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11edt: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{ED intro}}
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-07 15:06:14 UTC</tt>.<br>
: The original revision id was <tt>262681116</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[media type="custom" key="10763046"]]


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]], 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.
== 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-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.
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]].


Tuning in scala format is as follows:
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]].


! E:\cakewalk\scales\11_of_tritave.scl
=== Harmonics ===
!
{{Harmonics in equal|11|3|1|intervals=integer|columns=11}}
11 in tritave
{{Harmonics in equal|11|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 11edt (continued)}}
!
172.90500
345.81000
518.71500
691.62000
864.52500
1037.43000
1210.33500
1383.24000
1556.14500
1729.05000
3/1


=== 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]


[[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]].</pre></div>
== See also ==
<h4>Original HTML content:</h4>
* [[7edo]] – relative edo
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;11edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/10763046?h=0&amp;amp;w=0&amp;quot; class=&amp;quot;WikiMedia WikiMediaCustom&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;custom&amp;amp;quot; key=&amp;amp;quot;10763046&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;script type="text/javascript" src="http://mediaplayer.yahoo.com/js"&gt;
* [[18ed6]] – relative ed6
&lt;/script&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;&lt;br /&gt;
&lt;br /&gt;
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 &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;, 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.&lt;br /&gt;
&lt;br /&gt;
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.&lt;br /&gt;
&lt;br /&gt;
Tuning in scala format is as follows:&lt;br /&gt;
&lt;br /&gt;
! E:\cakewalk\scales\11_of_tritave.scl&lt;br /&gt;
!&lt;br /&gt;
11 in tritave&lt;br /&gt;
!&lt;br /&gt;
172.90500&lt;br /&gt;
345.81000&lt;br /&gt;
518.71500&lt;br /&gt;
691.62000&lt;br /&gt;
864.52500&lt;br /&gt;
1037.43000&lt;br /&gt;
1210.33500&lt;br /&gt;
1383.24000&lt;br /&gt;
1556.14500&lt;br /&gt;
1729.05000&lt;br /&gt;
3/1&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/tritave_in_11/11of_tritave_improv.mp3" rel="nofollow"&gt;Frozen Time Occupies Wall Street&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://www.chrisvaisvil.com" rel="nofollow" target="_blank"&gt;Chris Vaisvil&lt;/a&gt; =&amp;gt;&lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1392" rel="nofollow" target="_blank"&gt; information about the piece&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
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