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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
'''30edt''' (30 equal division of the tritave) is a stretched version of [[19edo|19edo]], but with the 3:1 rather than the 2:1 being just. The octave is about 4.5 cents sharp and the step size about 63.4 cents.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-21 00:26:46 UTC</tt>.<br>
: The original revision id was <tt>596310862</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">**30edt** (30 equal division of the tritave) is a stretched version of [[19edo]], but with the 3:1 rather than the 2:1 being just. The octave is about 4.5 cents sharp and the step size about 63.4 cents.


Because 19edo has the 3rd, 5th, 7th, and 13th harmonics all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.
Because 19edo has the 3rd, 5th, 7th, and 13th harmonics all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.
=== ===
===&lt;span style="font-size: 1.4em;"&gt;Intervals of 30edt&lt;/span&gt;===
|| Degrees || Cents || Approximate Ratios || Sigma scale name ||
|| 0 || 0 || &lt;span style="color: #660000;"&gt;[[1_1|1/1]]&lt;/span&gt; || C ||
|| 1 || 63.3985 || 28/27, 27/26 || C#/Dbb ||
|| 2 || 126.797 || [[14_13|14/13]], [[15_14|15/14]], [[16_15|16/15]], 29/27 || Cx/Db ||
|| 3 || 190.1955 || 10/9~9/8 || D ||
|| 4 || 253.594 || [[15_13|15/13]] || D#/Ebb ||
|| 5 || 316.9925 || 6/5 || Dx/Eb ||
|| 6 || 380.391 || &lt;span style="color: #660000;"&gt;[[5_4|5/4]]&lt;/span&gt; || E ||
|| 7 || 443.7895 || 9/7 || E#/Fb ||
|| 8 || 507.188 || [[4_3|4/3]] || F ||
|| 9 || 570.5865 || 7/5 || F#/Gbb ||
|| 10 || 633.985 || [[13_9|13/9]] || Fx/Gb ||
|| 11 || 697.3835 || 3/2 || G ||
|| 12 || 760.782 || &lt;span style="color: #660000;"&gt;[[14_9|14/9]]&lt;/span&gt; || G#/Hbb ||
|| 13 || 824.1805 || 8/5 || Gx/Hb ||
|| 14 || 887.579 || [[5_3|5/3]] || H ||
|| 15 || 950.9775 || 19/11 || H#/Jbb ||
|| 16 || 1014.376 || [[9_5|9/5]] || Hx/Jb ||
|| 17 || 1077.7745 || 13/7 || J ||
|| 18 || 1141.173 || &lt;span style="color: #660000;"&gt;[[27_14|27/14]]&lt;/span&gt; || J#/Kb ||
|| 19 || 1204.5715 || 2/1 || K ||
|| 20 || 1267.970 || [[27_13|27/13]] || K#/Lbb ||
|| 21 || 1331.3685 || 28/13 || Kx/Lb ||
|| 22 || 1394.767 || [[9_4|9/4]] ([[9_8|9/8]] plus an octave) || L ||
|| 23 || 1458.1655 || 7/3 || L#/Abb ||
|| 24 || 1521.564 || [[12_5|12/5]] (&lt;span style="color: #660000;"&gt;[[6_5|6/5]]&lt;/span&gt; plus an octave) || Lx/Ab ||
|| 25 || 1584.9625 || 5/2 || A ||
|| 26 || 1648.361 || [[13_5|13/5]] ([[13_10|13/10]] plus an octave) || A#/Bb ||
|| 27 || 1711.7595 || 8/3 || B ||
|| 28 || 1775.158 || [[14_5|14/5]] ([[7_5|7/5]] plus an octave) || B#/Cbb ||
|| 29 || 1838.5565 || 26/9 || Bx/Cb ||
|| 30 || 1901.955 || [[3_1|3/1]] || C ||


30edt contains all [[19edo]] intervals within 3/1, all temepered progressively sharper. The accumulation of the .241 cent sharpening of the unit step relative to 19edo leads to the excellent 6edt approximations of 6/5 and 5/2. Non-redundantly with simpler edts, the 41 degree ~9/2 is only .6615 cents flatter than that in 6edo.
=== ===
 
