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{{ED intro}} | |||
== Theory == | |||
11edt can be seen as a very [[stretched and compressed tuning|stretched]] version of [[7edo]], with octaves sharpened by 10.3 cents. The octave stretching makes the [[3/2]] perfect fifth in better tune, while preserving a just [[3/1]] tritave. | |||
From a no-2 point of view, 11edt has a [[5/3]] major sixth that is 19.8 cents flat. However, 11edt has an extremely inaccurate seventh harmonic [[7/1]], which is off by almost half a step (or about a semitone), which causes it to temper out [[49/45]] in the 7-limit. 11edt is at the extreme end of [[arcturus]] temperament, defined by tempering out [[15625/15309]] in the 3.5.7 subgroup. It gives an equalized interpretation for the [[9L 2s (3/1-equivalent)|sub-arcturus]] [[mos scale]]. | |||
The 11th harmonic, [[11/1]], only 1.6 cents flat, is very close to just. By exploiting the badly tuned seventh harmonic, 11edt tempers out [[35/33]] and [[77/75]] in the 11-limit. In the 3.5.11 subgroup, it tempers out [[125/121]]. | |||
=== Harmonics === | |||
{{Harmonics in equal|11|3|1|intervals=integer|columns=11}} | |||
{{Harmonics in equal|11|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 11edt (continued)}} | |||
=== Subsets and supersets === | |||
11edt is the fifth [[prime equal division|prime edt]], following [[7edt]] and before [[13edt]], so it does not contain any nontrivial subset edts. | |||
! | == Intervals == | ||
{| class="wikitable center-1 right-2 right-3" | |||
|- | |||
! # | |||
! [[Cent]]s | |||
! [[Hekt]]s | |||
! Approximate ratios* | |||
! [[Arcturus]]<br>enneatonic notation (J = 1/1) | |||
|- | |||
| 0 | |||
| 0.0 | |||
| 0.0 | |||
| [[1/1]] | |||
| J | |||
|- | |||
| 1 | |||
| 172.9 | |||
| 118.1 | |||
| [[10/9]], [[11/10]] | |||
| J#, Kb | |||
|- | |||
| 2 | |||
| 345.8 | |||
| 236.2 | |||
| [[5/4]], [[6/5]], [[11/9]], [[27/22]] | |||
| K | |||
|- | |||
| 3 | |||
| 518.7 | |||
| 354.3 | |||
| [[4/3]], [[15/11]] | |||
| L | |||
|- | |||
| 4 | |||
| 691.6 | |||
| 472.4 | |||
| [[3/2]] | |||
| M | |||
|- | |||
| 5 | |||
| 864.5 | |||
| 590.5 | |||
| [[5/3]], [[18/11]], [[33/20]] | |||
| N | |||
|- | |||
| 6 | |||
| 1037.4 | |||
| 708.6 | |||
| [[9/5]], [[11/6]], [[20/11]] | |||
| N#, Ob | |||
|- | |||
| 7 | |||
| 1210.3 | |||
| 826.7 | |||
| [[2/1]] | |||
| O | |||
|- | |||
| 8 | |||
| 1383.2 | |||
| 944.8 | |||
| [[9/4]], [[11/5]] | |||
| P | |||
|- | |||
| 9 | |||
| 1556.1 | |||
| 1062.9 | |||
| [[5/2]], [[12/5]], [[22/9]], [[27/11]] | |||
| Q | |||
|- | |||
| 10 | |||
| 1729.0 | |||
| 1181.0 | |||
| [[8/3]], [[11/4]] | |||
| R | |||
|- | |||
| 11 | |||
| 1902.0 | |||
| 1300.0 | |||
| [[3/1]] | |||
| J | |||
|} | |||
<nowiki/>* As a 2.3.5.11-subgroup temperament | |||
== Music == | |||
=== Modern renderings === | |||
; {{W|Wolfgang Amadeus Mozart}} | |||
* [https://web.archive.org/web/20201127012444/http://micro.soonlabel.com/6th-comma-meantone/K331-period/k331-walter-piano-11edt.mp3 ''Piano Sonata No. 11'' in A major, K. 331] – using a 11 → 12 key mapping so octaves become tritaves | |||
=== 21st century === | |||
; [[Chris Vaisvil]] | |||
* ''Frozen Time Occupies Wall Street'' (2011) – [https://www.chrisvaisvil.com/frozen-time-occupies-wall-street/ blog] | [https://web.archive.org/web/20220911143825/http://micro.soonlabel.com/tritave_in_11/11of_tritave_improv.mp3 play] | |||
* ''Molly's Playground'' (2011) – [https://www.chrisvaisvil.com/mollys-playground/ blog] | [https://web.archive.org/web/20201127013949/http://micro.soonlabel.com/11edt/daily20111118-3-11of-edt-mollys-playground.mp3 play] | |||
== See also == | |||
* [[7edo]] – relative edo | |||
* [[18ed6]] – relative ed6 | |||
[ | |||
[[ | |||