2190edo - Revision history

FloraC: Expand the harmonics table a little

2025-10-02T16:09:44Z

Expand the harmonics table a little

← Older revision		Revision as of 16:09, 2 October 2025
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|2190\|columns=9}}		{{Harmonics in equal\|2190\|columns=11}}
	{{Harmonics in equal\|2190\|columns=9\|start=10\|collapsed=true\|title=Approximation of prime harmonics in 2190edo (continued)}}		{{Harmonics in equal\|2190\|columns=11\|start=12\|collapsed=true\|title=Approximation of prime harmonics in 2190edo (continued)}}

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

FloraC: Expand

2025-03-07T08:07:18Z

Expand

← Older revision		Revision as of 08:07, 7 March 2025
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	{{ED intro}}		{{ED intro}}

	2190edo is a very strong [[13-limit]] system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and nothing beats it until [[2684edo\|2684]]. A basis for the 13-limit ~~commas~~ is {[[9801/9800]], [[10648/10647]], 105644/105625, [[140625/140608]], 196625/196608}; also [[tempering out\|tempered out]] are [[123201/123200]] ~~and~~ 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19~~.29~~ [[subgroup]], ~~holding~~ the record of relative error until [[14618edo\|14618]].		2190edo is a very strong [[13-limit]] system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and nothing beats it until [[2684edo\|2684]]. It is closely related to [[730edo]], the Woolhouse unit system, with which it shares the same tuning in the [[5-limit]], but the [[harmonic]]s [[7/1\|7]], [[11/1\|11]], and [[13/1\|13]] are all mapped differently. A basis for the 13-limit [[comma]]s is {[[9801/9800]], [[10648/10647]], 105644/105625, [[140625/140608]], 196625/196608}; also [[tempering out\|tempered out]] are [[123201/123200]], [[151263/151250]], and [[250047/250000]].

			It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19 [[subgroup]], where it holds the record of lowest relative error until [[6079edo\|6079]], and the 2.3.5.7.11.13.19.29 subgroup, where it holds the record of lowest relative error until [[14618edo\|14618]].

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|2190\|columns=11}}		{{Harmonics in equal\|2190\|columns=9}}
			{{Harmonics in equal\|2190\|columns=9\|start=10\|collapsed=true\|title=Approximation of prime harmonics in 2190edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	2190 factors into {{~~factorization~~\|~~2190~~}}~~; among its divisors~~ is ~~the~~ Woolhouse unit ~~system, [[730edo\|730]]~~.		Since 2190 factors into primes as {{nowrap\| 2 × 3 × 5 × 73 }}, 2190edo has subset edos {{EDOs\| 2, 3, 5, 6, 10, 12, 15, 30, 73, 146, 219, 365, 438, 730, and 1095 }}. A step of 2190edo is exactly {{frac\|1\|3}} Woolhouse unit.

	[[4380edo]], which doubles 2190edo, provides a good correction to the harmonics 17 and 23.		[[4380edo]], which doubles 2190edo, provides a good correction to the harmonics [[17/1\|17]] and [[23/1\|23]].

ArrowHead294 at 14:17, 20 February 2025

2025-02-20T14:17:40Z

← Older revision		Revision as of 14:17, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|2190~~}}		{{ED intro}}

	2190edo is a very strong [[13-limit]] system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and nothing beats it until [[2684edo\|2684]]. A basis for the 13-limit commas is {[[9801/9800]], [[10648/10647]], 105644/105625, [[140625/140608]], 196625/196608}; also [[tempering out\|tempered out]] are [[123201/123200]] and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 [[subgroup]], holding the record of relative error until [[14618edo\|14618]].		2190edo is a very strong [[13-limit]] system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and nothing beats it until [[2684edo\|2684]]. A basis for the 13-limit commas is {[[9801/9800]], [[10648/10647]], 105644/105625, [[140625/140608]], 196625/196608}; also [[tempering out\|tempered out]] are [[123201/123200]] and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 [[subgroup]], holding the record of relative error until [[14618edo\|14618]].

FloraC: Note its exceptional accuracy in the no-17 no-23 29-limit

2024-11-07T16:18:16Z

Note its exceptional accuracy in the no-17 no-23 29-limit

← Older revision		Revision as of 16:18, 7 November 2024
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	{{EDO intro\|2190}}		{{EDO intro\|2190}}

	2190edo is a very strong [[13-limit]] system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and nothing beats it until [[2684edo\|2684]]. A basis for the 13-limit commas is {[[9801/9800]], [[10648/10647]], 105644/105625, [[140625/140608]], 196625/196608}; also [[tempering out\|tempered out]] are [[123201/123200]] and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 [[subgroup]].		2190edo is a very strong [[13-limit]] system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and nothing beats it until [[2684edo\|2684]]. A basis for the 13-limit commas is {[[9801/9800]], [[10648/10647]], 105644/105625, [[140625/140608]], 196625/196608}; also [[tempering out\|tempered out]] are [[123201/123200]] and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 [[subgroup]], holding the record of relative error until [[14618edo\|14618]].

