12276edo - Revision history

Zhenlige at 08:57, 16 February 2026

2026-02-16T08:57:23Z

← Older revision		Revision as of 08:57, 16 February 2026
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	{{ED intro}}		{{ED intro}}

	12276 is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from [[6691edo\|6691]]. 12276 tempers out the [[Kirnberger's atom\|atom]] and the [[septimal ruthenia]], so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas, 240 and 220 steps respectively, and septimal comma is represented by 1/44 of the octave, 279 steps.		12276 is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from [[6691edo\|6691]]. 12276 tempers out the [[Kirnberger's atom\|atom]] and the [[septimal ruthenia]], so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas, 240 and 220 steps respectively, and septimal comma is represented by 1/44 of the octave, 279 steps. It is the smallest [[atomic]] EDO inside its [[5-odd-limit]] [[diamond tradeoff]] tuning range.

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

FloraC: Cleanup & + category

2025-07-28T16:34:34Z

Cleanup & + category

← Older revision		Revision as of 16:34, 28 July 2025
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	{{Harmonics in equal\|12276\|columns=11}}		{{Harmonics in equal\|12276\|columns=11}}

	=== ~~Interval size measure~~ ===		=== Subsets and supersets ===
	12276edo factors as 2<sup>2</sup> × 3<sup>2</sup> × 11 × 31, and among its divisors are [[12edo\|12]], [[22edo\|22]], [[31edo\|31]], [[99edo\|99]] and [[198edo\|198]]. This creates a unit known as the ''[[prima]]'', useful for measurement of 11-limit intervals and commas. A prima is almost exactly three [[tuning unit]]s.		12276edo factors into primes as {{nowrap\| 2<sup>2</sup> × 3<sup>2</sup> × 11 × 31 }}, and among its divisors are [[12edo\|12]], [[22edo\|22]], [[31edo\|31]], [[99edo\|99]] and [[198edo\|198]]. This creates a unit known as the ''[[prima]]'', useful for measurement of 11-limit intervals and commas. A prima is almost exactly three [[tuning unit]]s.

	[[Category:~~Equal divisions of the octave~~\|#####]] <!-- 5-digit number ~~-->~~		[[Category:3-limit record edos\|#####]] <!-- 5-digit number -->
	~~[[Category:12276edo\| ]] <!-- main article~~ -->

ArrowHead294 at 16:58, 18 February 2025

2025-02-18T16:58:19Z

← Older revision		Revision as of 16:58, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|12276~~}}		{{ED intro}}

	12276 is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from [[6691edo\|6691]]. 12276 tempers out the [[Kirnberger's atom\|atom]] and the [[septimal ruthenia]], so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas, 240 and 220 steps respectively, and septimal comma is represented by 1/44 of the octave, 279 steps.		12276 is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from [[6691edo\|6691]]. 12276 tempers out the [[Kirnberger's atom\|atom]] and the [[septimal ruthenia]], so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas, 240 and 220 steps respectively, and septimal comma is represented by 1/44 of the octave, 279 steps.

BudjarnLambeth at 07:11, 9 July 2023

2023-07-09T07:11:53Z

← Older revision		Revision as of 07:11, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|12276}}		{{EDO intro\|12276}}

BudjarnLambeth at 04:16, 9 July 2023

2023-07-09T04:16:13Z

← Older revision		Revision as of 04:16, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|12276}}		{{EDO intro\|12276}}

Eliora: not sure why reduplicate how much are commas in steps in different sections, write that more concisely

2023-06-10T12:56:51Z

not sure why reduplicate how much are commas in steps in different sections, write that more concisely

← Older revision		Revision as of 12:56, 10 June 2023
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	{{EDO intro\|12276}}		{{EDO intro\|12276}}

	12276 is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from [[6691edo\|6691]]. 12276 tempers out the [[Kirnberger's atom\|atom]], so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas respectively~~. In addition~~, ~~12276edo tempers out the [[~~septimal ~~ruthenia]], meaning that [[64/63]]~~ is ~~exactly~~ 1/44 of the octave, or 279 ~~primas~~.		12276 is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from [[6691edo\|6691]]. 12276 tempers out the [[Kirnberger's atom\|atom]] and the [[septimal ruthenia]], so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas, 240 and 220 steps respectively, and septimal comma is represented by 1/44 of the octave, 279 steps.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 8:		Line 8:

