11-limit: Difference between revisions
It is best to include EDOs which represent 11-limit consistently. |
→Intervals 1: Corrected information as it was previously referring to 11-odd-limit. |
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While the [[7-limit]] introduces subminor and supermajor intervals, which can sound like dramatic inflections of the familiar interval categories of [[12edo]], the 11-limit introduces neutral intervals, [[superfourth]]s and [[subfifth]]s, which fall in between major, minor and perfect [[interval category|interval categories]] and thus demand new distinctions. It is thus inescapably xenharmonic. | While the [[7-limit]] introduces subminor and supermajor intervals, which can sound like dramatic inflections of the familiar interval categories of [[12edo]], the 11-limit introduces neutral intervals, [[superfourth]]s and [[subfifth]]s, which fall in between major, minor and perfect [[interval category|interval categories]] and thus demand new distinctions. It is thus inescapably xenharmonic. | ||
Examples of [[EDO]]s which | Examples of [[EDO]]s which represent 11-limit intervals well include: {{EDOs|22, 26, 31, 41, 46, 63, 72, 87, 109, 118, 152, and 161edo }}. | ||
[[File:11-limit_compare.png|alt=11-limit_compare.png|11-limit_compare.png]] | [[File:11-limit_compare.png|alt=11-limit_compare.png|11-limit_compare.png]] | ||
== Intervals 2 == | ==Intervals 2== | ||
Here are all the 15-odd-limit intervals of 11: | Here are all the 15-odd-limit intervals of 11: | ||
{| class="wikitable center-all right-2" | {| class="wikitable center-all right-2" | ||
! Ratio | !Ratio | ||
! Site ([[cents|¢]]) | !Site ([[cents|¢]]) | ||
! colspan="2" | [[Color name]] | ! colspan="2" |[[Color name]] | ||
|- | |- | ||
| [[12/11]] | |[[12/11]] | ||
| 150.637 | |150.637 | ||
| 1u2 | |1u2 | ||
| lu 2nd | |lu 2nd | ||
|- | |- | ||
| [[11/10]] | |[[11/10]] | ||
| 165.004 | |165.004 | ||
| 1og2 | | 1og2 | ||
| logu 2nd | |logu 2nd | ||
|- | |- | ||
| [[11/9]] | |[[11/9]] | ||
| 347.408 | |347.408 | ||
| 1o3 | |1o3 | ||
| ilo 3rd | |ilo 3rd | ||
|- | |- | ||
| [[14/11]] | |[[14/11]] | ||
| 417.508 | |417.508 | ||
| 1uz4 | | 1uz4 | ||
| lu 4th | |lu 4th | ||
|- | |- | ||
| [[15/11]] | |[[15/11]] | ||
| 536.951 | |536.951 | ||
| 1uy4 | | 1uy4 | ||
| luyo 4th | |luyo 4th | ||
|- | |- | ||
| [[11/8]] | |[[11/8]] | ||
| 551.318 | |551.318 | ||
| 1o4 | |1o4 | ||
| ilo 4th | |ilo 4th | ||
|- | |- | ||
| [[16/11]] | |[[16/11]] | ||
| 648.682 | |648.682 | ||
| 1u5 | |1u5 | ||
| lu 5th | |lu 5th | ||
|- | |- | ||
| [[22/15]] | |[[22/15]] | ||
| 663.049 | |663.049 | ||
| 1og5 | | 1og5 | ||
| logu 5th | |logu 5th | ||
|- | |- | ||
| [[11/7]] | |[[11/7]] | ||
| 782.492 | |782.492 | ||
| 1or5 | | 1or5 | ||
| loru 5th | |loru 5th | ||
|- | |- | ||
| [[18/11]] | |[[18/11]] | ||
| 852.592 | |852.592 | ||
| 1u6 | |1u6 | ||
| lu 6th | |lu 6th | ||
|- | |- | ||
| [[20/11]] | |[[20/11]] | ||
| 1034.996 | |1034.996 | ||
| 1uy7 | | 1uy7 | ||
| luyo 7th | |luyo 7th | ||
|- | |- | ||
| [[11/6]] | |[[11/6]] | ||
| 1049.363 | |1049.363 | ||
| 1o7 | |1o7 | ||
| ilo 7th | |ilo 7th | ||
|} | |} | ||
== Music == | ==Music== | ||
* [http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm Study #3] [http://sonic-arts.org/hill/10-passages-ji/04_hill_study-3.mp3 play] by [[Dave Hill]] | *[http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm Study #3] [http://sonic-arts.org/hill/10-passages-ji/04_hill_study-3.mp3 play] by [[Dave Hill]] | ||
* [http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm Brief 11-ratio composition] [http://sonic-arts.org/hill/10-passages-ji/09_hill_brief-11-ratio-composition.mp3 play] by Dave Hill | *[http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm Brief 11-ratio composition] [http://sonic-arts.org/hill/10-passages-ji/09_hill_brief-11-ratio-composition.mp3 play] by Dave Hill | ||
* [http://micro.soonlabel.com/just/11-limit/20120210-piano-11-limit.mp3 11 Limit Piano] by [[Chris Vaisvil]] | *[http://micro.soonlabel.com/just/11-limit/20120210-piano-11-limit.mp3 11 Limit Piano] by [[Chris Vaisvil]] | ||
* [https://soundcloud.com/andrew_heathwaite/11-limit-singtervals 11-limit singtervals] by [[Andrew Heathwaite]] | *[https://soundcloud.com/andrew_heathwaite/11-limit-singtervals 11-limit singtervals] by [[Andrew Heathwaite]] | ||
== See also == | ==See also== | ||
* [[Gallery of just intervals]] | *[[Gallery of just intervals]] | ||
* [[Harmonic limit]] | *[[Harmonic limit]] | ||
* [[11-odd-limit]] | *[[11-odd-limit]] | ||
[[Category:11-limit]] | [[Category:11-limit]] | ||