122edo - Revision history

Lucius Chiaraviglio: /* Subsets and supersets */ 244 also corrects harmonic 7

2026-03-18T08:21:52Z

Subsets and supersets: 244 also corrects harmonic 7

← Older revision		Revision as of 08:21, 18 March 2026
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 122 factors into {{factorization\|122}}, 122edo contains [[2edo]] and [[61edo]] as its subsets. [[244edo]] (double 122edo) provides a good correction to ~~harmonic~~ 25.		Since 122 factors into {{factorization\|122}}, 122edo contains [[2edo]] and [[61edo]] as its subsets. [[244edo]] (double 122edo) provides a good correction to harmonics 7 and 25.

	[[Category:Tritonic]]		[[Category:Tritonic]]
	[[Category:Meantone]]		[[Category:Meantone]]

ArrowHead294 at 16:58, 18 February 2025

2025-02-18T16:58:38Z

← Older revision		Revision as of 16:58, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	122 is flat in tendency, with the [[prime harmonic]]s from 3 to 13 tuned flat. As an equal temperament, it [[tempering out\|tempers out]] 78732/78125 ([[sensipent comma]]) in the [[5-limit]]; [[225/224]] in the [[7-limit]]; [[385/384]] and [[4000/3993]] in the [[11-limit]]; and [[351/350]] and [[364/363]] in the [[13-limit]]. It provides the [[optimal patent val]] for the 7-limit [[tritonic]] temperament and the 11-limit [[Marvel temperaments #Tritoni\|tritoni]] temperament, and the [[rank-3\|planar]] temperament [[squalentine]].		122 is flat in tendency, with the [[prime harmonic]]s from 3 to 13 tuned flat. As an equal temperament, it [[tempering out\|tempers out]] 78732/78125 ([[sensipent comma]]) in the [[5-limit]]; [[225/224]] in the [[7-limit]]; [[385/384]] and [[4000/3993]] in the [[11-limit]]; and [[351/350]] and [[364/363]] in the [[13-limit]]. It provides the [[optimal patent val]] for the 7-limit [[tritonic]] temperament and the 11-limit [[Marvel temperaments #Tritoni\|tritoni]] temperament, and the [[rank-3\|planar]] temperament [[squalentine]].

FloraC: Cleanup

2025-01-17T15:21:07Z

Cleanup

← Older revision		Revision as of 15:21, 17 January 2025
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	{{EDO intro}}		{{EDO intro}}

	122 is flat in tendency, with the [[prime harmonic]]s from 3 to 13 tuned flat. ~~This~~ equal temperament [[tempers out]] 78732/78125 in the [[5-limit]]; 225/224 in the [[7-limit]]; [[385/384]] and [[4000/3993]] in the [[11-limit]]; and [[351/350]] and [[364/363]] in the [[13-limit]]. It provides the [[optimal patent val]] for the 7-limit [[tritonic]] temperament and the 11-limit [[Marvel temperaments #Tritoni\|tritoni]] temperament, and the [[rank-3\|planar]] temperament [[squalentine]].		122 is flat in tendency, with the [[prime harmonic]]s from 3 to 13 tuned flat. As an equal temperament, it [[tempering out\|tempers out]] 78732/78125 ([[sensipent comma]]) in the [[5-limit]]; [[225/224]] in the [[7-limit]]; [[385/384]] and [[4000/3993]] in the [[11-limit]]; and [[351/350]] and [[364/363]] in the [[13-limit]]. It provides the [[optimal patent val]] for the 7-limit [[tritonic]] temperament and the 11-limit [[Marvel temperaments #Tritoni\|tritoni]] temperament, and the [[rank-3\|planar]] temperament [[squalentine]].

	122 = [[55edo\|55]] + [[67edo\|67]], and so using the 122c [[val]] it is the [[convergent]] towards [[1/6-comma meantone]], with a fifth just a hundredth of a cent flatter.		122 = [[55edo\|55]] + [[67edo\|67]], and so using the 122c [[val]] it is the [[convergent]] towards [[1/6-comma meantone]], with a fifth just a hundredth of a cent flatter.

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|122~~\|23=~~}}		{{Harmonics in equal\|122}}

	Harmonic 25 (two 5/4 major thirds) is about halfway between 122edo's steps.		Harmonic 25 (two 5/4 major thirds) is about halfway between 122edo's steps.

