1308edo - Revision history

Overthink: links

2026-05-30T20:01:41Z

links

← Older revision		Revision as of 20:01, 30 May 2026
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	1308edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]], and is the 15th [[zeta gap edo]]. With [[23/17]] and [[27/23]] barely missing the line, it has reasonable approximations up to the 37-limit.		1308edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]], and is the 15th [[zeta gap edo]]. With [[23/17]] and [[27/23]] barely missing the line, it has reasonable approximations up to the 37-limit.

	It [[tempering out\|tempers out]] {{monzo\| 37 25 -33 }} (whoosh comma) and {{monzo\| -46 51 -15 }} (171 & 1137 comma) in the [[5-limit]]; [[250047/250000]], [[2460375/2458624]], and {{monzo\| 47 4 0 -19 }} in the [[7-limit]]; [[9801/9800]], [[151263/151250]], [[234375/234256]], and 67110351/67108864 in the [[11-limit]]; [[4225/4224]], [[6656/6655]], 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; [[2601/2600]], [[5832/5831]], [[11016/11011]], 11271/11264, [[12376/12375]], and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.		It [[tempering out\|tempers out]] {{monzo\| 37 25 -33 }} (whoosh comma) and {{monzo\| -46 51 -15 }} (171 & 1137 comma) in the [[5-limit]]; [[250047/250000]], [[2460375/2458624]], and {{monzo\| 47 4 0 -19 }} in the [[7-limit]]; [[9801/9800]], [[151263/151250]], [[234375/234256]], and 67110351/67108864 in the [[11-limit]]; [[4225/4224]], [[6656/6655]], 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; [[2601/2600]], [[5832/5831]], [[11016/11011]], 11271/11264, [[12376/12375]], and 108086/108045 in the 17-limit; [[5491/5488]], [[5776/5775]], [[5985/5984]], [[6175/6174]], 10241/10240, and 10830/10829 in the 19-limit.

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

FloraC: Cleanup

2026-01-30T06:33:56Z

Cleanup

← Older revision		Revision as of 06:33, 30 January 2026
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	1308edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]], and is the 15th [[zeta gap edo]]. With [[23/17]] and [[27/23]] barely missing the line, it has reasonable approximations up to the 37-limit.		1308edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]], and is the 15th [[zeta gap edo]]. With [[23/17]] and [[27/23]] barely missing the line, it has reasonable approximations up to the 37-limit.

	It [[tempering out\|tempers out]] {{monzo\| 37 25 -33 }} (whoosh comma) and {{monzo\| -46 51 -15 }} (171 &~~amp;~~ 1137 comma) in the 5-limit; [[250047/250000]], [[2460375/2458624]], and {{monzo\| 47 4 0 -19 }} in the 7-limit; [[9801/9800]], 151263/151250, 234375/234256, and 67110351/67108864 in the 11-limit; [[4225/4224]], [[6656/6655]], 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; [[2601/2600]], [[5832/5831]], [[11016/11011]], 11271/11264, [[12376/12375]], and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.		It [[tempering out\|tempers out]] {{monzo\| 37 25 -33 }} (whoosh comma) and {{monzo\| -46 51 -15 }} (171 & 1137 comma) in the [[5-limit]]; [[250047/250000]], [[2460375/2458624]], and {{monzo\| 47 4 0 -19 }} in the [[7-limit]]; [[9801/9800]], [[151263/151250]], [[234375/234256]], and 67110351/67108864 in the [[11-limit]]; [[4225/4224]], [[6656/6655]], 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; [[2601/2600]], [[5832/5831]], [[11016/11011]], 11271/11264, [[12376/12375]], and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 1308 factors into {{~~factorization~~\|~~1308~~}}, 1308edo has subset edos 2, 3, ~~{{EDOs\|~~4, 6, 12, 109, 218, 327, 436, and 654}}.		Since 1308 factors into primes as {{nowrap\| 2<sup>2</sup> × 3 × 109 }}, 1308edo has subset edos {{EDOs\| 2, 3, 4, 6, 12, 109, 218, 327, 436, and 654 }}.

