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22edt: 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}} It supports [[mintaka]] temperament.
: This revision was by author [[User:Sarzadoce|Sarzadoce]] and made on <tt>2011-08-18 02:01:31 UTC</tt>.<br>
 
: The original revision id was <tt>246653063</tt>.<br>
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.
: 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>
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.
<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.
{{Harmonics in equal|22|3|1|intervals=prime|columns=15}}
22edt has good approximations of the 7th, 11th, 19th and 20th harmonics, as well as a few others approximated more vaguely.
 
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.</pre></div>
== Intervals ==
<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;
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.
22edt has good approximations of the 7th, 11th, 19th and 20th harmonics, as well as a few others approximated more vaguely.&lt;br /&gt;
 
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;/body&gt;&lt;/html&gt;</pre></div>
{| class="wikitable"
|-
! | Degree
! | Note ([[4L 5s (3/1-equivalent)#Notation|BPS-Lambda notation]])
! | Note (Macrodiatonic notation)
! | Approximate 3.7.11 subgroup interval
! | cents value
! | hekts
|-
| | 0
| | J
| | E
| | 1/1
| | 0
| | 0
|-
| | 1
| | J# = Kb
| | F
| | 81/77, 363/343
| | 86.453
| | 59.091
|-
| | 2
| | K
| | Gb = Dx
| | 2673/2401, 6561/5929
| | 172.905
| | 118.182
|-
| | 3
| | K#
| | E# = Abb
| | 343/297, 847/729
| | 259.358
| | 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"