111ed12 - Revision history

Overthink: /* Theory */ "to any edo" isn't best here because you're probably using it as stretched 31edo

2026-05-03T17:26:06Z

Theory: "to any edo" isn't best here because you're probably using it as stretched 31edo

← Older revision		Revision as of 17:26, 3 May 2026
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	== Theory ==		== Theory ==
	111ed12 is nearly identical to [[31edo]], but with the [[12/1\|12th]] [[harmonic]] rather than the [[2/1\|octave]] being just. The octave is about 1.45 cents stretched compared to just~~, or to any edo~~. Like 31edo, 111ed12 is [[consistent]] through the [[integer limit\|12-integer-limit]], and like [[80ed6]], it optimizes for the [[11-limit]] by trading the accuracy of the [[5/1\|5th]] and [[7/1\|7th harmonic]]s for improved [[3/1\|3rd]] and [[11/1\|11th harmonics]]. The stretch is quite mild, but still considerable: the [[11/1\|11th harmonic]] is only 4.4 cents flat of just (in comparison, 31edo's 11th harmonic is 9.4 cents flat). Also improved is the [[23/1\|23rd harmonic]], which is now only 2.4 cents flat of just.		111ed12 is nearly identical to [[31edo]], but with the [[12/1\|12th]] [[harmonic]] rather than the [[2/1\|octave]] being just. The octave is about 1.45 cents stretched compared to just. Like 31edo, 111ed12 is [[consistent]] through the [[integer limit\|12-integer-limit]], and like [[80ed6]], it optimizes for the [[11-limit]] by trading the accuracy of the [[5/1\|5th]] and [[7/1\|7th harmonic]]s for improved [[3/1\|3rd]] and [[11/1\|11th harmonics]]. The stretch is quite mild, but still considerable: the [[11/1\|11th harmonic]] is only 4.4 cents flat of just (in comparison, 31edo's 11th harmonic is 9.4 cents flat). Also improved is the [[23/1\|23rd harmonic]], which is now only 2.4 cents flat of just.

	=== Harmonics ===		=== Harmonics ===

Tonwood: /* Theory */ 31 is not special in this sentence

2026-04-15T04:19:53Z

Theory: 31 is not special in this sentence

← Older revision		Revision as of 04:19, 15 April 2026
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	== Theory ==		== Theory ==
	111ed12 is nearly identical to [[31edo]], but with the [[12/1\|12th]] [[harmonic]] rather than the [[2/1\|octave]] being just. The octave is about 1.45 cents stretched compared to ~~31edo~~. Like 31edo, 111ed12 is [[consistent]] through the [[integer limit\|12-integer-limit]], and like [[80ed6]], it optimizes for the [[11-limit]] by trading the accuracy of the [[5/1\|5th]] and [[7/1\|7th harmonic]]s for improved [[3/1\|3rd]] and [[11/1\|11th harmonics]]. The stretch is quite mild, but still considerable: the [[11/1\|11th harmonic]] is only 4.4 cents flat of just (in comparison, 31edo's 11th harmonic is 9.4 cents flat). Also improved is the [[23/1\|23rd harmonic]], which is now only 2.4 cents flat of just.		111ed12 is nearly identical to [[31edo]], but with the [[12/1\|12th]] [[harmonic]] rather than the [[2/1\|octave]] being just. The octave is about 1.45 cents stretched compared to just, or to any edo. Like 31edo, 111ed12 is [[consistent]] through the [[integer limit\|12-integer-limit]], and like [[80ed6]], it optimizes for the [[11-limit]] by trading the accuracy of the [[5/1\|5th]] and [[7/1\|7th harmonic]]s for improved [[3/1\|3rd]] and [[11/1\|11th harmonics]]. The stretch is quite mild, but still considerable: the [[11/1\|11th harmonic]] is only 4.4 cents flat of just (in comparison, 31edo's 11th harmonic is 9.4 cents flat). Also improved is the [[23/1\|23rd harmonic]], which is now only 2.4 cents flat of just.

	=== Harmonics ===		=== Harmonics ===

ArrowHead294: /* See also */

2025-07-16T15:01:45Z

ArrowHead294: /* See also */

2025-06-10T13:32:27Z

FloraC: /* Theory */ expand on its tuning characteristics

2025-03-30T17:59:19Z

Theory: expand on its tuning characteristics

← Older revision		Revision as of 17:59, 30 March 2025
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	== Theory ==		== Theory ==
	111ed12 is nearly identical to [[31edo]], but with the 12/1 rather than the [[2/1]] being just. The octave is about 1.45 cents stretched compared to 31edo. Like 31edo, 111ed12 is [[consistent]] through the [[integer limit\|12-integer-limit]].		111ed12 is nearly identical to [[31edo]], but with the [[12/1\|12th]] [[harmonic]] rather than the [[2/1\|octave]] being just. The octave is about 1.45 cents stretched compared to 31edo. Like 31edo, 111ed12 is [[consistent]] through the [[integer limit\|12-integer-limit]], and like [[80ed6]], it optimizes for the [[11-limit]] by trading the accuracy of the [[5/1\|5th]] and [[7/1\|7th harmonic]]s for improved [[3/1\|3rd]] and [[11/1\|11th harmonics]]. The stretch is quite mild, but still considerable: the [[11/1\|11th harmonic]] is only 4.4 cents flat of just (in comparison, 31edo's 11th harmonic is 9.4 cents flat). Also improved is the [[23/1\|23rd harmonic]], which is now only 2.4 cents flat of just.

