11-limit - Revision history

FloraC: Fix missing whitespace. Style

2026-04-19T10:19:10Z

Fix missing whitespace. Style

← Older revision		Revision as of 10:19, 19 April 2026
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	{{Prime limit navigation\|11}}		{{Prime limit navigation\|11}}
	The '''11-limit''' (~~AKA~~ ''yazala'' in [[color notation]])consists of all [[just intonation\|justly tuned]] [[interval]]s whose [[ratio\|numerators and denominators]] are both products of the [[prime]]s 2, 3, 5, 7 and 11. The 11-limit is the 5th [[prime limit]] and is a superset of the [[7-limit]] and a subset of the [[13-limit]]. Some examples of 11-limit intervals are [[14/11]], [[11/8]], [[27/22]] and [[99/98]].		The '''11-limit''' (a.k.a. ''yazala'' in [[color notation]]) consists of all [[just intonation\|justly tuned]] [[interval]]s whose [[ratio\|numerators and denominators]] are both products of the [[prime]]s 2, 3, 5, 7 and 11. The 11-limit is the 5th [[prime limit]] and is a superset of the [[7-limit]] and a subset of the [[13-limit]]. Some examples of 11-limit intervals are [[14/11]], [[11/8]], [[27/22]] and [[99/98]].

	The 11-limit is a [[rank and codimension\|rank-5]] system, and can be modeled in a 4-dimensional [[lattice]], with the primes 3, 5, 7, and 11 represented by each dimension. The prime 2 does not appear in the typical 11-limit lattice because [[octave equivalence]] is presumed. If octave equivalence is not presumed, a fifth dimension is needed.		The 11-limit is a [[rank and codimension\|rank-5]] system, and can be modeled in a 4-dimensional [[lattice]], with the primes 3, 5, 7, and 11 represented by each dimension. The prime 2 does not appear in the typical 11-limit lattice because [[octave equivalence]] is presumed. If octave equivalence is not presumed, a fifth dimension is needed.

Eufalesio: color notation

2026-04-19T09:43:53Z

color notation

← Older revision		Revision as of 09:43, 19 April 2026
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	{{Prime limit navigation\|11}}		{{Prime limit navigation\|11}}
	The '''11-limit''' consists of all [[just intonation\|justly tuned]] [[interval]]s whose [[ratio\|numerators and denominators]] are both products of the [[prime]]s 2, 3, 5, 7 and 11. The 11-limit is the 5th [[prime limit]] and is a superset of the [[7-limit]] and a subset of the [[13-limit]]. Some examples of 11-limit intervals are [[14/11]], [[11/8]], [[27/22]] and [[99/98]].		The '''11-limit''' (AKA ''yazala'' in [[color notation]])consists of all [[just intonation\|justly tuned]] [[interval]]s whose [[ratio\|numerators and denominators]] are both products of the [[prime]]s 2, 3, 5, 7 and 11. The 11-limit is the 5th [[prime limit]] and is a superset of the [[7-limit]] and a subset of the [[13-limit]]. Some examples of 11-limit intervals are [[14/11]], [[11/8]], [[27/22]] and [[99/98]].

	The 11-limit is a [[rank and codimension\|rank-5]] system, and can be modeled in a 4-dimensional [[lattice]], with the primes 3, 5, 7, and 11 represented by each dimension. The prime 2 does not appear in the typical 11-limit lattice because [[octave equivalence]] is presumed. If octave equivalence is not presumed, a fifth dimension is needed.		The 11-limit is a [[rank and codimension\|rank-5]] system, and can be modeled in a 4-dimensional [[lattice]], with the primes 3, 5, 7, and 11 represented by each dimension. The prime 2 does not appear in the typical 11-limit lattice because [[octave equivalence]] is presumed. If octave equivalence is not presumed, a fifth dimension is needed.

