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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}} It supports [[mintaka]] temperament.
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-09-12 15:47:11 UTC</tt>.<br>
: The original revision id was <tt>591722730</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">**22edt** is the [[@edt|equal division of the third harmonic]] into 22 tones, each 86.453 [[@cent]]s in size.


22edt has good approximations of the 7th, 11th, 19th and 20th harmonics. It also has the 4L+5s MOS with L=3 and s=2 approximating 5/3 somewhat fuzzily.
Like [[11edt]], both the [[octave]] and [[small whole tone]] ([[10/9]]) are about 10c off (sharp and flat respectively) dissonant but recognizable. Akin to [[16edt]] with [[Blackwood]], admitting the octave induces an interpretation into a tritave-based version of [[Whitewood]] temperament, therefore allowing the system to function as an octave stretch of [[14edo]]. However, it can just as well be treated as a pure no-twos system, which is the main interpretation used in the below article.


Like [[@11edt]], both the [[@octave]] and [[@minor whole tone]] [[@10_9|10:9]] are about 10c off (sharp and flat respectively) dissonant but recognizable. Like [[16edt]] and Blackwood, admitting the octave induces an interpretation into a tritave-based version of Whitewood temperament.
22edt has good approximations of the 7th, 11th, 19th and 20th harmonics, being better for its size in the 3.7.11 subgroup than even [[13edt]] is in 3.5.7. In this subgroup, it tempers out the commas [[1331/1323]] and [[387420489/386683451]], with the former comma allowing a hard [[5L 2s (3/1-equivalent)|5L 2s]] (macrodiatonic) scale generated by [[11/7]], two of which are equated to [[27/11]] and three of which are equated to [[9/7]] up a tritave. This [[9/7]] can also serve as the generator for a [[4L 5s (3/1-equivalent)|4L 5s]] (BPS Lambda) scale, supporting [[Bohlen-Pierce-Stearns]] harmony by tempering out [[245/243]], although its representation of the 3.5.7 subgroup is less accurate than that of 13edt, and tempered in the wrong direction relative to 13edt for ideal BPS.


=**Intervals**=
{{Harmonics in equal|22|3|1|intervals=prime|columns=15}}
86.4525
172.905
[[@tel:259.3575|259.3575]]
345.81
[[@tel:432.2625|432.2625]]
518.715
[[@tel:605.1675|605.1675]]
691.62
[[@tel:778.0725|778.0725]]
864.525
[[@tel:950.9775|950.9775]]
1037.43
1123.8825
1210.335
1296.7875
1383.24
1469.6925
1556.145
1642.5975
1729.05
1815.5025
3/1


=Compositions=  
== Intervals ==
[[@http://www.archive.org/details/TuneIn22Edt]] - Kosmorsky
&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;[[@http://micro.soonlabel.com/22-edt/daily20111206-22edt-improv.mp3|22 edt piano improvisation]]&lt;/span&gt; by [[@Chris Vaisvil]]