	=== Interval size measure ===		=== Interval size measure ===
	12276edo factors as 2<sup>2</sup> × 3<sup>2</sup> × 11 × 31, and among its divisors are [[12edo\|12]], [[22edo\|22]], [[31edo\|31]], [[99edo\|99]] and [[198edo\|198]]. This creates a unit known as the ''[[prima]]'', useful for measurement of 11-limit intervals and commas~~. The Pythagorean comma is represented by 240 prima, and the syntonic comma by 220~~. A prima is almost exactly three [[tuning unit]]s.		12276edo factors as 2<sup>2</sup> × 3<sup>2</sup> × 11 × 31, and among its divisors are [[12edo\|12]], [[22edo\|22]], [[31edo\|31]], [[99edo\|99]] and [[198edo\|198]]. This creates a unit known as the ''[[prima]]'', useful for measurement of 11-limit intervals and commas. A prima is almost exactly three [[tuning unit]]s.

	[[Category:Equal divisions of the octave\|#####]] <!-- 5-digit number -->		[[Category:Equal divisions of the octave\|#####]] <!-- 5-digit number -->
	[[Category:12276edo\| ]] <!-- main article -->		[[Category:12276edo\| ]] <!-- main article -->

FloraC: -section title for now since there's no other sections; +prime error table; +categories

2022-12-26T11:06:04Z

-section title for now since there's no other sections; +prime error table; +categories

← Older revision		Revision as of 11:06, 26 December 2022
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|12276}}		{{EDO intro\|12276}}
	~~==Theory==~~
	12276 is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from [[6691edo\|6691]]. 12276 tempers out the [[Kirnberger's atom\|atom]], so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas respectively.
	~~===Interval size measure===~~
	12276edo factors as 2<sup>2</sup> × 3<sup>2</sup> × 11 × 31, and among its divisors are [[12edo\|12]], [[22edo\|22]], [[31edo\|31]], [[99edo\|99]] and [[198edo\|198]]. This creates a unit known as the '''[[prima]]''', useful for measurement of 11-limit intervals and commas. The Pythagorean comma is represented by 240 prima, and the syntonic comma by 220. A prima is almost exactly three [[Tuning unit\|tuning units]].

	In addition, 12276edo tempers out the [[septimal ruthenia]], meaning that [[64/63]] is exactly 1/~~44th~~ of the octave, or 279 primas.		12276 is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from [[6691edo\|6691]]. 12276 tempers out the [[Kirnberger's atom\|atom]], so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas respectively. In addition, 12276edo tempers out the [[septimal ruthenia]], meaning that [[64/63]] is exactly 1/44 of the octave, or 279 primas.

			=== Prime harmonics ===
			{{Harmonics in equal\|12276\|columns=11}}

			=== Interval size measure ===
			12276edo factors as 2<sup>2</sup> × 3<sup>2</sup> × 11 × 31, and among its divisors are [[12edo\|12]], [[22edo\|22]], [[31edo\|31]], [[99edo\|99]] and [[198edo\|198]]. This creates a unit known as the ''[[prima]]'', useful for measurement of 11-limit intervals and commas. The Pythagorean comma is represented by 240 prima, and the syntonic comma by 220. A prima is almost exactly three [[tuning unit]]s.

	[[Category:Equal divisions of the octave\|#####]] <!-- 5-digit number -->		[[Category:Equal divisions of the octave\|#####]] <!-- 5-digit number -->
			[[Category:12276edo\| ]] <!-- main article -->

Lhearne at 06:40, 26 December 2022

2022-12-26T06:40:26Z

← Older revision		Revision as of 06:40, 26 December 2022
Line 4:		Line 4:
	12276 is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from [[6691edo\|6691]]. 12276 tempers out the [[Kirnberger's atom\|atom]], so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas respectively.		12276 is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from [[6691edo\|6691]]. 12276 tempers out the [[Kirnberger's atom\|atom]], so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas respectively.
	===Interval size measure===		===Interval size measure===
	12276edo factors as 2<sup>2</sup> × 3<sup>2</sup> × 11 × 31, and among its divisors are [[12edo\|12]], [[22edo\|22]], [[31edo\|31]], [[99edo\|99]] and [[198edo\|198]]. This creates a unit known as the '''prima''', useful for measurement of 11-limit intervals and commas. The Pythagorean comma is represented by 240 prima, and the syntonic comma by 220. A prima is almost exactly three [[Tuning unit\|tuning units]].		12276edo factors as 2<sup>2</sup> × 3<sup>2</sup> × 11 × 31, and among its divisors are [[12edo\|12]], [[22edo\|22]], [[31edo\|31]], [[99edo\|99]] and [[198edo\|198]]. This creates a unit known as the '''[[prima]]''', useful for measurement of 11-limit intervals and commas. The Pythagorean comma is represented by 240 prima, and the syntonic comma by 220. A prima is almost exactly three [[Tuning unit\|tuning units]].

