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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:JosephRuhf|JosephRuhf]] and made on <tt>2016-09-20 10:25:00 UTC</tt>.<br>
: The original revision id was <tt>592857390</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">=21 Equal Divisions of the Tritave=


|| Degrees || Cents || Approximate Ratio ||
== Intervals ==
|| 0 || 0 || [[1_1|1/1]] ||
{| class="wikitable"
|| 1 || 90.569 || [[21_20|21/20]], [[135_128|135/128]] ||
|-
|| 2 || 181.139 || [[10_9|10/9]] ||
! Degrees
|| 3 || 271.708 || [[7_6|7/6]] ||
! Cents
|| 4 || 362.277 || [[16_13|16/13]] ||
! Hekts
|| 5 || 452.846 || [[13_10|13/10]] ||
! Approximate Ratio
|| 6 || 543.416 || [[15_11|15/11]], [[11_8|11/8]] ||
|-
|| 7 || 633.985 || [[13_9|13/9]] ||
| colspan="3" style="text-align: center;" | 0
|| 8 || 724.554 || 35/23 ||
| [[1/1|1/1]]
|| 9 || 815.124 || [[8_5|8/5]] ||
|-
|| 10 || 905.693 || 27/16 ||
| 1
|| 11 || 996.262 || 16/9 ||
| 90.569
|| 12 || 1086.831 || [[15_8|15/8]] ||
| 61.905
|| 13 || 1177.401 || 69/35 ||
| [[21/20|21/20]], [[135/128|135/128]]
|| 14 || 1267.970 || 27/13 ||
|-
|| 15 || 1358.539 || 11/5 ([[11_10|11/10]] plus an octave), 24/11 (12/11 plus an octave) ||
| 2
|| 16 || 1449.109 || 30/13 ([[15_13|15/13]] plus an octave) ||
| 181.139
|| 17 || 1539.678 || 39/16 ||
| 123.81
|| 18 || 1630.247 || 18/7 ([[9_7|9/7]] plus an octave) ||
| [[10/9|10/9]]
|| 19 || 1720.816 || 27/10 ||
|-
|| 20 || 1811.386 || 20/7, 128/45 ||
| 3
|| 21 || 1901.955 || 3/1 ||
| 271.708
| 185.714
| [[7/6|7/6]]
|-
| 4
| 362.277
| 247.619
| [[16/13|16/13]]
|-
| 5
| 452.846
| 309.524
| [[13/10|13/10]]
|-
| 6
| 543.416
| 371.429
| [[15/11|15/11]], [[11/8|11/8]]
|-
| 7
| 633.985
| 433.333
| [[13/9|13/9]]
|-
| 8
| 724.554
| 495.238
| 35/23
|-
| 9
| 815.124
| 557.143
| [[8/5|8/5]]
|-
| 10
| 905.693
| 619.048
| 27/16
|-
| 11
| 996.262
| 680.952
| 16/9
|-
| 12
| 1086.831
| 742.857
| [[15/8|15/8]]
|-
| 13
| 1177.401
| 804.762
| 69/35
|-
| 14
| 1267.97
| 866.667
| 27/13
|-
| 15
| 1358.539
| 928.571
| 11/5 ([[11/10|11/10]] plus an octave), 24/11 (12/11 plus an octave)
|-
| 16
| 1449.109
| 990.476
| 30/13 ([[15/13|15/13]] plus an octave)
|-
| 17
| 1539.678
| 1052.381
| 39/16
|-
| 18
| 1630.247
| 1114.286
| 18/7 ([[9/7|9/7]] plus an octave)
|-
| 19
| 1720.816
| 1076.19
| 27/10
|-
| 20
| 1811.386
| 1238.095
| 20/7, 128/45
|-
| 21
| 1901.955
| 1300
| 3/1
|}


 
21edt contains 6 intervals from [[7edt|7edt]] and 2 intervals from [[3edt|3edt]], meaning that it introduces 12 new intervals not available in lower edt's. These new intervals allow for construction of strange chords like 9:10:13:16:22:27:30...
21edt contains 6 intervals from [[7edt]] and 2 intervals from [[3edt]], meaning that it introduces 12 new intervals not available in lower edt's. These new intervals allow for construction of strange chords like 9:10:13:16:22:27:30...


21edt contains a 7L7s MOS similar to Whitewood, which I call Ivory. It has a period of 1/7 of the tritave and the generator is one step. The major scale is LsLsLsLsLsLsLs, and the minor scale is sLsLsLsLsLsLsL.
21edt contains a 7L7s MOS similar to Whitewood, which I call Ivory. It has a period of 1/7 of the tritave and the generator is one step. The major scale is LsLsLsLsLsLsLs, and the minor scale is sLsLsLsLsLsLsL.


21edt also contains a 4L5s MOS similar to [[BP|BP]], with a 4:1 ratio of large to small; quite exaggerated from the optimal 2:1. Although the 7/3 is a little off, the 4L+5s BP scale is pretty. However, one of the star scales in 21edt is the 3L+6s (ssLssLssL and modes thereof) which is very harmonically rich, the cornerstone of which is the approximate 9:13:19 chord (which is just the [[3edt|3edt]] essentially tempered chord).