FloraC: - typo

2026-01-30T06:32:33Z

- typo

← Older revision		Revision as of 06:32, 30 January 2026
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	{{ED intro}}		{{ED intro}}

	1308edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]], and is the 15th [[zeta gap edo]]. With [[23/17]]and [[27/23]] barely missing the line, it has reasonable approximations up to the 37-limit.		1308edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]], and is the 15th [[zeta gap edo]]. With [[23/17]] and [[27/23]] barely missing the line, it has reasonable approximations up to the 37-limit.

	It [[tempering out\|tempers out]] {{monzo\| 37 25 -33 }} (whoosh comma) and {{monzo\| -46 51 -15 }} (171 & 1137 comma) in the 5-limit; [[250047/250000]], [[2460375/2458624]], and {{monzo\| 47 4 0 -19 }} in the 7-limit; [[9801/9800]], 151263/151250, 234375/234256, and 67110351/67108864 in the 11-limit; [[4225/4224]], [[6656/6655]], 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; [[2601/2600]], [[5832/5831]], [[11016/11011]], 11271/11264, [[12376/12375]], and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.		It [[tempering out\|tempers out]] {{monzo\| 37 25 -33 }} (whoosh comma) and {{monzo\| -46 51 -15 }} (171 & 1137 comma) in the 5-limit; [[250047/250000]], [[2460375/2458624]], and {{monzo\| 47 4 0 -19 }} in the 7-limit; [[9801/9800]], 151263/151250, 234375/234256, and 67110351/67108864 in the 11-limit; [[4225/4224]], [[6656/6655]], 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; [[2601/2600]], [[5832/5831]], [[11016/11011]], 11271/11264, [[12376/12375]], and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.

Overthink: 27/23 is also inconsistent

2026-01-30T04:57:59Z

27/23 is also inconsistent

← Older revision		Revision as of 04:57, 30 January 2026
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	{{ED intro}}		{{ED intro}}

	1308edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]], and is the 15th [[zeta gap edo]]. With [[23/17]] barely missing the line, it has reasonable approximations up to the 37-limit.		1308edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]], and is the 15th [[zeta gap edo]]. With [[23/17]]and [[27/23]] barely missing the line, it has reasonable approximations up to the 37-limit.

	It [[tempering out\|tempers out]] {{monzo\| 37 25 -33 }} (whoosh comma) and {{monzo\| -46 51 -15 }} (171 & 1137 comma) in the 5-limit; [[250047/250000]], [[2460375/2458624]], and {{monzo\| 47 4 0 -19 }} in the 7-limit; [[9801/9800]], 151263/151250, 234375/234256, and 67110351/67108864 in the 11-limit; [[4225/4224]], [[6656/6655]], 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; [[2601/2600]], [[5832/5831]], [[11016/11011]], 11271/11264, [[12376/12375]], and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.		It [[tempering out\|tempers out]] {{monzo\| 37 25 -33 }} (whoosh comma) and {{monzo\| -46 51 -15 }} (171 & 1137 comma) in the 5-limit; [[250047/250000]], [[2460375/2458624]], and {{monzo\| 47 4 0 -19 }} in the 7-limit; [[9801/9800]], 151263/151250, 234375/234256, and 67110351/67108864 in the 11-limit; [[4225/4224]], [[6656/6655]], 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; [[2601/2600]], [[5832/5831]], [[11016/11011]], 11271/11264, [[12376/12375]], and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.

Overthink: + Template:EDOs

2025-11-23T17:57:53Z

+ Template:EDOs

← Older revision		Revision as of 17:57, 23 November 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 1308 factors into {{factorization\|1308}}, 1308edo has subset edos 2, 3, 4, 6, 12, 109, 218, 327, 436, and 654.		Since 1308 factors into {{factorization\|1308}}, 1308edo has subset edos 2, 3, {{EDOs\|4, 6, 12, 109, 218, 327, 436, and 654}}.