===<span style="font-size: 1.4em;">Intervals of 30edt</span>===
 
{| class="wikitable"
|-
| | Degrees
| | Cents
| | Approximate Ratios
| | Sigma scale name
|-
| | 0
| | 0
| | <span style="color: #660000;">[[1/1|1/1]]</span>
| | C
|-
| | 1
| | 63.3985
| | 28/27, 27/26
| | C#/Dbb
|-
| | 2
| | 126.797
| | [[14/13|14/13]], [[15/14|15/14]], [[16/15|16/15]], 29/27
| | Cx/Db
|-
| | 3
| | 190.1955
| | 10/9~9/8
| | D
|-
| | 4
| | 253.594
| | [[15/13|15/13]]
| | D#/Ebb
|-
| | 5
| | 316.9925
| | 6/5
| | Dx/Eb
|-
| | 6
| | 380.391
| | <span style="color: #660000;">[[5/4|5/4]]</span>
| | E
|-
| | 7
| | 443.7895
| | 9/7
| | E#/Fb
|-
| | 8
| | 507.188
| | [[4/3|4/3]]
| | F
|-
| | 9
| | 570.5865
| | 7/5
| | F#/Gbb
|-
| | 10
| | 633.985
| | [[13/9|13/9]]
| | Fx/Gb
|-
| | 11
| | 697.3835
| | 3/2
| | G
|-
| | 12
| | 760.782
| | <span style="color: #660000;">[[14/9|14/9]]</span>
| | G#/Hbb
|-
| | 13
| | 824.1805
| | 8/5
| | Gx/Hb
|-
| | 14
| | 887.579
| | [[5/3|5/3]]
| | H
|-
| | 15
| | 950.9775
| | 19/11
| | H#/Jbb
|-
| | 16
| | 1014.376
| | [[9/5|9/5]]
| | Hx/Jb
|-
| | 17
| | 1077.7745
| | 13/7
| | J
|-
| | 18
| | 1141.173
| | <span style="color: #660000;">[[27/14|27/14]]</span>
| | J#/Kb
|-
| | 19
| | 1204.5715
| | 2/1
| | K
|-
| | 20
| | 1267.970
| | [[27/13|27/13]]
| | K#/Lbb
|-
| | 21
| | 1331.3685
| | 28/13
| | Kx/Lb
|-
| | 22
| | 1394.767
| | [[9/4|9/4]] ([[9/8|9/8]] plus an octave)
| | L
|-
| | 23
| | 1458.1655
| | 7/3
| | L#/Abb
|-
| | 24
| | 1521.564
| | [[12/5|12/5]] (<span style="color: #660000;">[[6/5|6/5]]</span> plus an octave)
| | Lx/Ab
|-
| | 25
| | 1584.9625
| | 5/2
| | A
|-
| | 26
| | 1648.361
| | [[13/5|13/5]] ([[13/10|13/10]] plus an octave)
| | A#/Bb
|-
| | 27
| | 1711.7595
| | 8/3
| | B
|-
| | 28
| | 1775.158
| | [[14/5|14/5]] ([[7/5|7/5]] plus an octave)
| | B#/Cbb
|-
| | 29
| | 1838.5565
| | 26/9
| | Bx/Cb
|-
| | 30
| | 1901.955
| | [[3/1|3/1]]
| | C
|}
 
30edt contains all [[19edo|19edo]] intervals within 3/1, all temepered progressively sharper. The accumulation of the .241 cent sharpening of the unit step relative to 19edo leads to the excellent 6edt approximations of 6/5 and 5/2. Non-redundantly with simpler edts, the 41 degree ~9/2 is only .6615 cents flatter than that in 6edo.


30edt also contains all the MOS contained in 15edt, being the double of this equal division. Being even, 30edt introduces
30edt also contains all the MOS contained in 15edt, being the double of this equal division. Being even, 30edt introduces
MOS with an even number of periods per tritave such as a 6L 6s similar to Hexe Dodecatonic. This MOS has a period of 1/6 of the tritave and the generator is a single or double step. The major scale is sLsLsLsLsLsL, and the minor scale is LsLsLsLsLsLs. Being a "real" 3/2, the interval of 11 degrees generates an unfair Sigma scale of 8L 3s and the major scale is LLsLLLsLLsL. The sharp 9/7 of 7 degrees, in addition to generating a Lambda MOS will generate a 4L 9s unfair Superlambda MOS which does not border on being atonal as the 17edt rendition does.
MOS with an even number of periods per tritave such as a 6L 6s similar to Hexe Dodecatonic. This MOS has a period of 1/6 of the tritave and the generator is a single or double step. The major scale is sLsLsLsLsLsL, and the minor scale is LsLsLsLsLsLs. Being a "real" 3/2, the interval of 11 degrees generates an unfair Sigma scale of 8L 3s and the major scale is LLsLLLsLLsL. The sharp 9/7 of 7 degrees, in addition to generating a Lambda MOS will generate a 4L 9s unfair Superlambda MOS which does not border on being atonal as the 17edt rendition does.


