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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:guest|guest]] and made on <tt>2012-05-09 12:14:28 UTC</tt>.<br>
: The original revision id was <tt>332536070</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]], the both the [[octave]] and [[minor whole tone]] [[10_9|10:9]] are about 10c off (sharp and flat respectively) dissonant but recognizable.
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
259.3575
345.81
432.2625
518.715
605.1675
691.62
778.0725
864.525
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"&gt;equal division of the third harmonic&lt;/a&gt; into 22 tones, each 86.453 &lt;a class="wiki_link" href="/cent"&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"&gt;11edt&lt;/a&gt;, the both the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; and &lt;a class="wiki_link" href="/minor%20whole%20tone"&gt;minor whole tone&lt;/a&gt; &lt;a class="wiki_link" href="/10_9"&gt;10:9&lt;/a&gt; are about 10c off (sharp and flat respectively) dissonant but recognizable.&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;
|-
259.3575&lt;br /&gt;
| | 0
345.81&lt;br /&gt;
| | J
432.2625&lt;br /&gt;
| | E
518.715&lt;br /&gt;
| | 1/1
605.1675&lt;br /&gt;
| | 0
691.62&lt;br /&gt;
| | 0
778.0725&lt;br /&gt;
|-
864.525&lt;br /&gt;
| | 1
950.9775&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"&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"&gt;22 edt piano improvisation&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&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"