	=== Prime harmonics ===		=== Prime harmonics ===

FloraC: -typo; +links

2024-11-07T16:16:20Z

-typo; +links

← Older revision		Revision as of 16:16, 7 November 2024
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	{{EDO intro\|2190}}		{{EDO intro\|2190}}

	2190edo is is a very strong 13-limit system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and nothing beats it until [[2684edo\|2684]]. A basis for the 13-limit commas is {[[9801/9800]], [[10648/10647]], 105644/105625, 140625/140608, 196625/196608}; also [[tempering out\|tempered out]] are 123201/123200 and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 [[subgroup]].		2190edo is a very strong [[13-limit]] system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and nothing beats it until [[2684edo\|2684]]. A basis for the 13-limit commas is {[[9801/9800]], [[10648/10647]], 105644/105625, [[140625/140608]], 196625/196608}; also [[tempering out\|tempered out]] are [[123201/123200]] and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 [[subgroup]].

	=== Prime harmonics ===		=== Prime harmonics ===

FloraC: Adopt template: Factorization

2023-10-30T10:52:52Z

Adopt template: Factorization

← Older revision		Revision as of 10:52, 30 October 2023
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|2190}} It is is a very strong 13-limit system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and nothing beats it until [[2684edo\|2684]]. A basis for the 13-limit commas is {9801/9800, 10648/10647, 105644/105625, 140625/140608, 196625/196608}; also tempered out are 123201/123200 and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 subgroup.		{{EDO intro\|2190}}

			2190edo is is a very strong 13-limit system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and nothing beats it until [[2684edo\|2684]]. A basis for the 13-limit commas is {[[9801/9800]], [[10648/10647]], 105644/105625, 140625/140608, 196625/196608}; also [[tempering out\|tempered out]] are 123201/123200 and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 [[subgroup]].

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	2190 factors ~~as 2 × 3 × 5 × 73~~; among its divisors is the Woolhouse unit system, [[730edo\|730]].		2190 factors into {{factorization\|2190}}; among its divisors is the Woolhouse unit system, [[730edo\|730]].

	[[4380edo]], which doubles 2190edo, provides a good correction to the harmonics 17 and 23.		[[4380edo]], which doubles 2190edo, provides a good correction to the harmonics 17 and 23.

Eliora: /* Subsets and supersets */

2023-09-18T21:24:57Z

Subsets and supersets

← Older revision		Revision as of 21:24, 18 September 2023
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	2190 factors as 2 × 3 × 5 × 73; among its divisors is the Woolhouse unit system, [[730edo\|730]].		2190 factors as 2 × 3 × 5 × 73; among its divisors is the Woolhouse unit system, [[730edo\|730]].

	4380edo, which doubles 2190edo, provides a good correction to the harmonics 17 and 23.		[[4380edo]], which doubles 2190edo, provides a good correction to the harmonics 17 and 23.

BudjarnLambeth at 07:01, 9 July 2023

2023-07-09T07:01:22Z

← Older revision		Revision as of 07:01, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|2190}} It is is a very strong 13-limit system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and nothing beats it until [[2684edo\|2684]]. A basis for the 13-limit commas is {9801/9800, 10648/10647, 105644/105625, 140625/140608, 196625/196608}; also tempered out are 123201/123200 and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 subgroup.		{{EDO intro\|2190}} It is is a very strong 13-limit system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and nothing beats it until [[2684edo\|2684]]. A basis for the 13-limit commas is {9801/9800, 10648/10647, 105644/105625, 140625/140608, 196625/196608}; also tempered out are 123201/123200 and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 subgroup.

BudjarnLambeth at 04:38, 9 July 2023

2023-07-09T04:38:04Z

← Older revision		Revision as of 04:38, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|2190}} It is is a very strong 13-limit system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and nothing beats it until [[2684edo\|2684]]. A basis for the 13-limit commas is {9801/9800, 10648/10647, 105644/105625, 140625/140608, 196625/196608}; also tempered out are 123201/123200 and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 subgroup.		{{EDO intro\|2190}} It is is a very strong 13-limit system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and nothing beats it until [[2684edo\|2684]]. A basis for the 13-limit commas is {9801/9800, 10648/10647, 105644/105625, 140625/140608, 196625/196608}; also tempered out are 123201/123200 and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 subgroup.

FloraC: Beyond the 13-limit

2023-02-19T13:05:00Z

Beyond the 13-limit

← Older revision		Revision as of 13:05, 19 February 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~The '''~~2190 ~~equal division''' divides the octave into 2190 equal parts of 0.5479 [[cent]]s each.~~ It is is a very strong 13-limit system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and nothing beats it until [[2684edo\|2684]]. A basis for the 13-limit commas is {9801/9800, 10648/10647, 105644/105625, 140625/140608, 196625/196608}; also tempered out are 123201/123200 and 151263/151250.		{{EDO intro\|2190}} It is is a very strong 13-limit system; no smaller division has a smaller 13-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]], and nothing beats it until [[2684edo\|2684]]. A basis for the 13-limit commas is {9801/9800, 10648/10647, 105644/105625, 140625/140608, 196625/196608}; also tempered out are 123201/123200 and 151263/151250. It is not as impressive beyond the 13-limit, though it does well in the 2.3.5.7.11.13.19.29 subgroup.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|2190\|columns=11}}		{{Harmonics in equal\|2190\|columns=11}}

	=== ~~Miscellaneous properties~~ ===		=== Subsets and supersets ===
	2190 factors as 2 × 3 × 5 × 73; among its divisors is the Woolhouse unit system, [[730edo\|730]].		2190 factors as 2 × 3 × 5 × 73; among its divisors is the Woolhouse unit system, [[730edo\|730]].

	~~[[Category:Equal divisions of~~ the ~~octave\|####]] <!-- 4-digit number -->~~		4380edo, which doubles 2190edo, provides a good correction to the harmonics 17 and 23.