7315edo - Revision history

Eufalesio: Higher limit usage description

2026-01-28T11:18:00Z

Higher limit usage description

← Older revision		Revision as of 11:18, 28 January 2026
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	7315edo is [[consistent]] up to the [[27-odd-limit]]. 7315 = 11 × 665, and 7315edo shares its excellent approximation to [[harmonic]] [[3/1\|3]] with [[665edo]]. It notably demonstrates 3-2 [[telicity]], and is in fact the largest multiple of 665edo to do so. It has a sharp tendency, with most lower harmonics tuned sharp. In the 13-limit it [[tempering out\|tempers out]] [[123201/123200]]; in the 17-limit, [[14400/14399]] and [[194481/194480]]; in the 19-limit, 14080/14079, 23409/23408, 27456/27455, 89376/89375; in the 23-limit, 23276/23275, 52326/52325 among others.		7315edo is [[consistent]] up to the [[27-odd-limit]]. 7315 = 11 × 665, and 7315edo shares its excellent approximation to [[harmonic]] [[3/1\|3]] with [[665edo]]. It notably demonstrates 3-2 [[telicity]], and is in fact the largest multiple of 665edo to do so. It has a sharp tendency, with most lower harmonics tuned sharp. In the 13-limit it [[tempering out\|tempers out]] [[123201/123200]]; in the 17-limit, [[14400/14399]] and [[194481/194480]]; in the 19-limit, 14080/14079, 23409/23408, 27456/27455, 89376/89375; in the 23-limit, 23276/23275, 52326/52325 among others.

			It can be used in higher limits, notably the [[31-odd-limit]], and even the no-41 [[59-odd-limit]], due to a large number of the harmonics being either sharp, or not too negative. The inconsistencies here largely happen with primes 29, 37, and 43, which are slightly flat; namely: 49/29, 49/37, 49/43, 29/19, 37/19, 43/38, 59/58, 59/37, 59/43, and [[octave complement]]<nowiki/>s.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|7315}}		{{Harmonics in equal\|7315}}{{Harmonics in equal\|7315\|columns=11\|start=12\|collapsed=true\|title=Approximation of prime harmonics in 7315edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 7315 factors into {{factorization\|7315}}, 7315edo contains subset edos 5, 7, 11, 19, 35, 55, 77, 95, 133, 209, 385, 665, 1045, and 1463.		Since 7315 factors into {{factorization\|7315}}, 7315edo contains subset edos 5, 7, 11, 19, 35, 55, 77, 95, 133, 209, 385, 665, 1045, and 1463.

Overthink: + telicity

2025-09-22T06:02:44Z

+ telicity

← Older revision		Revision as of 06:02, 22 September 2025
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	{{ED intro}}		{{ED intro}}

	7315edo is [[consistent]] up to the [[27-odd-limit]]. 7315 = 11 × 665, and 7315edo shares its excellent approximation to [[harmonic]] [[3/1\|3]] with [[665edo]]. It has a sharp tendency, with most lower harmonics tuned sharp. In the 13-limit it [[tempering out\|tempers out]] [[123201/123200]]; in the 17-limit, [[14400/14399]] and [[194481/194480]]; in the 19-limit, 14080/14079, 23409/23408, 27456/27455, 89376/89375; in the 23-limit, 23276/23275, 52326/52325 among others.		7315edo is [[consistent]] up to the [[27-odd-limit]]. 7315 = 11 × 665, and 7315edo shares its excellent approximation to [[harmonic]] [[3/1\|3]] with [[665edo]]. It notably demonstrates 3-2 [[telicity]], and is in fact the largest multiple of 665edo to do so. It has a sharp tendency, with most lower harmonics tuned sharp. In the 13-limit it [[tempering out\|tempers out]] [[123201/123200]]; in the 17-limit, [[14400/14399]] and [[194481/194480]]; in the 19-limit, 14080/14079, 23409/23408, 27456/27455, 89376/89375; in the 23-limit, 23276/23275, 52326/52325 among others.