	=== Harmonics ===		=== Harmonics ===

FloraC: +see also

2025-03-24T12:32:13Z

+see also

← Older revision		Revision as of 12:32, 24 March 2025
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	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

			== See also ==
			* [[18edf]] – relative edf
			* [[31edo]] – relative edo
			* [[49edt]] – relative edt
			* [[72ed5]] – relative ed5
			* [[80ed6]] – relative ed6
			* [[87ed7]] – relative ed7
			* [[39cET]]

FloraC: /* Theory */

2025-03-24T12:30:37Z

Theory

← Older revision		Revision as of 12:30, 24 March 2025
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	== Theory ==		== Theory ==
	111ed12 is nearly identical to [[31edo]], but with the 12/1 rather than the [[2/1]] being just. The octave is about 1.45 cents stretched compared to 31edo. Like 31edo, 111ed12 is [[consistent]] through the [[integer limit\|12-integer-limit]]		111ed12 is nearly identical to [[31edo]], but with the 12/1 rather than the [[2/1]] being just. The octave is about 1.45 cents stretched compared to 31edo. Like 31edo, 111ed12 is [[consistent]] through the [[integer limit\|12-integer-limit]].

	=== Harmonics ===		=== Harmonics ===

FloraC: /* Theory */ note consistency and +subsets and supersets

2025-03-24T12:30:23Z

Theory: note consistency and +subsets and supersets

← Older revision		Revision as of 12:30, 24 March 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	111ed12 is nearly identical to [[31edo]], but with the 12/1 rather than the [[2/1]] being just. The octave is about 1.45 cents stretched compared to 31edo.		111ed12 is nearly identical to [[31edo]], but with the 12/1 rather than the [[2/1]] being just. The octave is about 1.45 cents stretched compared to 31edo. Like 31edo, 111ed12 is [[consistent]] through the [[integer limit\|12-integer-limit]]

	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|111\|12\|1\|intervals=integer\|columns=11}}		{{Harmonics in equal\|111\|12\|1\|intervals=integer\|columns=11}}
	{{Harmonics in equal\|111\|12\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 111ed12 (continued)}}		{{Harmonics in equal\|111\|12\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 111ed12 (continued)}}

			=== Subsets and supersets ===
			Since 111 factors into primes as {{nowrap\| 3 × 37 }}, 111ed12 contains [[3ed12]] and [[37ed12]] as subset ed12's.

	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

FloraC: Cleanup

2025-03-24T12:29:10Z

Cleanup

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 {{ED intro}}
-ed12 is nearly identical to [[31edo]] but with the 12/1 rather than the [[2/1]] being just. The octave is about 1.45 cents stretched compared to 31edo.
+== Theory ==
 == Intervals ==
 {{Interval table}}

BudjarnLambeth at 07:19, 4 October 2024

2024-10-04T07:19:19Z

← Older revision		Revision as of 07:19, 4 October 2024
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	{{Stub}}		{{Stub}}
	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}} 111ed12 is nearly identical to [[31edo]] but with the 12/1 rather than the [[2/1]] being just. The octave is about 1.45 cents stretched compared to 31edo.		{{ED intro}}

			111ed12 is nearly identical to [[31edo]] but with the 12/1 rather than the [[2/1]] being just. The octave is about 1.45 cents stretched compared to 31edo.

	== Intervals ==		== Intervals ==

← Older revision		Revision as of 15:01, 16 July 2025
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	* [[80ed6]] – relative ed6		* [[80ed6]] – relative ed6
	* [[87ed7]] – relative ed7		* [[87ed7]] – relative ed7
			* [[107ed11]] – relative ed11
			* [[138ed22]] – relative ed22
	* [[204ed96]] – close to the zeta-optimized tuning for 31edo		* [[204ed96]] – close to the zeta-optimized tuning for 31edo
	* [[39cET]]		* [[39cET]]

	[[Category:31edo]]		[[Category:31edo]]

← Older revision		Revision as of 13:32, 10 June 2025
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	* [[80ed6]] – relative ed6		* [[80ed6]] – relative ed6
	* [[87ed7]] – relative ed7		* [[87ed7]] – relative ed7
			* [[204ed96]] – close to the zeta-optimized tuning for 31edo
	* [[39cET]]		* [[39cET]]

			[[Category:31edo]]