1236edo - Revision history

ArrowHead294 at 16:58, 18 February 2025

2025-02-18T16:58:53Z

← Older revision		Revision as of 16:58, 18 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1236~~}}		{{ED intro}}

	1236edo is a [[zeta peak edo]], though not [[zeta integral edo\|zeta integral]] nor [[zeta gap edo\|zeta gap]]. It is a strong 17-limit system and [[consistency\|distinctly consistent]] through the [[17-odd-limit]], with a 17-limit [[comma basis]] of {[[2601/2600]], [[4096/4095]], [[5832/5831]], [[6656/6655]], [[9801/9800]], 105644/105625}.		1236edo is a [[zeta peak edo]], though not [[zeta integral edo\|zeta integral]] nor [[zeta gap edo\|zeta gap]]. It is a strong 17-limit system and [[consistency\|distinctly consistent]] through the [[17-odd-limit]], with a 17-limit [[comma basis]] of {[[2601/2600]], [[4096/4095]], [[5832/5831]], [[6656/6655]], [[9801/9800]], 105644/105625}.

FloraC: Adopt template: Factorization; misc. cleanup

2023-10-31T09:54:28Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 09:54, 31 October 2023
Line 2:		Line 2:
	{{EDO intro\|1236}}		{{EDO intro\|1236}}

	1236edo is a [[~~The Riemann zeta function and tuning #Zeta EDO lists\|~~zeta peak edo]], though not zeta integral nor zeta gap. It is a strong 17-limit system and ~~uniquely~~ [[consistent]] through the [[17-odd-limit]], with a 17-limit [[comma basis]] of {[[2601/2600]], [[4096/4095]], [[5832/5831]], [[6656/6655]], [[9801/9800]], 105644/105625}.		1236edo is a [[zeta peak edo]], though not [[zeta integral edo\|zeta integral]] nor [[zeta gap edo\|zeta gap]]. It is a strong 17-limit system and [[consistency\|distinctly consistent]] through the [[17-odd-limit]], with a 17-limit [[comma basis]] of {[[2601/2600]], [[4096/4095]], [[5832/5831]], [[6656/6655]], [[9801/9800]], 105644/105625}.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|1236\|columns=11}}		{{Harmonics in equal\|1236\|columns=11}}

	=== ~~Divisors~~ ===		=== Subsets and supersets ===
	1236 ~~= 2<sup>2</sup> × 3 × 103~~, ~~with~~ subset edos 2, 3, 6, 12, 103, 206, 309, and 618. It is divisible by 12, and is an [[atomic]] system.		Since 1236 factors into {{factorization\|1236}}, 1236edo has subset edos {{EDOs\| 2, 3, 6, 12, 103, 206, 309, and 618 }}. It is divisible by 12, and is an [[atomic]] system.

BudjarnLambeth at 06:52, 9 July 2023

2023-07-09T06:52:00Z

← Older revision		Revision as of 06:52, 9 July 2023
Line 1:		Line 1:
	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1236}}		{{EDO intro\|1236}}

BudjarnLambeth at 05:16, 9 July 2023

2023-07-09T05:16:50Z

← Older revision		Revision as of 05:16, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|1236}}		{{EDO intro\|1236}}

FloraC: Improve intro and separate a section for divisors

2023-01-08T04:35:02Z

Improve intro and separate a section for divisors

← Older revision		Revision as of 04:35, 8 January 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~The '''1236 divisions of the octave''' divides the [[octave]] into 1236 [[equal]] parts of 0.9709 [[cent]]s each. It is a [[The Riemann zeta function and tuning #Zeta~~ EDO ~~lists~~\|zeta peak edo]], though not zeta integral nor zeta gap. It is a strong 17-limit system and uniquely [[consistent]] through the 17-odd-limit, with a 17-limit [[comma basis]] of {[[2601/2600]], [[4096/4095]], [[5832/5831]], [[6656/6655]], [[9801/9800]], 105644/105625}.		{{EDO intro\|1236}}

	~~1236 = 2<sup>2</sup> × 3 × 103~~, with ~~subset edos 2~~, 3, 6, 12, ~~103, 206, 309, and 618. It is divisible by 12, and is an~~ [[~~atomic~~]] ~~system~~.		1236edo is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak edo]], though not zeta integral nor zeta gap. It is a strong 17-limit system and uniquely [[consistent]] through the [[17-odd-limit]], with a 17-limit [[comma basis]] of {[[2601/2600]], [[4096/4095]], [[5832/5831]], [[6656/6655]], [[9801/9800]], 105644/105625}.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|1236\|columns=11}}		{{Harmonics in equal\|1236\|columns=11}}

	[[~~Category:Equal divisions of the octave\|####~~]] ~~<!-- 4-digit number -->~~		=== Divisors ===
			1236 = 2<sup>2</sup> × 3 × 103, with subset edos 2, 3, 6, 12, 103, 206, 309, and 618. It is divisible by 12, and is an [[atomic]] system.

FloraC: sectioning and one more column for the prime error table

2022-10-29T09:19:32Z

sectioning and one more column for the prime error table

← Older revision		Revision as of 09:19, 29 October 2022
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	The '''1236 divisions of the octave''' divides the [[octave]] into 1236 [[equal]] parts of 0.9709 [[cent]]s each. It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak edo]], though not zeta integral nor zeta gap. It is a strong 17-limit system and uniquely [[consistent]] through the 17-odd-limit, with a 17-limit [[comma basis]] of {[[2601/2600]], [[4096/4095]], [[5832/5831]], [[6656/6655]], [[9801/9800]], 105644/105625}.		The '''1236 divisions of the octave''' divides the [[octave]] into 1236 [[equal]] parts of 0.9709 [[cent]]s each. It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak edo]], though not zeta integral nor zeta gap. It is a strong 17-limit system and uniquely [[consistent]] through the 17-odd-limit, with a 17-limit [[comma basis]] of {[[2601/2600]], [[4096/4095]], [[5832/5831]], [[6656/6655]], [[9801/9800]], 105644/105625}.

