291edo - Revision history

FloraC: OPV for 13-limit hemiwuerschmidt (whatever that is) may be notable enough

2026-06-08T19:31:01Z

OPV for 13-limit hemiwuerschmidt (whatever that is) may be notable enough

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Overthink: nominate for deletion

2026-06-08T15:59:36Z

nominate for deletion

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ArrowHead294 at 19:29, 20 February 2025

2025-02-20T19:29:29Z

← Older revision		Revision as of 19:29, 20 February 2025
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	291edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val\| 291 461 676 }} ([[patent val]]), {{val\| 291 462 676 }} (291b), and {{val\| 291 461 675 }} (291c).		291edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val\| 291 461 676 }} ([[patent val]]), {{val\| 291 462 676 }} (291b), and {{val\| 291 461 675 }} (291c).

FloraC: Rework

2024-03-04T09:18:02Z

Rework

← Older revision		Revision as of 09:18, 4 March 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''291edo''' is the [[~~EDO\|equal division of the octave]] into 291 parts of 4.1237 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <291 461 676\| (patent val), <291 462 676\| (291b), and <291 461 675\| (291c).		{{EDO intro}}

	~~Using the patent val, it tempers out 393216/390625 and \|-47 37 -5>~~ in the 5-~~limit; 2401/2400, 3136/3125, and 1162261467/1146880000 in the 7~~-limit~~; 243/242, 441/440, 5632/5625,~~ and ~~58720256/58461513 in the 11-limit; 351/350~~, ~~1001/1000, 1575/1573, 3584/3575, and 43940/43923 in~~ the 13-limit~~, so that it provides the~~ [[~~optimal~~ patent val]] ~~for the 13-limit [[Würschmidt family~~\|~~hemiwürschmidt temperament]]~~.		291edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val\| 291 461 676 }} ([[patent val]]), {{val\| 291 462 676 }} (291b), and {{val\| 291 461 675 }} (291c).

	Using the 291b val, it tempers out 15625/15552 and \|80 -46 -3~~>~~ in the 5-limit.		Using the patent val, it [[tempering out\|tempers out]] [[393216/390625]] and {{monzo\| -47 37 -5 }} in the 5-limit; [[2401/2400]], [[3136/3125]], and 1162261467/1146880000 in the 7-limit; [[243/242]], [[441/440]], [[5632/5625]], and 58720256/58461513 in the 11-limit; [[351/350]], [[1001/1000]], [[1575/1573]], 3584/3575, and 43940/43923 in the 13-limit, so that it provides the [[optimal patent val]] for the 13-limit [[hemiwürschmidt]] temperament.

			Using the 291b val, it tempers out 15625/15552 and {{monzo\| 80 -46 -3 }} in the 5-limit.

	Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit.		Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit.

			=== Prime harmonics ===
	{{Harmonics in equal\|291}}		{{Harmonics in equal\|291}}
	[[Category:~~Equal divisions of the octave\|###~~]] ~~<!-- 3-digit number -->~~
			=== Subsets and supersets ===
			Since 291 factors into {{factorization\|291}}, 291edo contains [[3edo]] and [[97edo]] as its subsets.

			[[Category:Hemiwürschmidt]]

BudjarnLambeth: Added "harmonics in equal" table

2023-06-24T03:17:34Z

Added "harmonics in equal" table

← Older revision		Revision as of 03:17, 24 June 2023
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	{{Infobox ET}}		{{Infobox ET}}
	'''291edo''' is the [[EDO\|equal division of the octave]] into 291 parts of 4.1237 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <291 461 676\| (patent val), <291 462 676\| (291b), and <291 461 675\| (291c). Using the patent val, it tempers out 393216/390625 and \|-47 37 -5> in the 5-limit; 2401/2400, 3136/3125, and 1162261467/1146880000 in the 7-limit; 243/242, 441/440, 5632/5625, and 58720256/58461513 in the 11-limit; 351/350, 1001/1000, 1575/1573, 3584/3575, and 43940/43923 in the 13-limit, so that it provides the [[Optimal_patent_val\|optimal patent val]] for the 13-limit [[Würschmidt family\|hemiwürschmidt temperament]]. Using the 291b val, it tempers out 15625/15552 and \|80 -46 -3> in the 5-limit. Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit.		'''291edo''' is the [[EDO\|equal division of the octave]] into 291 parts of 4.1237 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <291 461 676\| (patent val), <291 462 676\| (291b), and <291 461 675\| (291c).

