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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>
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| : The original revision id was <tt>596310862</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <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. |
| === ===
| |
| ===<span style="font-size: 1.4em;">Intervals of 30edt</span>===
| |
| || 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 ||
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| || 28 || 1775.158 || [[14_5|14/5]] ([[7_5|7/5]] plus an octave) || B#/Cbb ||
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| || 29 || 1838.5565 || 26/9 || Bx/Cb ||
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| || 30 || 1901.955 || [[3_1|3/1]] || C ||
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|
| |
|
| 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**===
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| | |
| * "[[https://soundcloud.com/mason-l-green/room-full-of-steam|Room Full Of Steam]]", Mason Green. In the key of "Eb subminor".</pre></div>
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| <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"><html><head><title>30edt</title></head><body><strong>30edt</strong> (30 equal division of the tritave) is a stretched version of <a class="wiki_link" href="/19edo">19edo</a>, 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.<br />
| |
| <br />
| |
| 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.<br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><!-- ws:end:WikiTextHeadingRule:0 --> </h3>
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| <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x--Intervals of 30edt"></a><!-- ws:end:WikiTextHeadingRule:2 --><span style="font-size: 1.4em;">Intervals of 30edt</span></h3>
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| <table class="wiki_table">
| | ==='''Compositions in 30edt'''=== |
| <tr>
| |
| <td>Degrees<br />
| |
| </td>
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| <td>Cents<br />
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| </td>
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| <td>Approximate Ratios<br />
| |
| </td>
| |
| <td>Sigma scale name<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td>0<br />
| |
| </td>
| |
| <td>0<br />
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| </td>
| |
| <td><span style="color: #660000;"><a class="wiki_link" href="/1_1">1/1</a></span><br />
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| </td>
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| <td>C<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td>1<br />
| |
| </td>
| |
| <td>63.3985<br />
| |
| </td>
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| <td>28/27, 27/26<br />
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| </td>
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| <td>C#/Dbb<br />
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| </td>
| |
| </tr>
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| <tr>
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| <td>2<br />
| |
| </td>
| |
| <td>126.797<br />
| |
| </td>
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| <td><a class="wiki_link" href="/14_13">14/13</a>, <a class="wiki_link" href="/15_14">15/14</a>, <a class="wiki_link" href="/16_15">16/15</a>, 29/27<br />
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| </td>
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| <td>Cx/Db<br />
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| </td>
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| </tr>
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| <tr>
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| <td>3<br />
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| </td>
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| <td>190.1955<br />
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| </td>
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| <td>10/9~9/8<br />
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| </td>
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| <td>D<br />
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| </td>
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| </tr>
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| <tr>
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| <td>4<br />
| |
| </td>
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| <td>253.594<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/15_13">15/13</a><br />
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| </td>
| |
| <td>D#/Ebb<br />
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| </td>
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| </tr>
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| <tr>
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| <td>5<br />
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| </td>
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| <td>316.9925<br />
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| </td>
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| <td>6/5<br />
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| </td>
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| <td>Dx/Eb<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>6<br />
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| </td>
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| <td>380.391<br />
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| </td>
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| <td><span style="color: #660000;"><a class="wiki_link" href="/5_4">5/4</a></span><br />
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| </td>
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| <td>E<br />
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| </td>
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| </tr>
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| <tr>
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| <td>7<br />
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| </td>
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| <td>443.7895<br />
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| </td>
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| <td>9/7<br />
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| </td>
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| <td>E#/Fb<br />
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| </td>
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| </tr>
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| <tr>
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| <td>8<br />
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| </td>
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| <td>507.188<br />
| |
| </td>
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| <td><a class="wiki_link" href="/4_3">4/3</a><br />
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| </td>
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| <td>F<br />
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| </td>
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| </tr>
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| <tr>
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| <td>9<br />
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| </td>
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| <td>570.5865<br />
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| </td>
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| <td>7/5<br />
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| </td>
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| <td>F#/Gbb<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>10<br />