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

ArrowHead294 at 23:15, 20 February 2025

2025-02-20T23:15:40Z

← Older revision		Revision as of 23:15, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|7315~~}}		{{ED intro}}

	7315edo is [[consistent]] up to the [[27-odd-limit]]. 7315 = 11 × 665, and 7315edo shares its excellent approximation to [[harmonic]] [[3/1\|3]] with [[665edo]]. It has a sharp tendency, with most lower harmonics tuned sharp. In the 13-limit it [[tempering out\|tempers out]] [[123201/123200]]; in the 17-limit, [[14400/14399]] and [[194481/194480]]; in the 19-limit, 14080/14079, 23409/23408, 27456/27455, 89376/89375; in the 23-limit, 23276/23275, 52326/52325 among others.		7315edo is [[consistent]] up to the [[27-odd-limit]]. 7315 = 11 × 665, and 7315edo shares its excellent approximation to [[harmonic]] [[3/1\|3]] with [[665edo]]. It has a sharp tendency, with most lower harmonics tuned sharp. In the 13-limit it [[tempering out\|tempers out]] [[123201/123200]]; in the 17-limit, [[14400/14399]] and [[194481/194480]]; in the 19-limit, 14080/14079, 23409/23408, 27456/27455, 89376/89375; in the 23-limit, 23276/23275, 52326/52325 among others.

FloraC: Expand and unstub

2024-08-21T12:26:01Z

Expand and unstub

← Older revision		Revision as of 12:26, 21 August 2024
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	{{EDO intro\|7315}}		{{EDO intro\|7315}}

	7315edo is [[consistent]] up to the [[27-odd-limit]]. 7315 = 11 × 665, and 7315edo shares its [[3/2\|~~fifth~~]] with [[665edo]].		7315edo is [[consistent]] up to the [[27-odd-limit]]. 7315 = 11 × 665, and 7315edo shares its excellent approximation to [[harmonic]] [[3/1\|3]] with [[665edo]]. It has a sharp tendency, with most lower harmonics tuned sharp. In the 13-limit it [[tempering out\|tempers out]] [[123201/123200]]; in the 17-limit, [[14400/14399]] and [[194481/194480]]; in the 19-limit, 14080/14079, 23409/23408, 27456/27455, 89376/89375; in the 23-limit, 23276/23275, 52326/52325 among others.

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 7315 factors into {{factorization\|7315}}, 7315edo contains subset edos 5, 7, 11, 19, 35, 55, 77, 95, 133, 209, 385, 665, 1045, and 1463.		Since 7315 factors into {{factorization\|7315}}, 7315edo contains subset edos 5, 7, 11, 19, 35, 55, 77, 95, 133, 209, 385, 665, 1045, and 1463.

	~~{{Stub}}~~

FloraC: Expand

2024-08-20T16:57:32Z

Expand

← Older revision		Revision as of 16:57, 20 August 2024
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	{{EDO intro\|7315}}		{{EDO intro\|7315}}

	~~== Theory ==~~		7315edo is [[consistent]] up to the [[27-odd-limit]]. 7315 = 11 × 665, and 7315edo shares its [[3/2\|fifth]] with [[665edo]].
	~~This EDO~~ is consistent up to the 27-odd-limit, ~~which is rather impressive~~.

			=== Prime harmonics ===
	{{Harmonics in equal\|7315}}		{{Harmonics in equal\|7315}}

			=== Subsets and supersets ===
			Since 7315 factors into {{factorization\|7315}}, 7315edo contains subset edos 5, 7, 11, 19, 35, 55, 77, 95, 133, 209, 385, 665, 1045, and 1463.

	{{Stub}}		{{Stub}}

FloraC: Mark stub

2023-09-24T05:22:26Z

Mark stub

← Older revision		Revision as of 05:22, 24 September 2023
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	{{Harmonics in equal\|7315}}		{{Harmonics in equal\|7315}}

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

BudjarnLambeth at 07:10, 9 July 2023

2023-07-09T07:10:14Z

← Older revision		Revision as of 07:10, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|7315}}		{{EDO intro\|7315}}

BudjarnLambeth at 04:19, 9 July 2023

2023-07-09T04:19:56Z

← Older revision		Revision as of 04:19, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|7315}}		{{EDO intro\|7315}}

Aura: Created page with "{{Infobox ET}} {{EDO intro|7315}} == Theory == This EDO is consistent up to the 27-odd-limit, which is rather impressive. {{Harmonics in equal|7315}} Category:Equal divi..."

2022-12-22T11:41:36Z

Created page with "{{Infobox ET}} {{EDO intro|7315}} == Theory == This EDO is consistent up to the 27-odd-limit, which is rather impressive. {{Harmonics in equal|7315}} Category:Equal divi..."

New page

{{Infobox ET}}
{{EDO intro|7315}}

== Theory ==
This EDO is consistent up to the 27-odd-limit, which is rather impressive.

{{Harmonics in equal|7315}}

[[Category:Equal divisions of the octave|####]]