BudjarnLambeth: Add links

2025-01-07T05:25:32Z

Add links

← Older revision		Revision as of 05:25, 7 January 2025
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	{{EDO intro}}		{{EDO intro}}

	122 is flat in tendency, with the [[prime harmonic]]s from 3 to 13 tuned flat. ~~The~~ equal temperament [[~~tempering out\|~~tempers out]] 78732/78125 in the [[5-limit]]; 225/224 in the [[7-limit]]; [[385/384]] and [[4000/3993]] in the [[11-limit]]; and [[351/350]] and [[364/363]] in the [[13-limit]]. It provides the [[optimal patent val]] for the 7-limit [[tritonic]] temperament and the 11-limit [[Marvel temperaments #Tritoni\|tritoni]] temperament, and the [[rank-3 ~~temperament~~\|planar]] [[squalentine]] ~~temperament~~.		122 is flat in tendency, with the [[prime harmonic]]s from 3 to 13 tuned flat. This equal temperament [[tempers out]] 78732/78125 in the [[5-limit]]; 225/224 in the [[7-limit]]; [[385/384]] and [[4000/3993]] in the [[11-limit]]; and [[351/350]] and [[364/363]] in the [[13-limit]]. It provides the [[optimal patent val]] for the 7-limit [[tritonic]] temperament and the 11-limit [[Marvel temperaments #Tritoni\|tritoni]] temperament, and the [[rank-3\|planar]] temperament [[squalentine]].

	122 = [[55edo\|55]] + [[67edo\|67]], and so using the 122c val it is the convergent towards [[1/6-comma meantone]], with a fifth just a hundredth of a cent flatter.		122 = [[55edo\|55]] + [[67edo\|67]], and so using the 122c [[val]] it is the [[convergent]] towards [[1/6-comma meantone]], with a fifth just a hundredth of a cent flatter.

	=== Odd harmonics ===		=== Odd harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 122 factors into {{factorization\|122}}, 122edo contains [[2edo]] and [[61edo]] as its subsets. 244edo (double 122edo) provides a good correction to harmonic 25.		Since 122 factors into {{factorization\|122}}, 122edo contains [[2edo]] and [[61edo]] as its subsets. [[244edo]] (double 122edo) provides a good correction to harmonic 25.

	[[Category:Tritonic]]		[[Category:Tritonic]]
	[[Category:Meantone]]		[[Category:Meantone]]

MisterShafXen at 20:05, 11 October 2024

2024-10-11T20:05:41Z

← Older revision		Revision as of 20:05, 11 October 2024
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 122 factors into {{factorization\|122}}, 122edo contains [[2edo]] and [[61edo]] as its subsets.		Since 122 factors into {{factorization\|122}}, 122edo contains [[2edo]] and [[61edo]] as its subsets. 244edo (double 122edo) provides a good correction to harmonic 25.

	[[Category:Tritonic]]		[[Category:Tritonic]]
	[[Category:Meantone]]		[[Category:Meantone]]

MisterShafXen at 20:03, 11 October 2024

2024-10-11T20:03:40Z

← Older revision		Revision as of 20:03, 11 October 2024
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|122}}		{{Harmonics in equal\|122\|23=}}

			Harmonic 25 (two 5/4 major thirds) is about halfway between 122edo's steps.

	=== Subsets and supersets ===		=== Subsets and supersets ===

FloraC: Rework

2024-05-29T08:34:27Z

Rework

← Older revision		Revision as of 08:34, 29 May 2024
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	{{EDO intro}}		{{EDO intro}}

	It is ~~the [[optimal patent val]] for the 7-limit [[tritonic]] temperament and the 11-limit [[Marvel temperaments #Tritoni\|tritoni]] temperament~~, ~~and~~ the ~~planar~~ [[~~squalentine~~]] temperament~~. It~~ [[tempering out\|tempers out]] 78732/78125 in the [[5-limit]]; 225/224 in the [[7-limit]]; [[385/384]] and [[4000/3993]] in the [[11-limit]]; and [[351/350]] and [[364/363]] in the [[13-limit]].		122 is flat in tendency, with the [[prime harmonic]]s from 3 to 13 tuned flat. The equal temperament [[tempering out\|tempers out]] 78732/78125 in the [[5-limit]]; 225/224 in the [[7-limit]]; [[385/384]] and [[4000/3993]] in the [[11-limit]]; and [[351/350]] and [[364/363]] in the [[13-limit]]. It provides the [[optimal patent val]] for the 7-limit [[tritonic]] temperament and the 11-limit [[Marvel temperaments #Tritoni\|tritoni]] temperament, and the [[rank-3 temperament\|planar]] [[squalentine]] temperament.