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| </td>
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| <td>633.985<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/13_9">13/9</a><br />
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| </td>
| |
| <td>Fx/Gb<br />
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| </td>
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| </tr>
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| <tr>
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| <td>11<br />
| |
| </td>
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| <td>697.3835<br />
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| </td>
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| <td>3/2<br />
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| </td>
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| <td>G<br />
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| </td>
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| </tr>
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| <tr>
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| <td>12<br />
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| </td>
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| <td>760.782<br />
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| </td>
| |
| <td><span style="color: #660000;"><a class="wiki_link" href="/14_9">14/9</a></span><br />
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| </td>
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| <td>G#/Hbb<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>13<br />
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| </td>
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| <td>824.1805<br />
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| </td>
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| <td>8/5<br />
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| </td>
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| <td>Gx/Hb<br />
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| </td>
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| </tr>
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| <tr>
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| <td>14<br />
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| </td>
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| <td>887.579<br />
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| </td>
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| <td><a class="wiki_link" href="/5_3">5/3</a><br />
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| </td>
| |
| <td>H<br />
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| </td>
| |
| </tr>
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| <tr>
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| <td>15<br />
| |
| </td>
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| <td>950.9775<br />
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| </td>
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| <td>19/11<br />
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| </td>
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| <td>H#/Jbb<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16<br />
| |
| </td>
| |
| <td>1014.376<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/9_5">9/5</a><br />
| |
| </td>
| |
| <td>Hx/Jb<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17<br />
| |
| </td>
| |
| <td>1077.7745<br />
| |
| </td>
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| <td>13/7<br />
| |
| </td>
| |
| <td>J<br />
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| </td>
| |
| </tr>
| |
| <tr>
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| <td>18<br />
| |
| </td>
| |
| <td>1141.173<br />
| |
| </td>
| |
| <td><span style="color: #660000;"><a class="wiki_link" href="/27_14">27/14</a></span><br />
| |
| </td>
| |
| <td>J#/Kb<br />
| |
| </td>
| |
| </tr>
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| <tr>
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| <td>19<br />
| |
| </td>
| |
| <td>1204.5715<br />
| |
| </td>
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| <td>2/1<br />
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| </td>
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| <td>K<br />
| |
| </td>
| |
| </tr>
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| <tr>
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| <td>20<br />
| |
| </td>
| |
| <td>1267.970<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/27_13">27/13</a><br />
| |
| </td>
| |
| <td>K#/Lbb<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td>21<br />
| |
| </td>
| |
| <td>1331.3685<br />
| |
| </td>
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| <td>28/13<br />
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| </td>
| |
| <td>Kx/Lb<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22<br />
| |
| </td>
| |
| <td>1394.767<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/9_4">9/4</a> (<a class="wiki_link" href="/9_8">9/8</a> plus an octave)<br />
| |
| </td>
| |
| <td>L<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23<br />
| |
| </td>
| |
| <td>1458.1655<br />
| |
| </td>
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| <td>7/3<br />
| |
| </td>
| |
| <td>L#/Abb<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>24<br />
| |
| </td>
| |
| <td>1521.564<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/12_5">12/5</a> (<span style="color: #660000;"><a class="wiki_link" href="/6_5">6/5</a></span> plus an octave)<br />
| |
| </td>
| |
| <td>Lx/Ab<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25<br />
| |
| </td>
| |
| <td>1584.9625<br />
| |
| </td>
| |
| <td>5/2<br />
| |
| </td>
| |
| <td>A<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>26<br />
| |
| </td>
| |
| <td>1648.361<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/13_5">13/5</a> (<a class="wiki_link" href="/13_10">13/10</a> plus an octave)<br />
| |
| </td>
| |
| <td>A#/Bb<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27<br />
| |
| </td>
| |
| <td>1711.7595<br />
| |
| </td>
| |
| <td>8/3<br />
| |
| </td>
| |
| <td>B<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>28<br />
| |
| </td>
| |
| <td>1775.158<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/14_5">14/5</a> (<a class="wiki_link" href="/7_5">7/5</a> plus an octave)<br />
| |
| </td>
| |
| <td>B#/Cbb<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>29<br />
| |
| </td>
| |
| <td>1838.5565<br />
| |
| </td>
| |
| <td>26/9<br />
| |
| </td>
| |
| <td>Bx/Cb<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>30<br />
| |
| </td>
| |
| <td>1901.955<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/3_1">3/1</a><br />
| |
| </td>
| |
| <td>C<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | <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 <a class="wiki_link" href="/19edo">19edo</a> 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.<br />
| | [[Category:listen]] |
| <br />
| |
| 30edt also contains all the MOS contained in 15edt, being the double of this equal division. Being even, 30edt introduces<br />
| |
| 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 &quot;real&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.<br />
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| <br />
| |
| <hr />
| |
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x--Compositions in 30edt"></a><!-- ws:end:WikiTextHeadingRule:4 --><strong>Compositions in 30edt</strong></h3>
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| <br />
| |
| <ul><li>&quot;<a class="wiki_link_ext" href="https://soundcloud.com/mason-l-green/room-full-of-steam" rel="nofollow">Room Full Of Steam</a>&quot;, Mason Green. In the key of &quot;Eb subminor&quot;.</li></ul></body></html></pre></div>
| |