103169edo - Revision history

Tristanbay: Giving most edo pages over 100000 the mathematical interest note

2025-09-08T17:50:25Z

Giving most edo pages over 100000 the mathematical interest note

← Older revision		Revision as of 17:50, 8 September 2025
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			{{Mathematical interest}}
	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}}		{{ED intro}}

ArrowHead294 at 22:42, 20 February 2025

2025-02-20T22:42:53Z

← Older revision		Revision as of 22:42, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|103169~~}}		{{ED intro}}

	103169edo provides an extraordinarily strong 7-limit system, tempering out {{monzo\| 9 -28 37 -18 }}, {{monzo\| -92 -17 21 25 }}, and {{monzo\| 110 -71 -11 10 }}. It maps the starling comma ([[126/125]]) to 1186 steps, the gamelisma (1029/1024) to 725 steps, the marvel comma ([[225/224]]) to 663 steps, the hemifamity comma (5120/5103) to 495 steps, the breedsma ([[2401/2400]]) to 62 steps, and the ragisma ([[4375/4374]]) to 34 steps. The [[patent val]] tempers out {{monzo\| 20 3 -9 -10 7 }}, {{monzo\| -29 16 5 -9 5 }}, {{monzo\| 3 -26 13 -7 8 }}, and {{monzo\| -6 2 -24 11 8 }} in the 11-limit, and 5767168/5767125, 1610510000/1610497161, 12784876137/12784844800, 26796875000/26796587103, and {{monzo\| -17 -5 -13 0 17 -1 }} in the 13-limit.		103169edo provides an extraordinarily strong 7-limit system, tempering out {{monzo\| 9 -28 37 -18 }}, {{monzo\| -92 -17 21 25 }}, and {{monzo\| 110 -71 -11 10 }}. It maps the starling comma ([[126/125]]) to 1186 steps, the gamelisma (1029/1024) to 725 steps, the marvel comma ([[225/224]]) to 663 steps, the hemifamity comma (5120/5103) to 495 steps, the breedsma ([[2401/2400]]) to 62 steps, and the ragisma ([[4375/4374]]) to 34 steps. The [[patent val]] tempers out {{monzo\| 20 3 -9 -10 7 }}, {{monzo\| -29 16 5 -9 5 }}, {{monzo\| 3 -26 13 -7 8 }}, and {{monzo\| -6 2 -24 11 8 }} in the 11-limit, and 5767168/5767125, 1610510000/1610497161, 12784876137/12784844800, 26796875000/26796587103, and {{monzo\| -17 -5 -13 0 17 -1 }} in the 13-limit.

BudjarnLambeth at 07:19, 9 July 2023

2023-07-09T07:19:05Z

← Older revision		Revision as of 07:19, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|103169}}		{{EDO intro\|103169}}

BudjarnLambeth at 04:03, 9 July 2023

2023-07-09T04:03:31Z

← Older revision		Revision as of 04:03, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|103169}}		{{EDO intro\|103169}}

FloraC: Cleanup and +subset edos

2023-02-20T08:52:49Z

Cleanup and +subset edos

← Older revision		Revision as of 08:52, 20 February 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''103169edo''' is the [[~~EDO\|~~equal division of the octave]] into~~ 103169 parts of 0.011631401 [[cent]]s each. It provides an extraordinarily strong 7-limit system, tempering out \|9 -28 37 -18>, \|-92 -17 21 25>, and \|110 -71 -11 10>. It maps the starling comma ([[126/125]]) to 1186 steps, the gamelisma (1029/1024) to 725 steps, the marvel comma ([[225/224]]) to 663 steps, the hemifamity comma (5120/5103) to 495 steps, the breedsma ([[2401/2400]]) to 62 steps, and the ragisma ([[4375/4374]]) to 34 steps. The patent val tempers out \|20 3 -9 -10 7>, \|-29 16 5 -9 5>, \|3 -26 13 -7 8>, and \|-6 2 -24 11 8> in the 11-limit, and 5767168/5767125, 1610510000/1610497161, 12784876137/12784844800, 26796875000/26796587103, and \|-17 -5 -13 0 17 -1> in the 13-limit.		{{EDO intro\|103169}}

