo]], which doubles it, is a notable tuning.		Since 116 factors into {{factorisation\|116}}, 116edo has subset edos {{EDOs\| 2, 4, 29, and 58 }}. [[232edo]], which doubles it, is a notable tuning.

	== Intervals ==		== Intervals ==

BudjarnLambeth: +collapsed interval table

2024-10-02T12:45:34Z

+collapsed interval table

← Older revision		Revision as of 12:45, 2 October 2024
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 116 factors into 2<sup>2</sup> × 29, 116edo has subset edos {{EDOs\| 2, 4, 29, and 58 }}. [[232edo]], which doubles it, is a notable tuning.		Since 116 factors into 2<sup>2</sup> × 29, 116edo has subset edos {{EDOs\| 2, 4, 29, and 58 }}. [[232edo]], which doubles it, is a notable tuning.

			== Intervals ==
			{{Interval table}}

	[[Category:Submajor (temperament)]]		[[Category:Submajor (temperament)]]

FloraC: Update

2024-06-04T06:16:58Z

Update

← Older revision		Revision as of 06:16, 4 June 2024
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	116edo is only [[consistent]] to the [[5-odd-limit]], and is not quite accurate for its size. It can be viewed as splitting [[58edo]]'s step in two, and the [[enfactoring\|enfactored]] 116cef [[val]] comes out on top accuracy in the 7-, 11-, and 13-limit. In the 5-limit, however, the [[patent val]] {{val\| 116 184 '''269''' }} beats the enfactored 116c val {{val\| 116 184 '''270''' }} by a thin margin, and it [[Tempering out\|tempers out]] 20000/19683 ([[tetracot comma]]) and 2197265625/2147483648 (wizard comma).		116edo is only [[consistent]] to the [[5-odd-limit]], and is not quite accurate for its size. It can be viewed as splitting [[58edo]]'s step in two, and the [[enfactoring\|enfactored]] 116cef [[val]] comes out on top accuracy in the 7-, 11-, and 13-limit. In the 5-limit, however, the [[patent val]] {{val\| 116 184 '''269''' }} beats the enfactored 116c val {{val\| 116 184 '''270''' }} by a thin margin, and it [[Tempering out\|tempers out]] 20000/19683 ([[tetracot comma]]) and 2197265625/2147483648 (wizard comma).

	In the 7-, 11- and 13-limit, the patent val {{val\| 116 184 '''269''' 326 '''401''' '''429''' }} comes in second best after the enfactored 116cef val {{val\| 116 184 '''270''' 326 '''402''' '''430''' }} , and it tempers out [[225/224]], 15625/15309, and 51200/50421 in the 7-limit; [[385/384]], [[540/539]], [[4000/3993]], and 6655/6561 in the 11-limit; [[169/168]], [[275/273]], [[352/351]], and [[640/637]] in the 13-limit. 116edo provides the [[optimal patent val]] for [[submajor]] temperament in the 11- and 13-limit.		In the 7-, 11- and 13-limit, the patent val {{val\| 116 184 '''269''' 326 '''401''' '''429''' }} comes in second best after the enfactored 116cef val {{val\| 116 184 '''270''' 326 '''402''' '''430''' }} , and it tempers out [[225/224]], 15625/15309, and 51200/50421 in the 7-limit; [[385/384]], [[540/539]], [[4000/3993]], and 6655/6561 in the 11-limit; [[169/168]], [[275/273]], [[352/351]], and [[640/637]] in the 13-limit. 116edo provides the [[optimal patent val]] for the [[submajor (temperament)\|submajor]] temperament in the 11- and 13-limit.

	=== Prime harmonics ===		=== Prime harmonics ===

FloraC: Rework, expand, +categories

2023-10-02T14:16:27Z

Rework, expand, +categories

← Older revision		Revision as of 14:16, 2 October 2023
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	{{EDO intro\|116}}		{{EDO intro\|116}}

	116edo ~~tempers out 20000/19683 (tetracot comma) and 2197265625/2147483648 (wizard comma) in~~ the 5-limit. ~~Using~~ the ~~patent~~ val~~, it tempers~~ out ~~225/224, 15625/15309, and 51200/50421~~ in the 7-~~limit; 385/384~~, ~~540/539, 4000/3993, and 6655/6561 in the~~ 11-~~limit; 169/168, 275/273, 352/351~~, and ~~640/637 in the~~ 13-limit. ~~116edo provides~~ the ~~optimal~~ patent val ~~for~~ [[~~Marvel temperaments~~\|~~submajor temperament~~]].		116edo is only [[consistent]] to the [[5-odd-limit]], and is not quite accurate for its size. It can be viewed as splitting [[58edo]]'s step in two, and the [[enfactoring\|enfactored]] 116cef [[val]] comes out on top accuracy in the 7-, 11-, and 13-limit. In the 5-limit, however, the [[patent val]] {{val\| 116 184 '''269''' }} beats the enfactored 116c val {{val\| 116 184 '''270''' }} by a thin margin, and it [[Tempering out\|tempers out]] 20000/19683 ([[tetracot comma]]) and 2197265625/2147483648 (wizard comma).