ArrowHead294 at 17:41, 20 February 2025

2025-02-20T17:41:51Z

← Older revision		Revision as of 17:41, 20 February 2025
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	1308edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]], and is the 15th [[zeta gap edo]]. With [[23/17]] barely missing the line, it has reasonable approximations up to the 37-limit.		1308edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]], and is the 15th [[zeta gap edo]]. With [[23/17]] barely missing the line, it has reasonable approximations up to the 37-limit.

	~~The equal temperament~~ [[tempering out\|tempers out]] {{monzo\| 37 25 -33 }} (whoosh comma) and {{monzo\| -46 51 -15 }} (171 & 1137 comma) in the 5-limit; [[250047/250000]], [[2460375/2458624]], and {{monzo\| 47 4 0 -19 }} in the 7-limit; [[9801/9800]], 151263/151250, 234375/234256, and 67110351/67108864 in the 11-limit; [[4225/4224]], [[6656/6655]], 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; [[2601/2600]], [[5832/5831]], [[11016/11011]], 11271/11264, [[12376/12375]], and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.		It [[tempering out\|tempers out]] {{monzo\| 37 25 -33 }} (whoosh comma) and {{monzo\| -46 51 -15 }} (171 & 1137 comma) in the 5-limit; [[250047/250000]], [[2460375/2458624]], and {{monzo\| 47 4 0 -19 }} in the 7-limit; [[9801/9800]], 151263/151250, 234375/234256, and 67110351/67108864 in the 11-limit; [[4225/4224]], [[6656/6655]], 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; [[2601/2600]], [[5832/5831]], [[11016/11011]], 11271/11264, [[12376/12375]], and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.

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

Francium: changed EDO intro to ED intro

2025-02-20T17:13:28Z

changed EDO intro to ED intro

← Older revision		Revision as of 17:13, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1308~~}}		{{ED intro}}

	1308edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]], and is the 15th [[zeta gap edo]]. With [[23/17]] barely missing the line, it has reasonable approximations up to the 37-limit.		1308edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]], and is the 15th [[zeta gap edo]]. With [[23/17]] barely missing the line, it has reasonable approximations up to the 37-limit.

FloraC: Rework on theory; adopt template: Factorization

2023-10-31T09:44:12Z

Rework on theory; adopt template: Factorization

← Older revision		Revision as of 09:44, 31 October 2023
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	{{EDO intro\|1308}}		{{EDO intro\|1308}}

	1308edo is [[consistent]] to the [[21-odd-limit]] ~~distinctly~~, ~~tempering out {{monzo\| 37 25 -33 }} (whoosh comma)~~ and ~~{{monzo\| -46 51 -15}} (171 & 453 comma) in~~ the ~~5-limit;~~ [[~~250047/250000~~]], [[~~2460375~~/~~2458624~~]]~~, and {{monzo\| 47 4 0 -19 }} in~~ the ~~7-limit; [[9801/9800]]~~, ~~151263/151250, 234375/234256, and 67110351/67108864 in~~ the 11-limit; [[4225/4224]], [[6656/6655]], 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; [[2601/2600]], [[5832/5831]], [[11016/11011]], 11271/11264, [[12376/12375]], and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.		1308edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]], and is the 15th [[zeta gap edo]]. With [[23/17]] barely missing the line, it has reasonable approximations up to the 37-limit.