	1236 = 2<sup>2</sup> × 3 × 103, with subset edos 2, 3, 6, 12, 103, 206, 309, and 618. It is divisible by 12, and is an [[atomic]] system.		1236 = 2<sup>2</sup> × 3 × 103, with subset edos 2, 3, 6, 12, 103, 206, 309, and 618. It is divisible by 12, and is an [[atomic]] system.

	{{Harmonics in equal\|1236}}		=== Prime harmonics ===
			{{Harmonics in equal\|1236\|columns=11}}

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

Plumtree: Infobox ET added

2022-10-04T22:09:01Z

Infobox ET added

← Older revision		Revision as of 22:09, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	The '''1236 divisions of the octave''' divides the [[octave]] into 1236 [[equal]] parts of 0.9709 [[cent]]s each. It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak edo]], though not zeta integral nor zeta gap. It is a strong 17-limit system and uniquely [[consistent]] through the 17-odd-limit, with a 17-limit [[comma basis]] of {[[2601/2600]], [[4096/4095]], [[5832/5831]], [[6656/6655]], [[9801/9800]], 105644/105625}.		The '''1236 divisions of the octave''' divides the [[octave]] into 1236 [[equal]] parts of 0.9709 [[cent]]s each. It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak edo]], though not zeta integral nor zeta gap. It is a strong 17-limit system and uniquely [[consistent]] through the 17-odd-limit, with a 17-limit [[comma basis]] of {[[2601/2600]], [[4096/4095]], [[5832/5831]], [[6656/6655]], [[9801/9800]], 105644/105625}.

Fredg999 category edits: Sort key

2022-07-04T01:14:29Z

Sort key

← Older revision		Revision as of 01:14, 4 July 2022
Line 5:		Line 5:
	{{Harmonics in equal\|1236}}		{{Harmonics in equal\|1236}}

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

FloraC: Hmmm

2022-04-19T16:33:12Z

Hmmm

← Older revision		Revision as of 16:33, 19 April 2022
Line 1:		Line 1:
	The '''1236 divisions of the octave''' divides the [[octave]] into 1236 [[equal]] parts of 0.9709 [[cent]]s each. It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak edo]], though not zeta integral nor zeta gap. It is a strong 17-limit system and uniquely [[consistent]] through the 17-odd-limit, with a 17-limit [[comma basis]] of {[[2601/2600]], [[4096/4095]], [[~~6656~~/~~6655~~]], [[~~5832~~/~~5831~~]], [[9801/9800]], 105644/105625}.		The '''1236 divisions of the octave''' divides the [[octave]] into 1236 [[equal]] parts of 0.9709 [[cent]]s each. It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak edo]], though not zeta integral nor zeta gap. It is a strong 17-limit system and uniquely [[consistent]] through the 17-odd-limit, with a 17-limit [[comma basis]] of {[[2601/2600]], [[4096/4095]], [[5832/5831]], [[6656/6655]], [[9801/9800]], 105644/105625}.

	1236 = 2<sup>2</sup> × 3 × 103, with subset edos 2, 3, 6, 12, 103, 206, 309, and 618. It is divisible by 12, and is an [[atomic]] system.		1236 = 2<sup>2</sup> × 3 × 103, with subset edos 2, 3, 6, 12, 103, 206, 309, and 618. It is divisible by 12, and is an [[atomic]] system.

FloraC: Clarify, simplify comma basis, note it being an atomic system, and replace irrelevant number theory with factorization and subset edos

2022-04-19T16:32:07Z

Clarify, simplify comma basis, note it being an atomic system, and replace irrelevant number theory with factorization and subset edos

← Older revision		Revision as of 16:32, 19 April 2022
Line 1:		Line 1:
	The '''1236 divisions of the octave''' divides the [[octave]] into 1236 [[equal]] parts of 0.9709 [[cent]]s each. It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak edo]], though not zeta integral nor zeta gap. It is a strong 17-limit system and uniquely [[consistent]] through the 17-limit, with a 17-limit [[comma basis]] of [[2601/2600]], [[~~5832~~/~~5831~~]], [[~~9801~~/~~9800~~]], [[~~10648~~/~~10647~~]], ~~14875~~/~~14872 and~~ 105644/105625. It is divisible by 12, ~~which~~ is ~~also the sum of its digits (1 + 2 + 3 + 6 = 12 × 103 = 1236)~~.		The '''1236 divisions of the octave''' divides the [[octave]] into 1236 [[equal]] parts of 0.9709 [[cent]]s each. It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak edo]], though not zeta integral nor zeta gap. It is a strong 17-limit system and uniquely [[consistent]] through the 17-odd-limit, with a 17-limit [[comma basis]] of {[[2601/2600]], [[4096/4095]], [[6656/6655]], [[5832/5831]], [[9801/9800]], 105644/105625}.

			1236 = 2<sup>2</sup> × 3 × 103, with subset edos 2, 3, 6, 12, 103, 206, 309, and 618. It is divisible by 12, and is an [[atomic]] system.

	{{Harmonics in equal\|1236}}		{{Harmonics in equal\|1236}}

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