			In the 7-, 11- and 13-limit, the patent val {{val\| 116 184 '''269''' 326 '''401''' '''429''' }} comes in second best after the enfactored 116cef val {{val\| 116 184 '''270''' 326 '''402''' '''430''' }} , and it tempers out [[225/224]], 15625/15309, and 51200/50421 in the 7-limit; [[385/384]], [[540/539]], [[4000/3993]], and 6655/6561 in the 11-limit; [[169/168]], [[275/273]], [[352/351]], and [[640/637]] in the 13-limit. 116edo provides the [[optimal patent val]] for [[submajor]] temperament in the 11- and 13-limit.

			=== Prime harmonics ===
	{{Harmonics in equal\|116}}		{{Harmonics in equal\|116}}
	[[Category:~~Equal divisions of the octave\|###~~]] ~~<!-- 3-digit number -->~~
			=== Subsets and supersets ===
			Since 116 factors into 2<sup>2</sup> × 29, 116edo has subset edos {{EDOs\| 2, 4, 29, and 58 }}. [[232edo]], which doubles it, is a notable tuning.

			[[Category:Submajor (temperament)]]

Eliora at 21:19, 30 May 2023

2023-05-30T21:19:02Z

Show changes

Aura at 18:52, 4 October 2022

2022-10-04T18:52:01Z

← Older revision		Revision as of 18:52, 4 October 2022
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			{{Infobox ET}}
	'''116edo''' is the [[EDO\|equal division of the octave]] into 116 parts of 10.3448 cents each. It tempers out 20000/19683 (tetracot comma) and 2197265625/2147483648 (wizard comma) in the 5-limit. Using the patent val, it tempers out 225/224, 15625/15309, and 51200/50421 in the 7-limit; 385/384, 540/539, 4000/3993, and 6655/6561 in the 11-limit; 169/168, 275/273, 352/351, and 640/637 in the 13-limit. 116edo provides the optimal patent val for [[Marvel temperaments\|submajor temperament]].		'''116edo''' is the [[EDO\|equal division of the octave]] into 116 parts of 10.3448 cents each. It tempers out 20000/19683 (tetracot comma) and 2197265625/2147483648 (wizard comma) in the 5-limit. Using the patent val, it tempers out 225/224, 15625/15309, and 51200/50421 in the 7-limit; 385/384, 540/539, 4000/3993, and 6655/6561 in the 11-limit; 169/168, 275/273, 352/351, and 640/637 in the 13-limit. 116edo provides the optimal patent val for [[Marvel temperaments\|submajor temperament]].

Fredg999 category edits: Sort key

2022-07-02T16:22:45Z

Sort key

← Older revision		Revision as of 16:22, 2 July 2022
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	'''116edo''' is the [[EDO\|equal division of the octave]] into 116 parts of 10.3448 cents each. It tempers out 20000/19683 (tetracot comma) and 2197265625/2147483648 (wizard comma) in the 5-limit. Using the patent val, it tempers out 225/224, 15625/15309, and 51200/50421 in the 7-limit; 385/384, 540/539, 4000/3993, and 6655/6561 in the 11-limit; 169/168, 275/273, 352/351, and 640/637 in the 13-limit. 116edo provides the optimal patent val for [[Marvel temperaments\|submajor temperament]].		'''116edo''' is the [[EDO\|equal division of the octave]] into 116 parts of 10.3448 cents each. It tempers out 20000/19683 (tetracot comma) and 2197265625/2147483648 (wizard comma) in the 5-limit. Using the patent val, it tempers out 225/224, 15625/15309, and 51200/50421 in the 7-limit; 385/384, 540/539, 4000/3993, and 6655/6561 in the 11-limit; 169/168, 275/273, 352/351, and 640/637 in the 13-limit. 116edo provides the optimal patent val for [[Marvel temperaments\|submajor temperament]].