FloraC: Recategorize

2026-02-06T08:27:10Z

Recategorize

← Older revision		Revision as of 08:27, 6 February 2026
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	[[Category:11-limit\| ]] <!-- main article -->		[[Category:11-limit\| ]] <!-- main article -->
			[[Category:Rank-5 temperaments]]
	[[Category:Lists of intervals]]		[[Category:Lists of intervals]]
	[[Category:Listen]]		[[Category:Listen]]
	~~[[Category:Rank 5]]~~

Overthink: /* Edo approximation */ caps

2026-01-12T07:35:23Z

Edo approximation: caps

← Older revision		Revision as of 07:35, 12 January 2026
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	Here is a list of edos which tunes the 11-limit well relative to their size ([[TE relative error]] < 5%): {{EDOs\| 31, 41, 58, 72, 87, 118, 130, 152, 183, 190, 198, 212, 224, 239, 255, 270, 301, 311, 342, 369, 373, 400, 414, 422, 441, 453, 460, 463, 472, 494, 525, 552, 566, 581, 612 }} and so on.		Here is a list of edos which tunes the 11-limit well relative to their size ([[TE relative error]] < 5%): {{EDOs\| 31, 41, 58, 72, 87, 118, 130, 152, 183, 190, 198, 212, 224, 239, 255, 270, 301, 311, 342, 369, 373, 400, 414, 422, 441, 453, 460, 463, 472, 494, 525, 552, 566, 581, 612 }} and so on.

	{{Note\| [[~~wart~~ notation]] is used to specify the [[val]] chosen for the edo. In the above list, "27e" means taking the second closest approximation of harmonic 11. }}		{{Note\| [[Wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "27e" means taking the second closest approximation of harmonic 11. }}

	== Intervals ==		== Intervals ==

FloraC: /* Edo approximation */ adopt template

2025-12-27T17:42:04Z

Edo approximation: adopt template

← Older revision		Revision as of 17:42, 27 December 2025
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	Here is a list of edos which tunes the 11-limit well relative to their size ([[TE relative error]] < 5%): {{EDOs\| 31, 41, 58, 72, 87, 118, 130, 152, 183, 190, 198, 212, 224, 239, 255, 270, 301, 311, 342, 369, 373, 400, 414, 422, 441, 453, 460, 463, 472, 494, 525, 552, 566, 581, 612 }} and so on.		Here is a list of edos which tunes the 11-limit well relative to their size ([[TE relative error]] < 5%): {{EDOs\| 31, 41, 58, 72, 87, 118, 130, 152, 183, 190, 198, 212, 224, 239, 255, 270, 301, 311, 342, 369, 373, 400, 414, 422, 441, 453, 460, 463, 472, 494, 525, 552, 566, 581, 612 }} and so on.

	~~: '''~~Note~~''':~~ [[wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "27e" means taking the second closest approximation of harmonic 11.		{{Note\| [[wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "27e" means taking the second closest approximation of harmonic 11. }}

	== Intervals ==		== Intervals ==

FloraC: /* Edo approximation */ calibrate the list according to my research results

2025-08-20T16:29:49Z

Edo approximation: calibrate the list according to my research results

← Older revision		Revision as of 16:29, 20 August 2025
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	== Edo approximation ==		== Edo approximation ==
	Here is a list of [[edo]]s which represent 11-limit intervals with better accuracy (decreasing [[TE error]]): {{EDOs\| 22, 27e, 31, 41, 53, 58, 72, 118, 130, 152, 224, 270, 342, 612 }} and so on.		Here is a list of [[edo]]s which represent 11-limit intervals with better accuracy ([[monotonicity limit]] ≥ 11 and decreasing [[TE error]]): {{EDOs\| 12, 15, 19, 22, 27e, 31, 41, 53, 58, 72, 118, 130, 152, 224, 270, 342, 612 }} and so on. For a more comprehensive list, see [[Sequence of equal temperaments by error]].