	~~1308edo is~~ the ~~15th~~ [[~~zeta gap edo~~]].		The equal temperament [[tempering out\|tempers out]] {{monzo\| 37 25 -33 }} (whoosh comma) and {{monzo\| -46 51 -15 }} (171 & 1137 comma) in the 5-limit; [[250047/250000]], [[2460375/2458624]], and {{monzo\| 47 4 0 -19 }} in the 7-limit; [[9801/9800]], 151263/151250, 234375/234256, and 67110351/67108864 in the 11-limit; [[4225/4224]], [[6656/6655]], 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; [[2601/2600]], [[5832/5831]], [[11016/11011]], 11271/11264, [[12376/12375]], and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|1308}}		{{Harmonics in equal\|1308\|columns=12}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 1308 factors into ~~2<sup>2</sup> × 3 × 109~~, 1308edo has subset edos 2, 3, 4, 6, 12, 109, 218, 327, 436, and 654.		Since 1308 factors into {{factorization\|1308}}, 1308edo has subset edos 2, 3, 4, 6, 12, 109, 218, 327, 436, and 654.

FloraC: Cleanup; links; expansion

2023-07-29T07:35:23Z

Cleanup; links; expansion

← Older revision		Revision as of 07:35, 29 July 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''1308edo''' is the [[~~EDO\|~~equal division of the octave]] into~~ 1308 parts of 0.917431 cents each. It is consistent to the 21-limit distinctly, tempering out \|37 25 -33> (whoosh comma) and \|-46 51 -15> (171&453 comma) in the 5-limit; 250047/250000, 2460375/2458624, and \|47 4 0 -19> in the 7-limit; 9801/9800, 151263/151250, 234375/234256, and 67110351/67108864 in the 11-limit; 4225/4224, 6656/6655, 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; 2601/2600, 5832/5831, 11016/11011, 11271/11264, 12376/12375, and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.		{{EDO intro\|1308}}

	1308edo is the ~~15th~~ [[~~The Riemann Zeta Function~~ and ~~Tuning~~\|~~zeta gap edo~~]].		1308edo is [[consistent]] to the [[21-odd-limit]] distinctly, tempering out {{monzo\| 37 25 -33 }} (whoosh comma) and {{monzo\| -46 51 -15}} (171 & 453 comma) in the 5-limit; [[250047/250000]], [[2460375/2458624]], and {{monzo\| 47 4 0 -19 }} in the 7-limit; [[9801/9800]], 151263/151250, 234375/234256, and 67110351/67108864 in the 11-limit; [[4225/4224]], [[6656/6655]], 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; [[2601/2600]], [[5832/5831]], [[11016/11011]], 11271/11264, [[12376/12375]], and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.

	[[~~Category:Equal divisions of the octave\|####~~]] <~~!--~~ 4~~-digit number -->~~		1308edo is the 15th [[zeta gap edo]].

			=== Prime harmonics ===
			{{Harmonics in equal\|1308}}

			=== Subsets and supersets ===
			Since 1308 factors into 2<sup>2</sup> × 3 × 109, 1308edo has subset edos 2, 3, 4, 6, 12, 109, 218, 327, 436, and 654.

BudjarnLambeth at 06:52, 9 July 2023

2023-07-09T06:52:31Z

← Older revision		Revision as of 06:52, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	'''1308edo''' is the [[EDO\|equal division of the octave]] into 1308 parts of 0.917431 cents each. It is consistent to the 21-limit distinctly, tempering out \|37 25 -33> (whoosh comma) and \|-46 51 -15> (171&453 comma) in the 5-limit; 250047/250000, 2460375/2458624, and \|47 4 0 -19> in the 7-limit; 9801/9800, 151263/151250, 234375/234256, and 67110351/67108864 in the 11-limit; 4225/4224, 6656/6655, 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; 2601/2600, 5832/5831, 11016/11011, 11271/11264, 12376/12375, and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.		'''1308edo''' is the [[EDO\|equal division of the octave]] into 1308 parts of 0.917431 cents each. It is consistent to the 21-limit distinctly, tempering out \|37 25 -33> (whoosh comma) and \|-46 51 -15> (171&453 comma) in the 5-limit; 250047/250000, 2460375/2458624, and \|47 4 0 -19> in the 7-limit; 9801/9800, 151263/151250, 234375/234256, and 67110351/67108864 in the 11-limit; 4225/4224, 6656/6655, 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; 2601/2600, 5832/5831, 11016/11011, 11271/11264, 12376/12375, and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.