11-limit: Difference between revisions
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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''' (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. | |||
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: | ||
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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. | ||
{{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 == | ||
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== Music == | == 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]] | ; [[Brody Bigwood]] | ||
* [https://www.youtube.com/watch?v=i-FokV8dicQ ''Presence''] (2024) | * [https://www.youtube.com/watch?v=i-FokV8dicQ ''Presence''] (2024) | ||
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; [[Dave Hill]] | ; [[Dave Hill]] | ||
* [ | * [https://ralphdavidhill.bandcamp.com/track/study-3 ''Study #3''] | ||
* [ | * [https://ralphdavidhill.bandcamp.com/track/brief-11-limit-ratio-composition ''Brief 11-ratio composition''] | ||
; [[Ben Johnston]] | ; [[Ben Johnston]] | ||
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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]] | ||