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{{Infobox ET}}
{{Infobox ET}}
11edt means the division of 3, the tritave, into 11 equal parts of 175.905 cents each, corresponding to 6.940 edo. It can therefore be seen as a very stretched version of [[7edo|7edo]], with octaves sharpened by ten and a third cents. The octave stretching makes the fifth in better tune, and of course the twelfth is the pure 3/1 tritave.
{{ED intro}}


From a no-two point of view, it tempers out 49/45 and 15625/15309 in the 7-limit and 35/33 and 77/75 in the 11-limit.
== 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 ==
== Intervals ==
 
{| class="wikitable center-1 right-2 right-3"
{| class="wikitable center-all"
|-
! #
! #
! Cents
! [[Cent]]s
! Hekts
! [[Hekt]]s
! Approximate ratios
! Approximate ratios*
! [[Arcturus]] nonatonic notation
! [[Arcturus]]<br>enneatonic notation (J = 1/1)
|-
|-
| colspan = "3" | 0
| 0
| 0.0
| 0.0
| [[1/1]]
| [[1/1]]
| H
| J
|-
|-
| 1
| 1
| 172.9
| 172.9
| 118.1
| 118.1
| [[11/10]], [[10/9]]
| [[10/9]], [[11/10]]
| H#, Ib
| J#, Kb
|-
|-
| 2
| 2
| 345.8
| 345.8
| 236.2
| 236.2
| [[11/9]]
| [[5/4]], [[6/5]], [[11/9]], [[27/22]]
| I
| K
|-
|-
| 3
| 3
| 518.7
| 518.7
| 354.3
| 354.3
| [[4/3]], [[27/20]]
| [[4/3]], [[15/11]]
| J
| L
|-
|-
| 4
| 4
| 691.6
| 691.6
| 472.4
| 472.4
| [[3/2]], [[40/27]]
| [[3/2]]
| K
| M
|-
|-
| 5
| 5
| 864.5
| 864.5
| 590.5
| 590.5
| [[5/3]], [[28/17]], [[105/64]]
| [[5/3]], [[18/11]], [[33/20]]
| L
| N
|-
|-
| 6
| 6
| 1037.4
| 1037.4
| 708.6
| 708.6
| [[29/16]], [[20/11]], [[64/35]]
| [[9/5]], [[11/6]], [[20/11]]
| L#, Mb
| N#, Ob
|-
|-
| 7
| 7
Line 58: Line 71:
| 826.7
| 826.7
| [[2/1]]
| [[2/1]]
| M
| O
|-
|-
| 8
| 8
| 1383.2
| 1383.2
| 944.8
| 944.8
|
| [[9/4]], [[11/5]]
| N
| P
|-
|-
| 9
| 9
| 1556.1
| 1556.1
| 1062.9
| 1062.9
|  
| [[5/2]], [[12/5]], [[22/9]], [[27/11]]
| O
| Q
|-
|-
| 10
| 10
| 1729
| 1729.0
| 1181
| 1181.0
|
| [[8/3]], [[11/4]]
| P
| R
|-
|-
| 11
| 11
| 1902
| 1902.0
| 1300
| 1300.0
|
| [[3/1]]
| H
| J
|}
|}
<nowiki/>* As a 2.3.5.11-subgroup temperament


== Scala file ==
== Music ==
Tuning in scala format is as follows:
=== Modern renderings ===
 
; {{W|Wolfgang Amadeus Mozart}}
<pre>
* [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
! E:\cakewalk\scales\11_of_tritave.scl
 
!
 
11 in tritave
 
!
 
172.90500
 
345.81000
 
518.71500
 
691.62000
 
864.52500
 
1037.43000
 
1210.33500
 
1383.24000
 
1556.14500
 
1729.05000
 
3/1
</pre>
 
== Pieces ==
 
Mozart's [http://micro.soonlabel.com/6th-comma-meantone/K331-period/k331-walter-piano-11edt.mp3 sonata #11 in A Major K331 in 11 EDT] (using a 11 =&gt; 12 key mapping so octaves become tritaves)


[http://micro.soonlabel.com/tritave_in_11/11of_tritave_improv.mp3 Frozen Time Occupies Wall Street] by [http://www.chrisvaisvil.com Chris Vaisvil] =&gt;[http://chrisvaisvil.com/?p=1392  information about the piece]
=== 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]


[http://micro.soonlabel.com/11edt/daily20111118-3-11of-edt-mollys-playground.mp3 Molly's Playground] by [http://www.chrisvaisvil.com Chris Vaisvil] =&gt; [http://chrisvaisvil.com/?p=1716  information about the piece]
== See also ==
[[category:macrotonal]]
* [[7edo]] – relative edo
* [[18ed6]] – relative ed6
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