			Using the patent val, it tempers out 393216/390625 and \|-47 37 -5> in the 5-limit; 2401/2400, 3136/3125, and 1162261467/1146880000 in the 7-limit; 243/242, 441/440, 5632/5625, and 58720256/58461513 in the 11-limit; 351/350, 1001/1000, 1575/1573, 3584/3575, and 43940/43923 in the 13-limit, so that it provides the [[optimal patent val]] for the 13-limit [[Würschmidt family\|hemiwürschmidt temperament]].

			Using the 291b val, it tempers out 15625/15552 and \|80 -46 -3> in the 5-limit.

			Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit.

			{{Harmonics in equal\|291}}
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Plumtree: Infobox ET added

2022-10-04T21:47:41Z

Infobox ET added

← Older revision		Revision as of 21:47, 4 October 2022
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			{{Infobox ET}}
	'''291edo''' is the [[EDO\|equal division of the octave]] into 291 parts of 4.1237 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <291 461 676\| (patent val), <291 462 676\| (291b), and <291 461 675\| (291c). Using the patent val, it tempers out 393216/390625 and \|-47 37 -5> in the 5-limit; 2401/2400, 3136/3125, and 1162261467/1146880000 in the 7-limit; 243/242, 441/440, 5632/5625, and 58720256/58461513 in the 11-limit; 351/350, 1001/1000, 1575/1573, 3584/3575, and 43940/43923 in the 13-limit, so that it provides the [[Optimal_patent_val\|optimal patent val]] for the 13-limit [[Würschmidt family\|hemiwürschmidt temperament]]. Using the 291b val, it tempers out 15625/15552 and \|80 -46 -3> in the 5-limit. Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit.		'''291edo''' is the [[EDO\|equal division of the octave]] into 291 parts of 4.1237 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <291 461 676\| (patent val), <291 462 676\| (291b), and <291 461 675\| (291c). Using the patent val, it tempers out 393216/390625 and \|-47 37 -5> in the 5-limit; 2401/2400, 3136/3125, and 1162261467/1146880000 in the 7-limit; 243/242, 441/440, 5632/5625, and 58720256/58461513 in the 11-limit; 351/350, 1001/1000, 1575/1573, 3584/3575, and 43940/43923 in the 13-limit, so that it provides the [[Optimal_patent_val\|optimal patent val]] for the 13-limit [[Würschmidt family\|hemiwürschmidt temperament]]. Using the 291b val, it tempers out 15625/15552 and \|80 -46 -3> in the 5-limit. Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit.