	{{~~Primes in edo~~\|~~103169~~\|~~prec=~~7}}		103169edo provides an extraordinarily strong 7-limit system, tempering out {{monzo\| 9 -28 37 -18 }}, {{monzo\| -92 -17 21 25 }}, and {{monzo\| 110 -71 -11 10 }}. It maps the starling comma ([[126/125]]) to 1186 steps, the gamelisma (1029/1024) to 725 steps, the marvel comma ([[225/224]]) to 663 steps, the hemifamity comma (5120/5103) to 495 steps, the breedsma ([[2401/2400]]) to 62 steps, and the ragisma ([[4375/4374]]) to 34 steps. The [[patent val]] tempers out {{monzo\| 20 3 -9 -10 7 }}, {{monzo\| -29 16 5 -9 5 }}, {{monzo\| 3 -26 13 -7 8 }}, and {{monzo\| -6 2 -24 11 8 }} in the 11-limit, and 5767168/5767125, 1610510000/1610497161, 12784876137/12784844800, 26796875000/26796587103, and {{monzo\| -17 -5 -13 0 17 -1 }} in the 13-limit.

	~~[[Category:Equal divisions of the octave~~\|~~######]] <!-- 6-digit number -->~~		=== Prime harmonics ===
			{{Harmonics in equal\|103169\|prec=7}}

			=== Subsets and supersets ===
			Since 103169 factors into 11 × 83 × 113, 103169edo has subset edos 11, 83, 113, 913, 1243, and 9379.

Plumtree: Infobox ET added

2022-10-04T22:31:02Z

Infobox ET added

← Older revision		Revision as of 22:31, 4 October 2022
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			{{Infobox ET}}
	'''103169edo''' is the [[EDO\|equal division of the octave]] into 103169 parts of 0.011631401 [[cent]]s each. It provides an extraordinarily strong 7-limit system, tempering out \|9 -28 37 -18>, \|-92 -17 21 25>, and \|110 -71 -11 10>. It maps the starling comma ([[126/125]]) to 1186 steps, the gamelisma (1029/1024) to 725 steps, the marvel comma ([[225/224]]) to 663 steps, the hemifamity comma (5120/5103) to 495 steps, the breedsma ([[2401/2400]]) to 62 steps, and the ragisma ([[4375/4374]]) to 34 steps. The patent val tempers out \|20 3 -9 -10 7>, \|-29 16 5 -9 5>, \|3 -26 13 -7 8>, and \|-6 2 -24 11 8> in the 11-limit, and 5767168/5767125, 1610510000/1610497161, 12784876137/12784844800, 26796875000/26796587103, and \|-17 -5 -13 0 17 -1> in the 13-limit.		'''103169edo''' is the [[EDO\|equal division of the octave]] into 103169 parts of 0.011631401 [[cent]]s each. It provides an extraordinarily strong 7-limit system, tempering out \|9 -28 37 -18>, \|-92 -17 21 25>, and \|110 -71 -11 10>. It maps the starling comma ([[126/125]]) to 1186 steps, the gamelisma (1029/1024) to 725 steps, the marvel comma ([[225/224]]) to 663 steps, the hemifamity comma (5120/5103) to 495 steps, the breedsma ([[2401/2400]]) to 62 steps, and the ragisma ([[4375/4374]]) to 34 steps. The patent val tempers out \|20 3 -9 -10 7>, \|-29 16 5 -9 5>, \|3 -26 13 -7 8>, and \|-6 2 -24 11 8> in the 11-limit, and 5767168/5767125, 1610510000/1610497161, 12784876137/12784844800, 26796875000/26796587103, and \|-17 -5 -13 0 17 -1> in the 13-limit.

Fredg999 category edits: Sort key

2022-07-04T01:46:21Z

Sort key

← Older revision		Revision as of 01:46, 4 July 2022
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	{{Primes in edo\|103169\|prec=7}}		{{Primes in edo\|103169\|prec=7}}

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave\|######]] <!-- 6-digit number -->

Fredg999 category edits: Removing from Category:Theory using Cat-a-lot

2022-02-26T16:48:48Z

Removing from Category:Theory using Cat-a-lot

← Older revision		Revision as of 16:48, 26 February 2022
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	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave]]
	~~[[Category:Theory]]~~

Inthar: this does qualify for "extraordinarily" (basically no relative error, like 4296 does on the 5-limit)

2021-04-23T07:46:16Z

this does qualify for "extraordinarily" (basically no relative error, like 4296 does on the 5-limit)