	~~122 is flat in tendency, with the odd primes from 3 to 13 tuned flat. 122 = 2 × [[61edo\|61]].~~ 122 = [[55edo\|55]] + [[67edo\|67]], and so using the 122c val it is the convergent towards [[1/6-comma meantone]], with a fifth just a hundredth of a cent flatter.		122 = [[55edo\|55]] + [[67edo\|67]], and so using the 122c val it is the convergent towards [[1/6-comma meantone]], with a fifth just a hundredth of a cent flatter.

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|122}}		{{Harmonics in equal\|122}}

			=== Subsets and supersets ===
			Since 122 factors into {{factorization\|122}}, 122edo contains [[2edo]] and [[61edo]] as its subsets.

			[[Category:Tritonic]]
	[[Category:Meantone]]		[[Category:Meantone]]

FloraC: Adopt template: EDO intro; -redundant categories; misc. cleanup

2024-05-29T08:29:15Z

Adopt template: EDO intro; -redundant categories; misc. cleanup

← Older revision		Revision as of 08:29, 29 May 2024
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	{{Infobox ET}}		{{Infobox ET}}
	'''122edo''' is the [[Equal_division_of_the_octave\|equal division of the octave]] into 122 parts of 9.836 [[cent\|cent]]s each. It is the [[Optimal_patent_val\|optimal patent val]] for 7-limit [[Marvel_temperaments\|tritonic temperament]] and 11-limit [[Marvel_temperaments\|tritoni temperament]], and the planar [[Squalentine_temperament\|squalentine temperament]]. It [[tempering_out\|tempers out]] 78732/78125 in the [[5-limit\|5-limit]], 225/224 in the [[7-limit\|7-limit]], 385/384 and 4000/3993 in the [[11-limit\|11-limit]], and 351/350 and 364/363 in the [[13-limit\|13-limit]].		{{EDO intro}}

	122 is flat in tendency, with the odd primes from 3 to 13 tuned flat. 122 = 2 * [[61edo\|61]]. 122=[[55edo\|55]]+[[67edo\|67]], and so using the c val it is the convergent towards [[1/6-comma meantone]], with a fifth just a hundredth of a cent flatter.		It is the [[optimal patent val]] for the 7-limit [[tritonic]] temperament and the 11-limit [[Marvel temperaments #Tritoni\|tritoni]] temperament, and the planar [[squalentine]] temperament. It [[tempering out\|tempers out]] 78732/78125 in the [[5-limit]]; 225/224 in the [[7-limit]]; [[385/384]] and [[4000/3993]] in the [[11-limit]]; and [[351/350]] and [[364/363]] in the [[13-limit]].
	{{~~harmonics~~ in equal\|122}}
			122 is flat in tendency, with the odd primes from 3 to 13 tuned flat. 122 = 2 × [[61edo\|61]]. 122 = [[55edo\|55]] + [[67edo\|67]], and so using the 122c val it is the convergent towards [[1/6-comma meantone]], with a fifth just a hundredth of a cent flatter.

			=== Odd harmonics ===
			{{Harmonics in equal\|122}}

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

BudjarnLambeth: Replace deprecated template

2024-01-25T07:46:05Z

Replace deprecated template

← Older revision		Revision as of 07:46, 25 January 2024
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	122 is flat in tendency, with the odd primes from 3 to 13 tuned flat. 122 = 2 * [[61edo\|61]]. 122=[[55edo\|55]]+[[67edo\|67]], and so using the c val it is the convergent towards [[1/6-comma meantone]], with a fifth just a hundredth of a cent flatter.		122 is flat in tendency, with the odd primes from 3 to 13 tuned flat. 122 = 2 * [[61edo\|61]]. 122=[[55edo\|55]]+[[67edo\|67]], and so using the c val it is the convergent towards [[1/6-comma meantone]], with a fifth just a hundredth of a cent flatter.
	{{~~primes~~ in ~~edo~~\|122~~\|columns=10\|prec=3~~}}		{{harmonics in equal\|122}}

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
	[[Category:Meantone]]		[[Category:Meantone]]

Yourmusic Productions: Bypass redirect.

2023-10-01T09:24:29Z

Bypass redirect.