[[media type="custom" key="11601210"]]</pre></div>
The notation schemes below are based on the BPS-Lambda enneatonic scale presented in the symmetric (sLsLsLsLs, Cassiopeian) mode in J, and the Mintaka macrodiatonic scale presented in the macro-Phrygian (sLLLsLL) mode in E.
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;22edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;22edt&lt;/strong&gt; is the &lt;a class="wiki_link" href="/edt" target="_blank"&gt;equal division of the third harmonic&lt;/a&gt; into 22 tones, each 86.453 &lt;a class="wiki_link" href="/cent" target="_blank"&gt;cent&lt;/a&gt;s in size.&lt;br /&gt;
{| class="wikitable"
&lt;br /&gt;
|-
22edt has good approximations of the 7th, 11th, 19th and 20th harmonics. It also has the 4L+5s MOS with L=3 and s=2 approximating 5/3 somewhat fuzzily.&lt;br /&gt;
! | Degree
&lt;br /&gt;
! | Note ([[4L 5s (3/1-equivalent)#Notation|BPS-Lambda notation]])
Like &lt;a class="wiki_link" href="/11edt" target="_blank"&gt;11edt&lt;/a&gt;, both the &lt;a class="wiki_link" href="/octave" target="_blank"&gt;octave&lt;/a&gt; and &lt;a class="wiki_link" href="/minor%20whole%20tone" target="_blank"&gt;minor whole tone&lt;/a&gt; &lt;a class="wiki_link" href="/10_9" target="_blank"&gt;10:9&lt;/a&gt; are about 10c off (sharp and flat respectively) dissonant but recognizable. Like &lt;a class="wiki_link" href="/16edt"&gt;16edt&lt;/a&gt; and Blackwood, admitting the octave induces an interpretation into a tritave-based version of Whitewood temperament.&lt;br /&gt;
! | Note (Macrodiatonic notation)
&lt;br /&gt;
! | Approximate 3.7.11 subgroup interval
&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;&lt;strong&gt;Intervals&lt;/strong&gt;&lt;/h1&gt;
! | cents value
86.4525&lt;br /&gt;
! | hekts
172.905&lt;br /&gt;
|-
&lt;a class="wiki_link" href="http://tel.wikispaces.com/259.3575" target="_blank"&gt;259.3575&lt;/a&gt;&lt;br /&gt;
| | 0
345.81&lt;br /&gt;
| | J
&lt;a class="wiki_link" href="http://tel.wikispaces.com/432.2625" target="_blank"&gt;432.2625&lt;/a&gt;&lt;br /&gt;
| | E
518.715&lt;br /&gt;
| | 1/1
&lt;a class="wiki_link" href="http://tel.wikispaces.com/605.1675" target="_blank"&gt;605.1675&lt;/a&gt;&lt;br /&gt;
| | 0
691.62&lt;br /&gt;
| | 0
&lt;a class="wiki_link" href="http://tel.wikispaces.com/778.0725" target="_blank"&gt;778.0725&lt;/a&gt;&lt;br /&gt;
|-
864.525&lt;br /&gt;
| | 1
&lt;a class="wiki_link" href="http://tel.wikispaces.com/950.9775" target="_blank"&gt;950.9775&lt;/a&gt;&lt;br /&gt;
| | J# = Kb
1037.43&lt;br /&gt;
| | F
1123.8825&lt;br /&gt;
| | 81/77, 363/343
1210.335&lt;br /&gt;
| | 86.453
1296.7875&lt;br /&gt;
| | 59.091
1383.24&lt;br /&gt;
|-
1469.6925&lt;br /&gt;
| | 2
1556.145&lt;br /&gt;
| | K
1642.5975&lt;br /&gt;
| | Gb = Dx
1729.05&lt;br /&gt;
| | 2673/2401, 6561/5929
1815.5025&lt;br /&gt;
| | 172.905
3/1&lt;br /&gt;
| | 118.182
&lt;br /&gt;
|-
&lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;Compositions&lt;/h1&gt;
| | 3
&lt;a class="wiki_link_ext" href="http://www.archive.org/details/TuneIn22Edt" rel="nofollow" target="_blank"&gt;http://www.archive.org/details/TuneIn22Edt&lt;/a&gt; - Kosmorsky&lt;br /&gt;
| | K#
&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/22-edt/daily20111206-22edt-improv.mp3" rel="nofollow" target="_blank"&gt;22 edt piano improvisation&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil" target="_blank"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
| | E# = Abb
&lt;br /&gt;
| | 343/297, 847/729
&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/11601210?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;11601210&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;
| | 259.358
&lt;/script&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
| | 177.273
|-
| | 4
| | Lb
| | F#
| | 11/9, 147/121
| | 345.810
| | 236.364
|-
| | 5
| | L
| | G
| | 9/7
| | 432.263
| | 295.455
|-
| | 6
| | L# = Mb
| | Ab = Ex
| | 729/539
| | 518.715
| | 354.545
|-
| | 7
| | M
| | Fx = Bbb
| | 343/243
| | 605.168
| | 413.636
|-
| | 8
| | M#
| | G#
| | 49/33, 121/81
| | 691.620
| | 472.727
|-
| | 9
| | Nb
| | A
| | 11/7
| | 778.073
| | 531.818
|-
| | 10
| | N
| | Bb
| | 81/49
| | 864.525
| | 590.909
|-
| | 11
| | N# = Ob
| | Cb = Gx
| | 3773/2187, 6561/3773
| | 950.978
| | 650.
|-
| | 12
| | O
| | A# = Dbb
| | 49/27
| | 1037.430
| | 709.091
|-
| | 13
| | O#
| | B
| | 21/11
| | 1123.883
| | 768.182
|-
| | 14
| | Pb
| | C
| | 99/49, 243/121
| | 1210.335
| | 827.273
|-
| | 15
| | P
| | Db = Ax
| | 729/343
| | 1296.788
| | 886.364
|-
| | 16
| | P# = Qb
| | B# = Ebb
| | 539/243
| | 1383.240
| | 945.455
|-
| | 17
| | Q
| | C#
| | 7/3
| | 1469.693
| | 1004.545
|-
| | 18
| | Q#
| | D
| | 27/11, 121/49
| | 1556.145
| | 1063.636
|-
| | 19
| | Rb
| | Eb
| | 891/343, 2187/847
| | 1642.598
| | 1122.727
|-
| | 20
| | R
| | Fb = Cx
| | 2401/891, 5929/2187
| | 1729.050
| | 1181.818
|-
| | 21
| | R# = Jb
| | D# = Gbb
| | 77/27, 343/121
| | 1815.503
| | 1240.909
|-
| | 22
| | J
| | E
| | 3/1
| | 1901.955
| | 1300.
|}
 
== Audio examples ==
[[File:22ed3-1.mp3]]
 
A short composition by [[Wensik]], based on the 7:9:11 chord and its inversion, 63:77:99.
 
== Music ==
; [[Peter Kosmorsky]]
* [http://www.archive.org/details/TuneIn22Edt Tune in 22edt] (2011)
 
; [[Ray Perlner]]
* [https://www.youtube.com/watch?v=EWy0y_WsVNk ''Fugue in 22EDT Mintaka[7] sLLLsLL "Macro-Phrygian"''] (2025)
 
; [[Chris Vaisvil]]
* [http://micro.soonlabel.com/22-edt/daily20111206-22edt-improv.mp3 22 edt piano improvisation] {{dead link}}
 
[[Category:Nonoctave]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/22edt"