11664edo - Revision history

FloraC: Expand the harmonics table a little

2025-10-02T15:59:43Z

Expand the harmonics table a little

← Older revision		Revision as of 15:59, 2 October 2025
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|11664\|intervals=prime\|columns=9}}		{{Harmonics in equal\|11664\|intervals=prime\|columns=11}}
	{{Harmonics in equal\|11664\|intervals=prime\|columns=9\|start=10\|collapsed=true\|title=Approximation of prime harmonics in 11664edo (continued)}}		{{Harmonics in equal\|11664\|intervals=prime\|columns=11\|start=12\|collapsed=true\|title=Approximation of prime harmonics in 11664edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	11664 factors into primes as {{nowrap\| 2<sup>3</sup> × 3<sup>6</sup> }}. Among its divisiors are [[12edo\|12]], [[16edo\|16]], [[24edo\|24]], [[27edo\|27]], [[72edo\|72]], [[81edo\|81]] and [[243edo\|243]].		11664 factors into primes as {{nowrap\| 2<sup>3</sup> × 3<sup>6</sup> }}. Among its divisiors are [[12edo\|12]], [[16edo\|16]], [[24edo\|24]], [[27edo\|27]], [[72edo\|72]], [[81edo\|81]] and [[243edo\|243]].

FloraC: Expand a little

2025-08-03T13:20:34Z

Expand a little

← Older revision		Revision as of 13:20, 3 August 2025
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	{{ED intro}}		{{ED intro}}

	11664edo is a very strong 7-limit system, with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than any division until [[18355edo\|18355]]. It is a [[~~The Riemann zeta function and tuning #Zeta EDO lists\|~~zeta peak edo]] unlike other very strong 7-limit divisions in this size range, which has to do with the fact that it is also very strong in higher limits, being distinctly [[consistent]] through the 27-odd-limit and with a lower 23-limit relative error than any division until [[16808edo\|16808]]. Aside from this peculiar double threat property, it is also very composite, ~~since {{nowrap~~\|~~11664 {{=}} 2<sup>3<~~/~~sup> × 3<sup>6</sup>}}. Among its divisiors are~~ [[~~12edo\|12~~]], [[~~16edo\|16~~]], [[~~24edo\|24~~]], [[~~27edo\|27~~]], [[~~72edo\|72~~]], [[~~81edo\|81~~]] and [[~~243edo\|243~~]].		11664edo is a very strong [[7-limit]] system, with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than any division until [[18355edo\|18355]]. It is a [[zeta peak edo]] unlike other very strong 7-limit divisions in this size range, which has to do with the fact that it is also very strong in higher limits, being distinctly [[consistent]] through the [[27-odd-limit]] and with a lower [[23-limit]] relative error than any division until [[16808edo\|16808]]. Aside from this peculiar double threat property, it is also very composite, giving itself another edge over similar systems.

			Some of the simpler commas [[tempering out\|tempered out]] include [[123201/123200]] and [[1990656/1990625]] in the [[13-limit]]; [[194481/194480]] and [[336141/336140]] in the [[17-limit]]; 23409/23408 and 89376/89375 in the [[19-limit]]; 43264/43263, 71875/71874, and 76545/76544 in the [[23-limit]].

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|11664\|~~prec~~=5}}		{{Harmonics in equal\|11664\|intervals=prime\|columns=9}}
			{{Harmonics in equal\|11664\|intervals=prime\|columns=9\|start=10\|collapsed=true\|title=Approximation of prime harmonics in 11664edo (continued)}}

			=== Subsets and supersets ===
			11664 factors into primes as {{nowrap\| 2<sup>3</sup> × 3<sup>6</sup> }}. Among its divisiors are [[12edo\|12]], [[16edo\|16]], [[24edo\|24]], [[27edo\|27]], [[72edo\|72]], [[81edo\|81]] and [[243edo\|243]].

