4501edo - Revision history

FloraC: Oops

2026-04-17T14:20:38Z

Oops

← Older revision		Revision as of 14:20, 17 April 2026
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|4501\|columns=11}}		{{Harmonics in equal\|4501\|columns=11}}
	{{Harmonics in equal\|4501\|columns=11\|start=12\|~~collpased~~=true\|title=Approximation of prime harmonics in 4501edo (continued)}}		{{Harmonics in equal\|4501\|columns=11\|start=12\|collapsed=true\|title=Approximation of prime harmonics in 4501edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 4501 factors into primes as {{nowrap\| 7 × 643 }}, 4501edo has subset edos [[7edo\|7]] and [[643edo\|643]].		Since 4501 factors into primes as {{nowrap\| 7 × 643 }}, 4501edo has subset edos [[7edo\|7]] and [[643edo\|643]].

FloraC: Wrap

2026-04-17T14:20:14Z

Wrap

← Older revision		Revision as of 14:20, 17 April 2026
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	{{ED intro}}		{{ED intro}}

	4501edo is a very strong high-limit system, distinctly [[consistent]] through the 39-odd-limit, and has the lowest [[31-limit\|31-]] and [[37-limit]] [[~~Tenney-Euclidean~~ temperament measures #TE simple badness\|relative error]] of any equal temperament until [[16808edo\|16808]]. The 4501m val likewise performs well in the [[41-limit\|41-]] and [[43-limit]], with the lowest relative error of any equal temperament until [[7361edo\|7361]].		4501edo is a very strong high-limit system, distinctly [[consistent]] through the 39-odd-limit, and has the lowest [[31-limit\|31-]] and [[37-limit]] [[Tenney–Euclidean temperament measures #TE simple badness\|relative error]] of any equal temperament until [[16808edo\|16808]]. The 4501m val likewise performs well in the [[41-limit\|41-]] and [[43-limit]], with the lowest relative error of any equal temperament until [[7361edo\|7361]].

	Some of the simpler commas it [[tempering out\|tempers out]] include [[10648/10647]] and [[140625/140608]] in the 13-limit; [[14400/14399]], [[31213/31212]], and [[37180/37179]] in the 17-limit; 10830/10829, 14080/14079, and 27456/27455 in the 19-limit; 11662/11661, [[12168/12167]], 16929/16928, and 19551/19550 in the 23-limit; 11340/11339, 13312/13311, and 13456/13455 in the 29-limit; 7936/7935, 11935/11934, 15625/15624, [[19344/19343]], 23716/23715, 24025/24024, and 29792/29791 in the 31-limit.		Some of the simpler commas it [[tempering out\|tempers out]] include [[10648/10647]] and [[140625/140608]] in the 13-limit; [[14400/14399]], [[31213/31212]], and [[37180/37179]] in the 17-limit; 10830/10829, 14080/14079, and 27456/27455 in the 19-limit; 11662/11661, [[12168/12167]], 16929/16928, and 19551/19550 in the 23-limit; 11340/11339, 13312/13311, and 13456/13455 in the 29-limit; 7936/7935, 11935/11934, 15625/15624, [[19344/19343]], 23716/23715, 24025/24024, and 29792/29791 in the 31-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|4501\|columns=15}}		{{Harmonics in equal\|4501\|columns=11}}
			{{Harmonics in equal\|4501\|columns=11\|start=12\|collpased=true\|title=Approximation of prime harmonics in 4501edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 4501 factors into 7 × 643, 4501edo has subset edos [[7edo\|7]] and [[643edo\|643]].		Since 4501 factors into primes as {{nowrap\| 7 × 643 }}, 4501edo has subset edos [[7edo\|7]] and [[643edo\|643]].

ArrowHead294 at 14:58, 20 February 2025

2025-02-20T14:58:18Z

← Older revision		Revision as of 14:58, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|4501~~}}		{{ED intro}}

	4501edo is a very strong high-limit system, distinctly [[consistent]] through the 39-odd-limit, and has the lowest [[31-limit\|31-]] and [[37-limit]] [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] of any equal temperament until [[16808edo\|16808]]. The 4501m val likewise performs well in the [[41-limit\|41-]] and [[43-limit]], with the lowest relative error of any equal temperament until [[7361edo\|7361]].		4501edo is a very strong high-limit system, distinctly [[consistent]] through the 39-odd-limit, and has the lowest [[31-limit\|31-]] and [[37-limit]] [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] of any equal temperament until [[16808edo\|16808]]. The 4501m val likewise performs well in the [[41-limit\|41-]] and [[43-limit]], with the lowest relative error of any equal temperament until [[7361edo\|7361]].