← Older revision		Revision as of 07:46, 23 April 2021
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	'''103169edo''' is the [[EDO\|equal division of the octave]] into 103169 parts of 0.011631401 [[cent]]s each. It provides ~~a very~~ strong 7-limit system, tempering out \|9 -28 37 -18>, \|-92 -17 21 25>, and \|110 -71 -11 10>. It maps the starling comma ([[126/125]]) to 1186 steps, the gamelisma (1029/1024) to 725 steps, the marvel comma ([[225/224]]) to 663 steps, the hemifamity comma (5120/5103) to 495 steps, the breedsma ([[2401/2400]]) to 62 steps, and the ragisma ([[4375/4374]]) to 34 steps. The patent val tempers out \|20 3 -9 -10 7>, \|-29 16 5 -9 5>, \|3 -26 13 -7 8>, and \|-6 2 -24 11 8> in the 11-limit, and 5767168/5767125, 1610510000/1610497161, 12784876137/12784844800, 26796875000/26796587103, and \|-17 -5 -13 0 17 -1> in the 13-limit.		'''103169edo''' is the [[EDO\|equal division of the octave]] into 103169 parts of 0.011631401 [[cent]]s each. It provides an extraordinarily strong 7-limit system, tempering out \|9 -28 37 -18>, \|-92 -17 21 25>, and \|110 -71 -11 10>. It maps the starling comma ([[126/125]]) to 1186 steps, the gamelisma (1029/1024) to 725 steps, the marvel comma ([[225/224]]) to 663 steps, the hemifamity comma (5120/5103) to 495 steps, the breedsma ([[2401/2400]]) to 62 steps, and the ragisma ([[4375/4374]]) to 34 steps. The patent val tempers out \|20 3 -9 -10 7>, \|-29 16 5 -9 5>, \|3 -26 13 -7 8>, and \|-6 2 -24 11 8> in the 11-limit, and 5767168/5767125, 1610510000/1610497161, 12784876137/12784844800, 26796875000/26796587103, and \|-17 -5 -13 0 17 -1> in the 13-limit.

	{{Primes in edo\|103169\|prec=7}}		{{Primes in edo\|103169\|prec=7}}

Inthar at 07:44, 23 April 2021

2021-04-23T07:44:55Z

← Older revision		Revision as of 07:44, 23 April 2021
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	'''103169edo''' is the [[EDO\|equal division of the octave]] into 103169 parts of 0.011631401 [[cent]]s each. It provides a very strong 7-limit system, tempering out \|9 -28 37 -18>, \|-92 -17 21 25>, and \|110 -71 -11 10>. It maps the starling comma ([[126/125]]) to 1186 steps, the gamelisma (1029/1024) to 725 steps, the marvel comma ([[225/224]]) to 663 steps, the hemifamity comma (5120/5103) to 495 steps, the breedsma ([[2401/2400]]) to 62 steps, and the ragisma ([[4375/4374]]) to 34 steps. The patent val tempers out \|20 3 -9 -10 7>, \|-29 16 5 -9 5>, \|3 -26 13 -7 8>, and \|-6 2 -24 11 8> in the 11-limit, and 5767168/5767125, 1610510000/1610497161, 12784876137/12784844800, 26796875000/26796587103, and \|-17 -5 -13 0 17 -1> in the 13-limit.		'''103169edo''' is the [[EDO\|equal division of the octave]] into 103169 parts of 0.011631401 [[cent]]s each. It provides a very strong 7-limit system, tempering out \|9 -28 37 -18>, \|-92 -17 21 25>, and \|110 -71 -11 10>. It maps the starling comma ([[126/125]]) to 1186 steps, the gamelisma (1029/1024) to 725 steps, the marvel comma ([[225/224]]) to 663 steps, the hemifamity comma (5120/5103) to 495 steps, the breedsma ([[2401/2400]]) to 62 steps, and the ragisma ([[4375/4374]]) to 34 steps. The patent val tempers out \|20 3 -9 -10 7>, \|-29 16 5 -9 5>, \|3 -26 13 -7 8>, and \|-6 2 -24 11 8> in the 11-limit, and 5767168/5767125, 1610510000/1610497161, 12784876137/12784844800, 26796875000/26796587103, and \|-17 -5 -13 0 17 -1> in the 13-limit.

			{{Primes in edo\|103169\|prec=7}}

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave]]
	[[Category:Theory]]		[[Category:Theory]]