ArrowHead294 at 16:52, 18 February 2025

2025-02-18T16:52:08Z

← Older revision		Revision as of 16:52, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|11664~~}}		{{ED intro}}

	11664edo is a very strong 7-limit system, with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than any division until [[18355edo\|18355]]. It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak edo]] unlike other very strong 7-limit divisions in this size range, which has to do with the fact that it is also very strong in higher limits, being distinctly [[consistent]] through the 27-odd-limit and with a lower 23-limit relative error than any division until [[16808edo\|16808]]. Aside from this peculiar double threat property, it is also very composite, since 11664 = 2<sup>3</sup> × 3<sup>6</sup>. Among its divisiors are [[12edo\|12]], [[16edo\|16]], [[24edo\|24]], [[27edo\|27]], [[72edo\|72]], [[81edo\|81]] and [[243edo\|243]].		11664edo is a very strong 7-limit system, with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than any division until [[18355edo\|18355]]. It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak edo]] unlike other very strong 7-limit divisions in this size range, which has to do with the fact that it is also very strong in higher limits, being distinctly [[consistent]] through the 27-odd-limit and with a lower 23-limit relative error than any division until [[16808edo\|16808]]. Aside from this peculiar double threat property, it is also very composite, since {{nowrap\|11664 {{=}} 2<sup>3</sup> × 3<sup>6</sup>}}. Among its divisiors are [[12edo\|12]], [[16edo\|16]], [[24edo\|24]], [[27edo\|27]], [[72edo\|72]], [[81edo\|81]] and [[243edo\|243]].

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|11664\|prec=5}}		{{Harmonics in equal\|11664\|prec=5}}

BudjarnLambeth at 07:11, 9 July 2023

2023-07-09T07:11:30Z

← Older revision		Revision as of 07:11, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|11664}}		{{EDO intro\|11664}}

BudjarnLambeth at 04:16, 9 July 2023

2023-07-09T04:16:41Z

← Older revision		Revision as of 04:16, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|11664}}		{{EDO intro\|11664}}

FloraC: Improve intro and update the error table

2023-01-07T11:18:10Z

Improve intro and update the error table

← Older revision		Revision as of 11:18, 7 January 2023
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	{{Infobox ET}}		{{Infobox ET}}
	The '''11664 division''' divides the octave into 11664 parts of 0.10288 cents each. It is a very strong 7-limit system, with a lower 7-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]] than any division until [[18355edo\|18355]]. It is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO ~~lists~~\|zeta peak edo]] unlike other very strong 7-limit divisions in this size range, which has to do with the fact that it is also very strong in higher limits, being distinctly consistent through the 27 limit and with a lower 23-limit relative error than any division until [[16808edo\|16808]]. Aside from this peculiar double threat property, it is also highly composite, since 11664 ~~= 2^3 * 3^6. Among its divisiors are [[12edo\|12]], [[16edo\|16]], [[24edo\|24]], [[27edo\|27]], [[72edo\|72]], [[81edo\|81]] and [[243edo\|243]].~~		{{EDO intro\|11664}}

	~~{{Primes~~ in ~~edo~~\|11664\|~~prec=5}}~~		11664edo is a very strong 7-limit system, with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]] than any division until [[18355edo\|18355]]. It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak edo]] unlike other very strong 7-limit divisions in this size range, which has to do with the fact that it is also very strong in higher limits, being distinctly [[consistent]] through the 27-odd-limit and with a lower 23-limit relative error than any division until [[16808edo\|16808]]. Aside from this peculiar double threat property, it is also very composite, since 11664 = 2<sup>3</sup> × 3<sup>6</sup>. Among its divisiors are [[12edo\|12]], [[16edo\|16]], [[24edo\|24]], [[27edo\|27]], [[72edo\|72]], [[81edo\|81]] and [[243edo\|243]].

	~~[[Category:Equal divisions of the octave~~\|~~#####]] <!--~~ 5~~-digit number -->~~		=== Prime harmonics ===
			{{Harmonics in equal\|11664\|prec=5}}

Plumtree: Infobox ET added

2022-10-04T22:21:36Z

Infobox ET added

← Older revision		Revision as of 22:21, 4 October 2022
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			{{Infobox ET}}
	The '''11664 division''' divides the octave into 11664 parts of 0.10288 cents each. It is a very strong 7-limit system, with a lower 7-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]] than any division until [[18355edo\|18355]]. It is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists\|zeta peak edo]] unlike other very strong 7-limit divisions in this size range, which has to do with the fact that it is also very strong in higher limits, being distinctly consistent through the 27 limit and with a lower 23-limit relative error than any division until [[16808edo\|16808]]. Aside from this peculiar double threat property, it is also highly composite, since 11664 = 2^3 * 3^6. Among its divisiors are [[12edo\|12]], [[16edo\|16]], [[24edo\|24]], [[27edo\|27]], [[72edo\|72]], [[81edo\|81]] and [[243edo\|243]].		The '''11664 division''' divides the octave into 11664 parts of 0.10288 cents each. It is a very strong 7-limit system, with a lower 7-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]] than any division until [[18355edo\|18355]]. It is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists\|zeta peak edo]] unlike other very strong 7-limit divisions in this size range, which has to do with the fact that it is also very strong in higher limits, being distinctly consistent through the 27 limit and with a lower 23-limit relative error than any division until [[16808edo\|16808]]. Aside from this peculiar double threat property, it is also highly composite, since 11664 = 2^3 * 3^6. Among its divisiors are [[12edo\|12]], [[16edo\|16]], [[24edo\|24]], [[27edo\|27]], [[72edo\|72]], [[81edo\|81]] and [[243edo\|243]].