	Here is a list of edos which tunes the 11-limit well relative to their size ([[TE relative error]] < 5%): {{EDOs\| 31, 41, 58, 72, 87, 118, 130, 152, 183, 190, 198, 212, 224, 239, 255, 270, 301, 311, 342, 369, 373, 400, 414, 422, 441, 453, 460, 463, 472, 494, 525, 552, 566, 581, 612 }} and so on.		Here is a list of edos which tunes the 11-limit well relative to their size ([[TE relative error]] < 5%): {{EDOs\| 31, 41, 58, 72, 87, 118, 130, 152, 183, 190, 198, 212, 224, 239, 255, 270, 301, 311, 342, 369, 373, 400, 414, 422, 441, 453, 460, 463, 472, 494, 525, 552, 566, 581, 612 }} and so on.

Xenjacob: /* Music */ new links for Dave Hill

2025-07-25T20:13:03Z

Music: new links for Dave Hill

← Older revision		Revision as of 20:13, 25 July 2025
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	; [[Dave Hill]]		; [[Dave Hill]]
	* [~~http~~://~~sonic-arts~~.~~org~~/~~hill~~/10-~~passages-ji/10-passages-ji.htm~~ ''Study #3'']~~{{dead link}} [http://sonic-arts.org/hill/10-passages-ji/04_hill_study-3.mp3 play]{{dead link}}~~		* [https://ralphdavidhill.bandcamp.com/track/study-3 ''Study #3'']
	* [~~http~~://~~sonic-arts~~.~~org~~/~~hill~~/10-~~passages~~-~~ji/10~~-~~passages~~-~~ji.htm~~ ''Brief 11-ratio composition'']~~{{dead link}} [http://sonic-arts.org/hill/10-passages-ji/09_hill_brief-11-ratio-composition.mp3 play]{{dead link}}~~		* [https://ralphdavidhill.bandcamp.com/track/brief-11-limit-ratio-composition ''Brief 11-ratio composition'']

	; [[Ben Johnston]]		; [[Ben Johnston]]

FloraC: Fill in some info that's present in the other limits but not here somehow

2025-05-21T10:36:52Z

Fill in some info that's present in the other limits but not here somehow

← Older revision		Revision as of 10:36, 21 May 2025
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	{{Prime limit navigation\|11}}		{{Prime limit navigation\|11}}
	The '''11-limit''' consists of all [[just intonation\|justly tuned]] [[interval]]s whose [[ratio\|numerators and denominators]] are both products of the [[prime]]s 2, 3, 5, 7 and 11. The 11-limit is the 5th [[prime limit]] and is a superset of the [[7-limit]] and a subset of the [[13-limit]]. Some examples of 11-limit intervals are [[14/11]], [[11/8]], [[27/22]] and [[99/98]].		The '''11-limit''' consists of all [[just intonation\|justly tuned]] [[interval]]s whose [[ratio\|numerators and denominators]] are both products of the [[prime]]s 2, 3, 5, 7 and 11. The 11-limit is the 5th [[prime limit]] and is a superset of the [[7-limit]] and a subset of the [[13-limit]]. Some examples of 11-limit intervals are [[14/11]], [[11/8]], [[27/22]] and [[99/98]].

			The 11-limit is a [[rank and codimension\|rank-5]] system, and can be modeled in a 4-dimensional [[lattice]], with the primes 3, 5, 7, and 11 represented by each dimension. The prime 2 does not appear in the typical 11-limit lattice because [[octave equivalence]] is presumed. If octave equivalence is not presumed, a fifth dimension is needed.