FloraC: Expand with some commas

2025-01-12T09:55:38Z

Expand with some commas

← Older revision		Revision as of 09:55, 12 January 2025
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	{{EDO intro\|4501}}		{{EDO intro\|4501}}

	4501edo is a very strong high-limit system, distinctly [[consistent]] through the 39-odd-limit, and has the lowest 31- and 37-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] of any equal temperament until [[16808edo\|16808]]. The 4501m val likewise performs well in the 41- and 43-limit, with the lowest relative error of any equal temperament until [[7361edo\|7361]].		4501edo is a very strong high-limit system, distinctly [[consistent]] through the 39-odd-limit, and has the lowest [[31-limit\|31-]] and [[37-limit]] [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] of any equal temperament until [[16808edo\|16808]]. The 4501m val likewise performs well in the [[41-limit\|41-]] and [[43-limit]], with the lowest relative error of any equal temperament until [[7361edo\|7361]].

			Some of the simpler commas it [[tempering out\|tempers out]] include [[10648/10647]] and [[140625/140608]] in the 13-limit; [[14400/14399]], [[31213/31212]], and [[37180/37179]] in the 17-limit; 10830/10829, 14080/14079, and 27456/27455 in the 19-limit; 11662/11661, [[12168/12167]], 16929/16928, and 19551/19550 in the 23-limit; 11340/11339, 13312/13311, and 13456/13455 in the 29-limit; 7936/7935, 11935/11934, 15625/15624, [[19344/19343]], 23716/23715, 24025/24024, and 29792/29791 in the 31-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 8:		Line 10:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	4501edo has subset edos [[7edo\|7]] and [[643edo\|643]].		Since 4501 factors into 7 × 643, 4501edo has subset edos [[7edo\|7]] and [[643edo\|643]].

BudjarnLambeth at 07:07, 9 July 2023

2023-07-09T07:07:47Z

← Older revision		Revision as of 07:07, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|4501}}		{{EDO intro\|4501}}

BudjarnLambeth at 04:24, 9 July 2023

2023-07-09T04:24:13Z

← Older revision		Revision as of 04:24, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|4501}}		{{EDO intro\|4501}}

FloraC: 41- and 43-limit notability

2023-02-20T12:11:56Z

41- and 43-limit notability

← Older revision		Revision as of 12:11, 20 February 2023
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|4501}} It is a very strong 37-limit system, distinctly [[consistent]] through the 39-odd-limit, and has the lowest 31-~~limit~~ and 37-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] of any ~~division~~ until [[16808edo\|16808]].		{{EDO intro\|4501}}

			4501edo is a very strong high-limit system, distinctly [[consistent]] through the 39-odd-limit, and has the lowest 31- and 37-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] of any equal temperament until [[16808edo\|16808]]. The 4501m val likewise performs well in the 41- and 43-limit, with the lowest relative error of any equal temperament until [[7361edo\|7361]].

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|4501}}		{{Harmonics in equal\|4501\|columns=15}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	4501edo has subset edos [[7edo\|7]] and [[643edo\|643]].		4501edo has subset edos [[7edo\|7]] and [[643edo\|643]].

FloraC: Expansion

2023-02-19T10:59:31Z

Expansion

← Older revision		Revision as of 10:59, 19 February 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~The '''~~4501 ~~division''' divides the octave into 4501 equal parts of 0.26661 cents each.~~ It is a very strong 37-limit ~~division~~, distinctly consistent through the 39 limit, and has the lowest 31-limit and 37-limit [[Tenney-~~Euclidean_temperament_measures~~#TE simple badness\|relative error]] of any division until [[16808edo\|16808]].		{{EDO intro\|4501}} It is a very strong 37-limit system, distinctly [[consistent]] through the 39-odd-limit, and has the lowest 31-limit and 37-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] of any division until [[16808edo\|16808]].

	[[~~Category:Equal divisions of the octave~~\|~~####~~]] ~~<!-- 4-digit number -->~~		=== Prime harmonics ===
			{{Harmonics in equal\|4501}}

			=== Subsets and supersets ===
			4501edo has subset edos [[7edo\|7]] and [[643edo\|643]].

Plumtree: Infobox ET added

2022-10-04T22:18:43Z

Infobox ET added

← Older revision		Revision as of 22:18, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	The '''4501 division''' divides the octave into 4501 equal parts of 0.26661 cents each. It is a very strong 37-limit division, distinctly consistent through the 39 limit, and has the lowest 31-limit and 37-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]] of any division until [[16808edo\|16808]].		The '''4501 division''' divides the octave into 4501 equal parts of 0.26661 cents each. It is a very strong 37-limit division, distinctly consistent through the 39 limit, and has the lowest 31-limit and 37-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]] of any division until [[16808edo\|16808]].

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

Fredg999 category edits: Categories

2022-07-04T01:33:12Z

← Older revision		Revision as of 01:33, 4 July 2022
Line 1:		Line 1:
	The 4501 division divides the octave into 4501 equal parts of 0.26661 cents each. It is a very strong 37-limit division, distinctly consistent through the 39 limit, and has the lowest 31-limit and 37-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]] of any division until [[16808edo\|16808]].		The '''4501 division''' divides the octave into 4501 equal parts of 0.26661 cents each. It is a very strong 37-limit division, distinctly consistent through the 39 limit, and has the lowest 31-limit and 37-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]] of any division until [[16808edo\|16808]].

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