----
-----
===**Compositions in 30edt**===
 
* "[[https://soundcloud.com/mason-l-green/room-full-of-steam|Room Full Of Steam]]", Mason Green. In the key of "Eb subminor".</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;30edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;30edt&lt;/strong&gt; (30 equal division of the tritave) is a stretched version of &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, but with the 3:1 rather than the 2:1 being just. The octave is about 4.5 cents sharp and the step size about 63.4 cents.&lt;br /&gt;
&lt;br /&gt;
Because 19edo has the 3rd, 5th, 7th, and 13th harmonics all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt; &lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x--Intervals of 30edt"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;&lt;span style="font-size: 1.4em;"&gt;Intervals of 30edt&lt;/span&gt;&lt;/h3&gt;


&lt;table class="wiki_table"&gt;
==='''Compositions in 30edt'''===
    &lt;tr&gt;
        &lt;td&gt;Degrees&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Cents&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Approximate Ratios&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Sigma scale name&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;span style="color: #660000;"&gt;&lt;a class="wiki_link" href="/1_1"&gt;1/1&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C&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;63.3985&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;28/27, 27/26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C#/Dbb&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;126.797&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/14_13"&gt;14/13&lt;/a&gt;, &lt;a class="wiki_link" href="/15_14"&gt;15/14&lt;/a&gt;, &lt;a class="wiki_link" href="/16_15"&gt;16/15&lt;/a&gt;, 29/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Cx/Db&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;190.1955&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/9~9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;D&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;253.594&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/15_13"&gt;15/13&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;D#/Ebb&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;316.9925&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Dx/Eb&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;380.391&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;span style="color: #660000;"&gt;&lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;E&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;443.7895&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;E#/Fb&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;507.188&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/4_3"&gt;4/3&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;F&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;570.5865&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;F#/Gbb&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;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;td&gt;Fx/Gb&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;697.3835&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G&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;760.782&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;span style="color: #660000;"&gt;&lt;a class="wiki_link" href="/14_9"&gt;14/9&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G#/Hbb&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;824.1805&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gx/Hb&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;887.579&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/5_3"&gt;5/3&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;H&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;950.9775&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;H#/Jbb&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;1014.376&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/9_5"&gt;9/5&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hx/Jb&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;1077.7745&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;J&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;1141.173&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;span style="color: #660000;"&gt;&lt;a class="wiki_link" href="/27_14"&gt;27/14&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;J#/Kb&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;1204.5715&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;K&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;1267.970&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/27_13"&gt;27/13&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;K#/Lbb&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;1331.3685&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;28/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Kx/Lb&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1394.767&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/9_4"&gt;9/4&lt;/a&gt; (&lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt; plus an octave)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;L&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1458.1655&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;L#/Abb&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1521.564&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/12_5"&gt;12/5&lt;/a&gt; (&lt;span style="color: #660000;"&gt;&lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt;&lt;/span&gt; plus an octave)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Lx/Ab&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1584.9625&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1648.361&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/13_5"&gt;13/5&lt;/a&gt; (&lt;a class="wiki_link" href="/13_10"&gt;13/10&lt;/a&gt; plus an octave)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A#/Bb&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1711.7595&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;B&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1775.158&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/14_5"&gt;14/5&lt;/a&gt; (&lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt; plus an octave)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;B#/Cbb&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1838.5565&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;26/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Bx/Cb&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1901.955&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/3_1"&gt;3/1&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
<ul><li>"[https://soundcloud.com/mason-l-green/room-full-of-steam Room Full Of Steam]", Mason Green. In the key of "Eb subminor".</li></ul>     [[Category:edt]]
30edt contains all &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; intervals within 3/1, all temepered progressively sharper. The accumulation of the .241 cent sharpening of the unit step relative to 19edo leads to the excellent 6edt approximations of 6/5 and 5/2. Non-redundantly with simpler edts, the 41 degree ~9/2 is only .6615 cents flatter than that in 6edo.&lt;br /&gt;
[[Category:listen]]
&lt;br /&gt;
30edt also contains all the MOS contained in 15edt, being the double of this equal division. Being even, 30edt introduces&lt;br /&gt;
MOS with an even number of periods per tritave such as a 6L 6s similar to Hexe Dodecatonic. This MOS has a period of 1/6 of the tritave and the generator is a single or double step. The major scale is sLsLsLsLsLsL, and the minor scale is LsLsLsLsLsLs. Being a &amp;quot;real&amp;quot; 3/2, the interval of 11 degrees generates an unfair Sigma scale of 8L 3s and the major scale is LLsLLLsLLsL. The sharp 9/7 of 7 degrees, in addition to generating a Lambda MOS will generate a 4L 9s unfair Superlambda MOS which does not border on being atonal as the 17edt rendition does.&lt;br /&gt;
&lt;br /&gt;
&lt;hr /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x--Compositions in 30edt"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;strong&gt;Compositions in 30edt&lt;/strong&gt;&lt;/h3&gt;
&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&amp;quot;&lt;a class="wiki_link_ext" href="https://soundcloud.com/mason-l-green/room-full-of-steam" rel="nofollow"&gt;Room Full Of Steam&lt;/a&gt;&amp;quot;, Mason Green. In the key of &amp;quot;Eb subminor&amp;quot;.&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