	These things are contained by the 11-limit, but not the 7-limit:		These things are contained by the 11-limit, but not the 7-limit:

FloraC: Undo revision 193606 by VectorGraphics (talk). The sections are empty

2025-04-23T10:09:56Z

Undo revision 193606 by VectorGraphics (talk). The sections are empty

@@ Line 240: / Line 240: @@
 |ilo 7th
 |}
 == Music ==

VectorGraphics at 04:13, 23 April 2025

2025-04-23T04:13:01Z

@@ Line 240: / Line 240: @@
 |ilo 7th
 |}
 == Music ==

← Older revision		Revision as of 10:19, 19 April 2026
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	{{Prime limit navigation\|11}}		{{Prime limit navigation\|11}}
	The '''11-limit''' (~~AKA~~ ''yazala'' in [[color notation]])consists of all [[just intonation\|justly tuned]] [[interval]]s whose [[ratio\|numerators and denominators]] are both products of the [[prime]]s 2, 3, 5, 7 and 11. The 11-limit is the 5th [[prime limit]] and is a superset of the [[7-limit]] and a subset of the [[13-limit]]. Some examples of 11-limit intervals are [[14/11]], [[11/8]], [[27/22]] and [[99/98]].		The '''11-limit''' (a.k.a. ''yazala'' in [[color notation]]) consists of all [[just intonation\|justly tuned]] [[interval]]s whose [[ratio\|numerators and denominators]] are both products of the [[prime]]s 2, 3, 5, 7 and 11. The 11-limit is the 5th [[prime limit]] and is a superset of the [[7-limit]] and a subset of the [[13-limit]]. Some examples of 11-limit intervals are [[14/11]], [[11/8]], [[27/22]] and [[99/98]].

	The 11-limit is a [[rank and codimension\|rank-5]] system, and can be modeled in a 4-dimensional [[lattice]], with the primes 3, 5, 7, and 11 represented by each dimension. The prime 2 does not appear in the typical 11-limit lattice because [[octave equivalence]] is presumed. If octave equivalence is not presumed, a fifth dimension is needed.		The 11-limit is a [[rank and codimension\|rank-5]] system, and can be modeled in a 4-dimensional [[lattice]], with the primes 3, 5, 7, and 11 represented by each dimension. The prime 2 does not appear in the typical 11-limit lattice because [[octave equivalence]] is presumed. If octave equivalence is not presumed, a fifth dimension is needed.

← Older revision		Revision as of 09:43, 19 April 2026
Line 1:		Line 1:
	{{Prime limit navigation\|11}}		{{Prime limit navigation\|11}}
	The '''11-limit''' consists of all [[just intonation\|justly tuned]] [[interval]]s whose [[ratio\|numerators and denominators]] are both products of the [[prime]]s 2, 3, 5, 7 and 11. The 11-limit is the 5th [[prime limit]] and is a superset of the [[7-limit]] and a subset of the [[13-limit]]. Some examples of 11-limit intervals are [[14/11]], [[11/8]], [[27/22]] and [[99/98]].		The '''11-limit''' (AKA ''yazala'' in [[color notation]])consists of all [[just intonation\|justly tuned]] [[interval]]s whose [[ratio\|numerators and denominators]] are both products of the [[prime]]s 2, 3, 5, 7 and 11. The 11-limit is the 5th [[prime limit]] and is a superset of the [[7-limit]] and a subset of the [[13-limit]]. Some examples of 11-limit intervals are [[14/11]], [[11/8]], [[27/22]] and [[99/98]].

	The 11-limit is a [[rank and codimension\|rank-5]] system, and can be modeled in a 4-dimensional [[lattice]], with the primes 3, 5, 7, and 11 represented by each dimension. The prime 2 does not appear in the typical 11-limit lattice because [[octave equivalence]] is presumed. If octave equivalence is not presumed, a fifth dimension is needed.		The 11-limit is a [[rank and codimension\|rank-5]] system, and can be modeled in a 4-dimensional [[lattice]], with the primes 3, 5, 7, and 11 represented by each dimension. The prime 2 does not appear in the typical 11-limit lattice because [[octave equivalence]] is presumed. If octave equivalence is not presumed, a fifth dimension is needed.