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

Fredg999 category edits: Sort key

2022-07-03T19:08:56Z

Sort key

← Older revision		Revision as of 19:08, 3 July 2022
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	'''291edo''' is the [[EDO\|equal division of the octave]] into 291 parts of 4.1237 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <291 461 676\| (patent val), <291 462 676\| (291b), and <291 461 675\| (291c). Using the patent val, it tempers out 393216/390625 and \|-47 37 -5> in the 5-limit; 2401/2400, 3136/3125, and 1162261467/1146880000 in the 7-limit; 243/242, 441/440, 5632/5625, and 58720256/58461513 in the 11-limit; 351/350, 1001/1000, 1575/1573, 3584/3575, and 43940/43923 in the 13-limit, so that it provides the [[Optimal_patent_val\|optimal patent val]] for the 13-limit [[Würschmidt family\|hemiwürschmidt temperament]]. Using the 291b val, it tempers out 15625/15552 and \|80 -46 -3> in the 5-limit. Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit.		'''291edo''' is the [[EDO\|equal division of the octave]] into 291 parts of 4.1237 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <291 461 676\| (patent val), <291 462 676\| (291b), and <291 461 675\| (291c). Using the patent val, it tempers out 393216/390625 and \|-47 37 -5> in the 5-limit; 2401/2400, 3136/3125, and 1162261467/1146880000 in the 7-limit; 243/242, 441/440, 5632/5625, and 58720256/58461513 in the 11-limit; 351/350, 1001/1000, 1575/1573, 3584/3575, and 43940/43923 in the 13-limit, so that it provides the [[Optimal_patent_val\|optimal patent val]] for the 13-limit [[Würschmidt family\|hemiwürschmidt temperament]]. Using the 291b val, it tempers out 15625/15552 and \|80 -46 -3> in the 5-limit. Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit.

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

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

2020-12-04T23:13:23Z

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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	'''291edo''' is the [[EDO\|equal division of the octave]] into 291 parts of 4.1237 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <291 461 676\| (patent val), <291 462 676\| (291b), and <291 461 675\| (291c). Using the patent val, it tempers out 393216/390625 and \|-47 37 -5> in the 5-limit; 2401/2400, 3136/3125, and 1162261467/1146880000 in the 7-limit; 243/242, 441/440, 5632/5625, and 58720256/58461513 in the 11-limit; 351/350, 1001/1000, 1575/1573, 3584/3575, and 43940/43923 in the 13-limit, so that it provides the [[Optimal_patent_val\|optimal patent val]] for the 13-limit [[Würschmidt family\|hemiwürschmidt temperament]]. Using the 291b val, it tempers out 15625/15552 and \|80 -46 -3> in the 5-limit. Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit.		'''291edo''' is the [[EDO\|equal division of the octave]] into 291 parts of 4.1237 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <291 461 676\| (patent val), <291 462 676\| (291b), and <291 461 675\| (291c). Using the patent val, it tempers out 393216/390625 and \|-47 37 -5> in the 5-limit; 2401/2400, 3136/3125, and 1162261467/1146880000 in the 7-limit; 243/242, 441/440, 5632/5625, and 58720256/58461513 in the 11-limit; 351/350, 1001/1000, 1575/1573, 3584/3575, and 43940/43923 in the 13-limit, so that it provides the [[Optimal_patent_val\|optimal patent val]] for the 13-limit [[Würschmidt family\|hemiwürschmidt temperament]]. Using the 291b val, it tempers out 15625/15552 and \|80 -46 -3> in the 5-limit. Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit.

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

Xenllium: Created page with "'''291edo''' is the equal division of the octave into 291 parts of 4.1237 cents each. It is inconsistent to the 5-limit and higher limit, with three mappings possi..."

2019-03-13T11:58:19Z

Created page with "'''291edo''' is the equal division of the octave into 291 parts of 4.1237 cents each. It is inconsistent to the 5-limit and higher limit, with three mappings possi..."

New page

'''291edo''' is the [[EDO|equal division of the octave]] into 291 parts of 4.1237 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <291 461 676| (patent val), <291 462 676| (291b), and <291 461 675| (291c). Using the patent val, it tempers out 393216/390625 and |-47 37 -5> in the 5-limit; 2401/2400, 3136/3125, and 1162261467/1146880000 in the 7-limit; 243/242, 441/440, 5632/5625, and 58720256/58461513 in the 11-limit; 351/350, 1001/1000, 1575/1573, 3584/3575, and 43940/43923 in the 13-limit, so that it provides the [[Optimal_patent_val|optimal patent val]] for the 13-limit [[Würschmidt family|hemiwürschmidt temperament]]. Using the 291b val, it tempers out 15625/15552 and |80 -46 -3> in the 5-limit. Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit.

[[Category:Edo]]