30edt (30 equal division of the tritave) is a stretched version of 19edo, but with the 3:1 rather than the 2:1 being just. The octave is about 4.5 cents sharp and the step size about 63.4 cents.

Because 19edo has the 3rd, 5th, 7th, and 13th harmonics all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.

Intervals of 30edt

Degrees Cents Approximate Ratios Sigma scale name
0 0 1/1 C
1 63.3985 28/27, 27/26 C#/Dbb
2 126.797 14/13, 15/14, 16/15, 29/27 Cx/Db
3 190.1955 10/9~9/8 D
4 253.594 15/13 D#/Ebb
5 316.9925 6/5 Dx/Eb
6 380.391 5/4 E
7 443.7895 9/7 E#/Fb
8 507.188 4/3 F
9 570.5865 7/5 F#/Gbb
10 633.985 13/9 Fx/Gb
11 697.3835 3/2 G
12 760.782 14/9 G#/Hbb
13 824.1805 8/5 Gx/Hb
14 887.579 5/3 H
15 950.9775 19/11 H#/Jbb
16 1014.376 9/5 Hx/Jb
17 1077.7745 13/7 J
18 1141.173 27/14 J#/Kb
19 1204.5715 2/1 K
20 1267.970 27/13 K#/Lbb
21 1331.3685 28/13 Kx/Lb
22 1394.767 9/4 (9/8 plus an octave) L
23 1458.1655 7/3 L#/Abb
24 1521.564 12/5 (6/5 plus an octave) Lx/Ab
25 1584.9625 5/2 A
26 1648.361 13/5 (13/10 plus an octave) A#/Bb
27 1711.7595 8/3 B
28 1775.158 14/5 (7/5 plus an octave) B#/Cbb
29 1838.5565 26/9 Bx/Cb
30 1901.955 3/1 C

30edt contains all 19edo intervals within 3/1, all temepered progressively sharper. The accumulation of the .241 cent sharpening of the unit step relative to 19edo leads to the excellent 6edt approximations of 6/5 and 5/2. Non-redundantly with simpler edts, the 41 degree ~9/2 is only .6615 cents flatter than that in 6edo.

30edt also contains all the MOS contained in 15edt, being the double of this equal division. Being even, 30edt introduces

MOS with an even number of periods per tritave such as a 6L 6s similar to Hexe Dodecatonic. This MOS has a period of 1/6 of the tritave and the generator is a single or double step. The major scale is sLsLsLsLsLsL, and the minor scale is LsLsLsLsLsLs. Being a "real" 3/2, the interval of 11 degrees generates an unfair Sigma scale of 8L 3s and the major scale is LLsLLLsLLsL. The sharp 9/7 of 7 degrees, in addition to generating a Lambda MOS will generate a 4L 9s unfair Superlambda MOS which does not border on being atonal as the 17edt rendition does.

Compositions in 30edt

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