1131edo - Revision history

ArrowHead294 at 22:48, 20 February 2025

2025-02-20T22:48:52Z

← Older revision		Revision as of 22:48, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	1131edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. Otherwise, it has good approximations to harmonics [[5/1\|5]], [[7/1\|7]], [[9/1\|9]], [[13/1\|13]], making it suitable for a 2.9.5.7.13 [[subgroup]] interpretation.		1131edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. Otherwise, it has good approximations to harmonics [[5/1\|5]], [[7/1\|7]], [[9/1\|9]], [[13/1\|13]], making it suitable for a 2.9.5.7.13 [[subgroup]] interpretation.

ArrowHead294 at 22:48, 20 February 2025

2025-02-20T22:48:27Z

← Older revision		Revision as of 22:48, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro~~\|1131~~}}		{{EDO intro}}

	1131edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. Otherwise, it has good approximations to harmonics [[5/1\|5]], [[7/1\|7]], [[9/1\|9]], [[13/1\|13]], making it suitable for a 2.9.5.7.13 [[subgroup]] interpretation.		1131edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. Otherwise, it has good approximations to harmonics [[5/1\|5]], [[7/1\|7]], [[9/1\|9]], [[13/1\|13]], making it suitable for a 2.9.5.7.13 [[subgroup]] interpretation.

FloraC: Expand on theory; adopt template: Factorization

2023-10-31T10:22:30Z

Expand on theory; adopt template: Factorization

← Older revision		Revision as of 10:22, 31 October 2023
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	{{EDO intro\|1131}}		{{EDO intro\|1131}}

	~~Using the~~ [[~~patent val~~]], the ~~equal temperament~~ [[~~Tempering out\|tempers out~~]] ~~1600000/1594323 (~~[[~~amity comma~~]]~~) in the~~ [[~~5-limit~~]], ~~2401/2400 (~~[[~~breedsma]]) and 4802000~~/~~4782969 ([[canousma~~]]~~) in the~~ [[7~~-limit~~]], ~~3025/3024 (lehmerisma), 41503/41472, and 151262/151250 in the~~ [[~~11-limit~~]]~~. It provides the~~ [[~~optimal patent val~~]] for ~~[[amicable]] temperament, the rank-~~2 ~~temperament that tempers out 2401/2400 and 1600000/1594323, and for~~ [[~~canou temperament~~]]~~, the rank-3 temperament that tempers out 4802000/4782969~~.		1131edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway between its steps. Otherwise, it has good approximations to harmonics [[5/1\|5]], [[7/1\|7]], [[9/1\|9]], [[13/1\|13]], making it suitable for a 2.9.5.7.13 [[subgroup]] interpretation.

	1131 factors into ~~3 × 13 × 29 with divisors~~ 3, 13, 29, 39, 87 and 377, and it shares the ~~major third of [[~~5~~/4]]~~ with [[87edo]].		Meanwhile using the [[patent val]], the equal temperament [[Tempering out\|tempers out]] 1600000/1594323 ([[amity comma]]) in the [[5-limit]], 2401/2400 ([[breedsma]]) and 4802000/4782969 ([[canousma]]) in the [[7-limit]], [[3025/3024]], [[41503/41472]], and 151262/151250 in the [[11-limit]]. It provides the [[optimal patent val]] for [[amicable]] temperament, the rank-2 temperament that tempers out 2401/2400 and 1600000/1594323, and for [[canou temperament]], the rank-3 temperament that tempers out 4802000/4782969.

			=== Odd harmonics ===
			{{Harmonics in equal\|1131}}

			=== Subsets and supersets ===
			Since 1131 factors into {{factorization\|1131}}, 1131edo has subset edos 3, 13, 29, 39, 87 and 377, and it shares the excellent approximation to harmonic 5 with [[87edo]].

	[[Category:Amicable]]		[[Category:Amicable]]
	[[Category:Canou]]		[[Category:Canou]]

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

2023-10-17T13:11:43Z

Adopt template: EDO intro; cleanup;-redundant categories

← Older revision		Revision as of 13:11, 17 October 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''1131edo''' divides the octave into~~ 1131 ~~equal parts of 1.0610 cents each.~~		{{EDO intro\|1131}}

	Using the patent val, it tempers out 1600000/1594323 ([[amity comma]]) in the [[5-limit]], 2401/2400 ([[breedsma]]) and 4802000/4782969 ([[canousma]]) in the [[7-limit]], 3025/3024 (lehmerisma), 41503/41472, and 151262/151250 in the [[11-limit]]. It provides the [[optimal patent val]] for [[amicable]] temperament, the rank-2 temperament that tempers out 2401/2400 and 1600000/1594323, and for [[canou temperament]], the rank-3 temperament that tempers out 4802000/4782969.		Using the [[patent val]], the equal temperament [[Tempering out\|tempers out]] 1600000/1594323 ([[amity comma]]) in the [[5-limit]], 2401/2400 ([[breedsma]]) and 4802000/4782969 ([[canousma]]) in the [[7-limit]], 3025/3024 (lehmerisma), 41503/41472, and 151262/151250 in the [[11-limit]]. It provides the [[optimal patent val]] for [[amicable]] temperament, the rank-2 temperament that tempers out 2401/2400 and 1600000/1594323, and for [[canou temperament]], the rank-3 temperament that tempers out 4802000/4782969.

