11-limit: Difference between revisions

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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''' (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.

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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.

{{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 ==

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== Music ==

=== Modern renderings ===

; {{W|Kane Parsons}}, {{W|Instupendo}}, and {{W|Edo Van Breemen}}

* [https://www.youtube.com/shorts/iYEERDCNoik ''Old Home Not Yet Built''] (2026) – microtonal cover in 11-limit JI (scale [[1/1|1]] [[9/8]] [[5/4]] [[11/8]] [[3/2]] [[5/3]] [[15/8]] in seven diatonic manuals on the Lumatone, each with different sound) by [[Bryan Deister]] (2026)

=== 21st century ===

; [[Brody Bigwood]]

* [https://www.youtube.com/watch?v=i-FokV8dicQ ''Presence''] (2024)

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[[Category:11-limit| ]]

[[Category:Rank-5 temperaments]]

[[Category:Lists of intervals]]

[[Category:Listen]]

~~[[Category:Rank 5]]~~

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 {{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''' (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.
@@ Line 17: / Line 17: @@
 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 ==
@@ Line 244: / Line 244: @@
 == Music ==
+=== Modern renderings ===
+; {{W|Kane Parsons}}, {{W|Instupendo}}, and {{W|Edo Van Breemen}}
+* [https://www.youtube.com/shorts/iYEERDCNoik ''Old Home Not Yet Built''] (2026) – microtonal cover in 11-limit JI (scale [[1/1|1]] [[9/8]] [[5/4]] [[11/8]] [[3/2]] [[5/3]] [[15/8]] in seven diatonic manuals on the Lumatone, each with different sound) by [[Bryan Deister]] (2026)
+=== 21st century ===
 ; [[Brody Bigwood]]
 * [https://www.youtube.com/watch?v=i-FokV8dicQ ''Presence''] (2024)
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 [[Category:11-limit| ]] <!-- main article -->
+[[Category:Rank-5 temperaments]]
 [[Category:Lists of intervals]]
 [[Category:Listen]]
-[[Category:Rank 5]]