Fredg999 category edits: Sort key

2022-07-04T01:41:19Z

Sort key

← Older revision		Revision as of 01:41, 4 July 2022
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	The 11664 division divides the octave into 11664 parts of 0.10288 cents each. It is a very strong 7-limit system, with a lower 7-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]] than any division until [[18355edo\|18355]]. It is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists\|zeta peak edo]] unlike other very strong 7-limit divisions in this size range, which has to do with the fact that it is also very strong in higher limits, being distinctly consistent through the 27 limit and with a lower 23-limit relative error than any division until [[16808edo\|16808]]. Aside from this peculiar double threat property, it is also highly composite, since 11664 = 2^3 * 3^6. Among its divisiors are [[12edo\|12]], [[16edo\|16]], [[24edo\|24]], [[27edo\|27]], [[72edo\|72]], [[81edo\|81]] and [[243edo\|243]].		The '''11664 division''' divides the octave into 11664 parts of 0.10288 cents each. It is a very strong 7-limit system, with a lower 7-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]] than any division until [[18355edo\|18355]]. It is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists\|zeta peak edo]] unlike other very strong 7-limit divisions in this size range, which has to do with the fact that it is also very strong in higher limits, being distinctly consistent through the 27 limit and with a lower 23-limit relative error than any division until [[16808edo\|16808]]. Aside from this peculiar double threat property, it is also highly composite, since 11664 = 2^3 * 3^6. Among its divisiors are [[12edo\|12]], [[16edo\|16]], [[24edo\|24]], [[27edo\|27]], [[72edo\|72]], [[81edo\|81]] and [[243edo\|243]].

	{{Primes in edo\|11664\|prec=5}}		{{Primes in edo\|11664\|prec=5}}

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave\|#####]] <!-- 5-digit number -->

Fredg999: Categories

2021-12-10T02:21:53Z

Inthar at 07:37, 23 April 2021

2021-04-23T07:37:50Z

← Older revision		Revision as of 07:37, 23 April 2021
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	The 11664 division divides the octave into 11664 parts of 0.10288 cents each. It is a very strong 7-limit system, with a lower 7-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]] than any division until [[18355edo\|18355]]. It is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists\|zeta peak edo]] unlike other very strong 7-limit divisions in this size range, which has to do with the fact that it is also very strong in higher limits, being distinctly consistent through the 27 limit and with a lower 23-limit relative error than any division until [[16808edo\|16808]]. Aside from this peculiar double threat property, it is also highly composite, since 11664 = 2^3 * 3^6. Among its divisiors are [[12edo\|12]], [[16edo\|16]], [[24edo\|24]], [[27edo\|27]], [[72edo\|72]], [[81edo\|81]] and [[243edo\|243]].		The 11664 division divides the octave into 11664 parts of 0.10288 cents each. It is a very strong 7-limit system, with a lower 7-limit [[Tenney-Euclidean_temperament_measures#TE simple badness\|relative error]] than any division until [[18355edo\|18355]]. It is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists\|zeta peak edo]] unlike other very strong 7-limit divisions in this size range, which has to do with the fact that it is also very strong in higher limits, being distinctly consistent through the 27 limit and with a lower 23-limit relative error than any division until [[16808edo\|16808]]. Aside from this peculiar double threat property, it is also highly composite, since 11664 = 2^3 * 3^6. Among its divisiors are [[12edo\|12]], [[16edo\|16]], [[24edo\|24]], [[27edo\|27]], [[72edo\|72]], [[81edo\|81]] and [[243edo\|243]].

			{{Primes in edo\|11664\|prec=5}}

← Older revision		Revision as of 02:21, 10 December 2021
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	{{Primes in edo\|11664\|prec=5}}		{{Primes in edo\|11664\|prec=5}}

			[[Category:Equal divisions of the octave]]