	1131 factors into 3 × 13 × 29 with divisors 3, 13, 29, 39, 87 and 377, and it shares the major third of [[5/4]] with [[87edo]].		1131 factors into 3 × 13 × 29 with divisors 3, 13, 29, 39, 87 and 377, and it shares the major third of [[5/4]] with [[87edo]].

	~~[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->~~
	[[Category:Amicable]]		[[Category:Amicable]]
	[[Category:Canou]]		[[Category:Canou]]

BudjarnLambeth at 06:50, 9 July 2023

2023-07-09T06:50:36Z

← Older revision		Revision as of 06:50, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	'''1131edo''' divides the octave into 1131 equal parts of 1.0610 cents each.		'''1131edo''' divides the octave into 1131 equal parts of 1.0610 cents each.

BudjarnLambeth at 05:19, 9 July 2023

2023-07-09T05:19:35Z

← Older revision		Revision as of 05:19, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	'''1131edo''' divides the octave into 1131 equal parts of 1.0610 cents each.		'''1131edo''' divides the octave into 1131 equal parts of 1.0610 cents each.

Plumtree: Infobox ET added

2022-10-04T22:07:59Z

Infobox ET added

← Older revision		Revision as of 22:07, 4 October 2022
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			{{Infobox ET}}
	'''1131edo''' divides the octave into 1131 equal parts of 1.0610 cents each.		'''1131edo''' divides the octave into 1131 equal parts of 1.0610 cents each.

Fredg999 category edits: Sort key

2022-07-04T01:12:04Z

Sort key

← Older revision		Revision as of 01:12, 4 July 2022
Line 5:		Line 5:
	1131 factors into 3 × 13 × 29 with divisors 3, 13, 29, 39, 87 and 377, and it shares the major third of [[5/4]] with [[87edo]].		1131 factors into 3 × 13 × 29 with divisors 3, 13, 29, 39, 87 and 377, and it shares the major third of [[5/4]] with [[87edo]].

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->
	[[Category:Amicable]]		[[Category:Amicable]]
	[[Category:Canou]]		[[Category:Canou]]

Xenwolf: more specific link

2021-01-05T16:46:41Z

Xenwolf: more obvious linking

2020-12-25T19:47:26Z

← Older revision		Revision as of 16:46, 5 January 2021
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	'''1131edo''' divides the octave into 1131 equal parts of 1.0610 cents each.		'''1131edo''' divides the octave into 1131 equal parts of 1.0610 cents each.

	Using the patent val, it tempers out 1600000/1594323 ([[amity comma]]) in the [[5-limit]], 2401/2400 ([[breedsma]]) and 4802000/4782969 ([[canousma]]) in the [[7-limit]], 3025/3024 (lehmerisma), 41503/41472, and 151262/151250 in the [[11-limit]]. It provides the [[optimal patent val]] for [[amicable]] temperament, the rank-2 temperament that tempers out 2401/2400 and 1600000/1594323, and for [[~~canou family\|~~canou temperament]], the rank-3 temperament that tempers out 4802000/4782969.		Using the patent val, it tempers out 1600000/1594323 ([[amity comma]]) in the [[5-limit]], 2401/2400 ([[breedsma]]) and 4802000/4782969 ([[canousma]]) in the [[7-limit]], 3025/3024 (lehmerisma), 41503/41472, and 151262/151250 in the [[11-limit]]. It provides the [[optimal patent val]] for [[amicable]] temperament, the rank-2 temperament that tempers out 2401/2400 and 1600000/1594323, and for [[canou temperament]], the rank-3 temperament that tempers out 4802000/4782969.

	1131 factors into 3 × 13 × 29 with divisors 3, 13, 29, 39, 87 and 377, and it shares the major third of [[5/4]] with [[87edo]].		1131 factors into 3 × 13 × 29 with divisors 3, 13, 29, 39, 87 and 377, and it shares the major third of [[5/4]] with [[87edo]].

← Older revision		Revision as of 19:47, 25 December 2020
Line 1:		Line 1:
	'''1131edo''' divides the octave into 1131 equal parts of 1.0610 cents each.		'''1131edo''' divides the octave into 1131 equal parts of 1.0610 cents each.

	Using the patent val, it tempers out 1600000/1594323 ([[amity comma]]) in the [[5-limit]], 2401/2400 ([[breedsma]]) and 4802000/4782969 ([[canousma]]) in the [[7-limit]], 3025/3024 (lehmerisma), 41503/41472, and 151262/151250 in the [[11-limit]]. It provides the [[optimal patent val]] for [[amicable~~\|amicable temperament~~]], the rank-2 temperament that tempers out 2401/2400 and 1600000/1594323, and for [[canou family\|canou temperament]], the rank-3 temperament that tempers out 4802000/4782969.		Using the patent val, it tempers out 1600000/1594323 ([[amity comma]]) in the [[5-limit]], 2401/2400 ([[breedsma]]) and 4802000/4782969 ([[canousma]]) in the [[7-limit]], 3025/3024 (lehmerisma), 41503/41472, and 151262/151250 in the [[11-limit]]. It provides the [[optimal patent val]] for [[amicable]] temperament, the rank-2 temperament that tempers out 2401/2400 and 1600000/1594323, and for [[canou family\|canou temperament]], the rank-3 temperament that tempers out 4802000/4782969.

	1131 factors into 3 × 13 × 29 with divisors 3, 13, 29, 39, 87 and 377, and it shares the major third of [[5/4]] with [[87edo]].		1131 factors into 3 × 13 × 29 with divisors 3, 13, 29, 39, 87 and 377, and it shares the major third of [[5/4]] with [[87edo]].