	In addition, 12276edo tempers out the [[septimal ruthenia]], meaning that [[64/63]] is exactly 1/44th of the octave, or 279 primas.		In addition, 12276edo tempers out the [[septimal ruthenia]], meaning that [[64/63]] is exactly 1/44th of the octave, or 279 primas.

Eliora: cleanup

2022-12-21T15:36:56Z

cleanup

← Older revision		Revision as of 15:36, 21 December 2022
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~'''12276EDO'''~~ is the [[~~EDO~~\|~~equal division of~~ the ~~octave~~]] ~~into 12276 parts of exactly 0.09775171 cents each~~. This creates a unit known as the '''prima''', useful for measurement of 11-limit intervals and commas. The Pythagorean comma is represented by 240 prima, and the syntonic comma by 220. A prima is almost exactly three ~~'''~~[[Tuning unit\|tuning units]]~~'''~~.		{{EDO intro\|12276}}
			==Theory==
			12276 is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from [[6691edo\|6691]]. 12276 tempers out the [[Kirnberger's atom\|atom]], so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas respectively.
			===Interval size measure===
			12276edo factors as 2<sup>2</sup> × 3<sup>2</sup> × 11 × 31, and among its divisors are [[12edo\|12]], [[22edo\|22]], [[31edo\|31]], [[99edo\|99]] and [[198edo\|198]]. This creates a unit known as the '''prima''', useful for measurement of 11-limit intervals and commas. The Pythagorean comma is represented by 240 prima, and the syntonic comma by 220. A prima is almost exactly three [[Tuning unit\|tuning units]].

			In addition, 12276edo tempers out the [[septimal ruthenia]], meaning that [[64/63]] is exactly 1/44th of the octave, or 279 primas.


	12276 is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from [[6691edo\|6691]]. It factors as 12276 = 2<sup>2</sup> × 3<sup>2</sup> × 11 × 31, and among its divisors are [[12edo\|12]], [[22edo\|22]], [[31edo\|31]], [[99edo\|99]] and [[198edo\|198]]. 12276 tempers out the [[Kirnberger's atom\|atom]], so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas respectively.

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

Plumtree: Infobox ET added

2022-10-04T22:21:50Z

Infobox ET added

← Older revision		Revision as of 22:21, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''12276EDO''' is the [[EDO\|equal division of the octave]] into 12276 parts of exactly 0.09775171 cents each. This creates a unit known as the '''prima''', useful for measurement of 11-limit intervals and commas. The Pythagorean comma is represented by 240 prima, and the syntonic comma by 220. A prima is almost exactly three '''[[Tuning unit\|tuning units]]'''.		'''12276EDO''' is the [[EDO\|equal division of the octave]] into 12276 parts of exactly 0.09775171 cents each. This creates a unit known as the '''prima''', useful for measurement of 11-limit intervals and commas. The Pythagorean comma is represented by 240 prima, and the syntonic comma by 220. A prima is almost exactly three '''[[Tuning unit\|tuning units]]'''.

← Older revision		Revision as of 16:34, 28 July 2025
Line 7:		Line 7:
	{{Harmonics in equal\|12276\|columns=11}}		{{Harmonics in equal\|12276\|columns=11}}

	=== ~~Interval size measure~~ ===		=== Subsets and supersets ===
	12276edo factors as 2<sup>2</sup> × 3<sup>2</sup> × 11 × 31, and among its divisors are [[12edo\|12]], [[22edo\|22]], [[31edo\|31]], [[99edo\|99]] and [[198edo\|198]]. This creates a unit known as the ''[[prima]]'', useful for measurement of 11-limit intervals and commas. A prima is almost exactly three [[tuning unit]]s.		12276edo factors into primes as {{nowrap\| 2<sup>2</sup> × 3<sup>2</sup> × 11 × 31 }}, and among its divisors are [[12edo\|12]], [[22edo\|22]], [[31edo\|31]], [[99edo\|99]] and [[198edo\|198]]. This creates a unit known as the ''[[prima]]'', useful for measurement of 11-limit intervals and commas. A prima is almost exactly three [[tuning unit]]s.

	[[Category:~~Equal divisions of the octave~~\|#####]] <!-- 5-digit number ~~-->~~		[[Category:3-limit record edos\|#####]] <!-- 5-digit number -->
	~~[[Category:12276edo\| ]] <!-- main article~~ -->