21edt also contains a 4L5s MOS similar to [[BP]], with a 4:1 ratio of large to small; quite exaggerated from the optimal 2:1. Although the 7/3 is a little off, the 4L+5s BP scale is pretty. However, one of the star scales in 21edt is the 3L+6s (ssLssLssL and modes thereof) which is very harmonically rich, the cornerstone of which is the approximate 9:13:19 chord (which is just the [[3edt]] essentially tempered chord).
== Harmonics==
 
Not the best approximations but all within 20 cents: it has 5th&nbsp;(+20¢), 7th&nbsp;(&minus;16¢), 10th&nbsp;(+2¢), 11th&nbsp;(+15¢), 13th&nbsp;(&minus;3¢), 17th&nbsp;(&minus;14¢), 23rd&nbsp;(+6¢), and 37th&nbsp;(&minus;2¢) harmonics. For a lower division of the tritave that's quite a constellation! The chord is a little out of tune but it works, you can really sink into it.
Not the best approximations but all within 20 cents: it has 5th (+20c), 7th(-16c), 10th (+2c), 11th (+15c), 13th (-3c), 17th (-14c), 19th (-24 c), 23rd (+6 c), and 37th (-2c) harmonics. For a lower division of the tritave that's quite a constellation! The chord is a little out of tune but it works, you can really sink into it.</pre></div>
<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;21edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x21 Equal Divisions of the Tritave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;21 Equal Divisions of the Tritave&lt;/h1&gt;
&lt;br /&gt;
 


&lt;table class="wiki_table"&gt;
{{Harmonics in equal
    &lt;tr&gt;
| steps = 21
        &lt;td&gt;Degrees&lt;br /&gt;
| num = 3
&lt;/td&gt;
| denom = 1
        &lt;td&gt;Cents&lt;br /&gt;
| intervals = integer
&lt;/td&gt;
}}
        &lt;td&gt;Approximate Ratio&lt;br /&gt;
{{Harmonics in equal
&lt;/td&gt;
| steps = 21
    &lt;/tr&gt;
| num = 3
    &lt;tr&gt;
| denom = 1
        &lt;td&gt;0&lt;br /&gt;
| start = 12
&lt;/td&gt;
| collapsed = 1
        &lt;td&gt;0&lt;br /&gt;
| intervals = integer
&lt;/td&gt;
}}
        &lt;td&gt;&lt;a class="wiki_link" href="/1_1"&gt;1/1&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;90.569&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/21_20"&gt;21/20&lt;/a&gt;, &lt;a class="wiki_link" href="/135_128"&gt;135/128&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;181.139&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;271.708&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;362.277&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/16_13"&gt;16/13&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;452.846&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/13_10"&gt;13/10&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;543.416&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/15_11"&gt;15/11&lt;/a&gt;, &lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;633.985&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/13_9"&gt;13/9&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;724.554&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;35/23&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;815.124&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/8_5"&gt;8/5&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;905.693&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;27/16&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;996.262&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1086.831&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/15_8"&gt;15/8&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1177.401&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;69/35&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1267.970&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;27/13&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1358.539&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/5 (&lt;a class="wiki_link" href="/11_10"&gt;11/10&lt;/a&gt; plus an octave), 24/11 (12/11 plus an octave)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1449.109&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;30/13 (&lt;a class="wiki_link" href="/15_13"&gt;15/13&lt;/a&gt; plus an octave)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1539.678&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;39/16&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1630.247&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/7 (&lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt; plus an octave)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1720.816&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;27/10&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1811.386&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20/7, 128/45&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1901.955&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
[[Category:tritave]]
&lt;br /&gt;
{{todo|expand|improve synopsis}}
21edt contains 6 intervals from &lt;a class="wiki_link" href="/7edt"&gt;7edt&lt;/a&gt; and 2 intervals from &lt;a class="wiki_link" href="/3edt"&gt;3edt&lt;/a&gt;, meaning that it introduces 12 new intervals not available in lower edt's. These new intervals allow for construction of strange chords like 9:10:13:16:22:27:30...&lt;br /&gt;
&lt;br /&gt;
21edt contains a 7L7s MOS similar to Whitewood, which I call Ivory. It has a period of 1/7 of the tritave and the generator is one step. The major scale is LsLsLsLsLsLsLs, and the minor scale is sLsLsLsLsLsLsL.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
21edt also contains a 4L5s MOS similar to &lt;a class="wiki_link" href="/BP"&gt;BP&lt;/a&gt;, with a 4:1 ratio of large to small; quite exaggerated from the optimal 2:1. Although the 7/3 is a little off, the 4L+5s BP scale is pretty. However, one of the star scales in 21edt is the 3L+6s (ssLssLssL and modes thereof) which is very harmonically rich, the cornerstone of which is the approximate 9:13:19 chord (which is just the &lt;a class="wiki_link" href="/3edt"&gt;3edt&lt;/a&gt; essentially tempered chord).&lt;br /&gt;
&lt;br /&gt;
Not the best approximations but all within 20 cents: it has 5th (+20c), 7th(-16c), 10th (+2c), 11th (+15c), 13th (-3c), 17th (-14c), 19th (-24 c), 23rd (+6 c), and 37th (-2c) harmonics. For a lower division of the tritave that's quite a constellation! The chord is a little out of tune but it works, you can really sink into it.&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/21edt"