← Older revision		Revision as of 09:24, 1 October 2023
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	'''122edo''' is the [[Equal_division_of_the_octave\|equal division of the octave]] into 122 parts of 9.836 [[cent\|cent]]s each. It is the [[Optimal_patent_val\|optimal patent val]] for 7-limit [[Marvel_temperaments\|tritonic temperament]] and 11-limit [[Marvel_temperaments\|tritoni temperament]], and the planar [[Squalentine_temperament\|squalentine temperament]]. It [[tempering_out\|tempers out]] 78732/78125 in the [[5-limit\|5-limit]], 225/224 in the [[7-limit\|7-limit]], 385/384 and 4000/3993 in the [[11-limit\|11-limit]], and 351/350 and 364/363 in the [[13-limit\|13-limit]].		'''122edo''' is the [[Equal_division_of_the_octave\|equal division of the octave]] into 122 parts of 9.836 [[cent\|cent]]s each. It is the [[Optimal_patent_val\|optimal patent val]] for 7-limit [[Marvel_temperaments\|tritonic temperament]] and 11-limit [[Marvel_temperaments\|tritoni temperament]], and the planar [[Squalentine_temperament\|squalentine temperament]]. It [[tempering_out\|tempers out]] 78732/78125 in the [[5-limit\|5-limit]], 225/224 in the [[7-limit\|7-limit]], 385/384 and 4000/3993 in the [[11-limit\|11-limit]], and 351/350 and 364/363 in the [[13-limit\|13-limit]].

	122 is flat in tendency, with the odd primes from 3 to 13 tuned flat. 122 = 2 * [[61edo\|61]]. 122=[[55edo\|55]]+[[67edo\|67]], and so using the c val it is the convergent towards [[~~1/6_syntonic_comma_meantone\|~~1/6 comma meantone]], with a fifth just a hundredth of a cent flatter.		122 is flat in tendency, with the odd primes from 3 to 13 tuned flat. 122 = 2 * [[61edo\|61]]. 122=[[55edo\|55]]+[[67edo\|67]], and so using the c val it is the convergent towards [[1/6-comma meantone]], with a fifth just a hundredth of a cent flatter.
	{{primes in edo\|122\|columns=10\|prec=3}}		{{primes in edo\|122\|columns=10\|prec=3}}

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
	[[Category:Meantone]]		[[Category:Meantone]]

← Older revision		Revision as of 09:24, 1 October 2023
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	'''122edo''' is the [[Equal_division_of_the_octave\|equal division of the octave]] into 122 parts of 9.836 [[cent\|cent]]s each. It is the [[Optimal_patent_val\|optimal patent val]] for 7-limit [[Marvel_temperaments\|tritonic temperament]] and 11-limit [[Marvel_temperaments\|tritoni temperament]], and the planar [[Squalentine_temperament\|squalentine temperament]]. It [[tempering_out\|tempers out]] 78732/78125 in the [[5-limit\|5-limit]], 225/224 in the [[7-limit\|7-limit]], 385/384 and 4000/3993 in the [[11-limit\|11-limit]], and 351/350 and 364/363 in the [[13-limit\|13-limit]].		'''122edo''' is the [[Equal_division_of_the_octave\|equal division of the octave]] into 122 parts of 9.836 [[cent\|cent]]s each. It is the [[Optimal_patent_val\|optimal patent val]] for 7-limit [[Marvel_temperaments\|tritonic temperament]] and 11-limit [[Marvel_temperaments\|tritoni temperament]], and the planar [[Squalentine_temperament\|squalentine temperament]]. It [[tempering_out\|tempers out]] 78732/78125 in the [[5-limit\|5-limit]], 225/224 in the [[7-limit\|7-limit]], 385/384 and 4000/3993 in the [[11-limit\|11-limit]], and 351/350 and 364/363 in the [[13-limit\|13-limit]].

	122 is flat in tendency, with the odd primes from 3 to 13 tuned flat. 122 = 2 * [[61edo\|61]]. 122=[[55edo\|55]]+[[67edo\|67]], and so using the c val it is the convergent towards [[~~1/6_syntonic_comma_meantone\|~~1/6 comma meantone]], with a fifth just a hundredth of a cent flatter.		122 is flat in tendency, with the odd primes from 3 to 13 tuned flat. 122 = 2 * [[61edo\|61]]. 122=[[55edo\|55]]+[[67edo\|67]], and so using the c val it is the convergent towards [[1/6-comma meantone]], with a fifth just a hundredth of a cent flatter.
	{{primes in edo\|122\|columns=10\|prec=3}}		{{primes in edo\|122\|columns=10\|prec=3}}

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
	[[Category:Meantone]]		[[Category:Meantone]]