	Since 116edo has a step of 10.3448 cents, it also allows one to use its MOS scales as circulating temperaments.		Since 116edo has a step of 10.3448 cents, it also allows one to use its MOS scales as circulating temperaments.

	{\| class="wikitable"		{\| class="wikitable"
	\|+Circulating temperaments in 116edo		\|+Circulating temperaments in 116edo
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	\|24L 68s		\|24L 68s
	\|}		\|}
	[[Category:Equal divisions of the octave]]
			[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Moremajorthanmajor at 21:46, 21 April 2021

2021-04-21T21:46:47Z

Show changes

Keenan Pepper category edits: Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

2020-12-04T23:13:06Z

Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

← Older revision		Revision as of 23:13, 4 December 2020
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	'''116edo''' is the [[EDO\|equal division of the octave]] into 116 parts of 10.3448 cents each. It tempers out 20000/19683 (tetracot comma) and 2197265625/2147483648 (wizard comma) in the 5-limit. Using the patent val, it tempers out 225/224, 15625/15309, and 51200/50421 in the 7-limit; 385/384, 540/539, 4000/3993, and 6655/6561 in the 11-limit; 169/168, 275/273, 352/351, and 640/637 in the 13-limit. 116edo provides the optimal patent val for [[Marvel temperaments\|submajor temperament]].		'''116edo''' is the [[EDO\|equal division of the octave]] into 116 parts of 10.3448 cents each. It tempers out 20000/19683 (tetracot comma) and 2197265625/2147483648 (wizard comma) in the 5-limit. Using the patent val, it tempers out 225/224, 15625/15309, and 51200/50421 in the 7-limit; 385/384, 540/539, 4000/3993, and 6655/6561 in the 11-limit; 169/168, 275/273, 352/351, and 640/637 in the 13-limit. 116edo provides the optimal patent val for [[Marvel temperaments\|submajor temperament]].

	[[Category:~~Edo~~]]		[[Category:Equal divisions of the octave]]

← Older revision		Revision as of 14:16, 2 October 2023
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	{{EDO intro\|116}}		{{EDO intro\|116}}

	116edo ~~tempers out 20000/19683 (tetracot comma) and 2197265625/2147483648 (wizard comma) in~~ the 5-limit. ~~Using~~ the ~~patent~~ val~~, it tempers~~ out ~~225/224, 15625/15309, and 51200/50421~~ in the 7-~~limit; 385/384~~, ~~540/539, 4000/3993, and 6655/6561 in the~~ 11-~~limit; 169/168, 275/273, 352/351~~, and ~~640/637 in the~~ 13-limit. ~~116edo provides~~ the ~~optimal~~ patent val ~~for~~ [[~~Marvel temperaments~~\|~~submajor temperament~~]].		116edo is only [[consistent]] to the [[5-odd-limit]], and is not quite accurate for its size. It can be viewed as splitting [[58edo]]'s step in two, and the [[enfactoring\|enfactored]] 116cef [[val]] comes out on top accuracy in the 7-, 11-, and 13-limit. In the 5-limit, however, the [[patent val]] {{val\| 116 184 '''269''' }} beats the enfactored 116c val {{val\| 116 184 '''270''' }} by a thin margin, and it [[Tempering out\|tempers out]] 20000/19683 ([[tetracot comma]]) and 2197265625/2147483648 (wizard comma).

			In the 7-, 11- and 13-limit, the patent val {{val\| 116 184 '''269''' 326 '''401''' '''429''' }} comes in second best after the enfactored 116cef val {{val\| 116 184 '''270''' 326 '''402''' '''430''' }} , and it tempers out [[225/224]], 15625/15309, and 51200/50421 in the 7-limit; [[385/384]], [[540/539]], [[4000/3993]], and 6655/6561 in the 11-limit; [[169/168]], [[275/273]], [[352/351]], and [[640/637]] in the 13-limit. 116edo provides the [[optimal patent val]] for [[submajor]] temperament in the 11- and 13-limit.

			=== Prime harmonics ===
	{{Harmonics in equal\|116}}		{{Harmonics in equal\|116}}
	[[Category:~~Equal divisions of the octave\|###~~]] ~~<!-- 3-digit number -->~~
			=== Subsets and supersets ===
			Since 116 factors into 2<sup>2</sup> × 29, 116edo has subset edos {{EDOs\| 2, 4, 29, and 58 }}. [[232edo]], which doubles it, is a notable tuning.

			[[Category:Submajor (temperament)]]