30edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 220489138 - Original comment: ** |
Wikispaces>jdfreivald **Imported revision 233352062 - Original comment: Added comma list.** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 22:36:59 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>233352062</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>Added comma list.</tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<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> | <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">The //30 equal division// divides the octave into 30 equal steps of precisely 40 cents each. Its [[patent val]] is a doubled version of the patent val for [[15edo]] through the 11-limit, so 30 can be viewed as a [[contorted]] version of 15. However, 5\30 is 200 cents, which is a good (and familiar) approximation for 9/8, and hence 30 can be viewed inconsistently, as having a 9' at 95\30 as well as a 9 at 96\30. | <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">The //30 equal division// divides the octave into 30 equal steps of precisely 40 cents each. Its [[patent val]] is a doubled version of the patent val for [[15edo]] through the 11-limit, so 30 can be viewed as a [[contorted]] version of 15. However, 5\30 is 200 cents, which is a good (and familiar) approximation for 9/8, and hence 30 can be viewed inconsistently, as having a 9' at 95\30 as well as a 9 at 96\30. | ||
Instead of the 18\30 fifth of 720 cents, 30 also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30 is used for pelogic, 5\30 can again be used inconsistently as a 9/8. | Instead of the 18\30 fifth of 720 cents, 30 also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30 is used for pelogic, 5\30 can again be used inconsistently as a 9/8. | ||
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Below is a plot of the Z function around 30: | Below is a plot of the Z function around 30: | ||
[[image:plot30.png]]</pre></div> | [[image:plot30.png]] | ||
=Commas= | |||
30 EDO tempers out the following commas. (Note: This assumes the val < 30 48 70 84 104 111 |.) | |||
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | |||
|| 256/243 || | 8 -5 > || 90.22 || Limma || Pythagorean Minor 2nd || || | |||
|| 250/243 || | 1 -5 3 > || 49.17 || Maximal Diesis || Porcupine Comma || || | |||
|| 128/125 || | 7 0 -3 > || 41.06 || Diesis || Augmented Comma || || | |||
|| 15625/15552 || | -6 -5 6 > || 8.11 || Kleisma || Semicomma Majeur || || | |||
|| 1029/1000 || | -3 1 -3 3 > || 49.49 || Keega || || || | |||
|| 49/48 || | -4 -1 0 2 > || 35.70 || Slendro Diesis || || || | |||
|| 64/63 || | 6 -2 0 -1 > || 27.26 || Septimal Comma || Archytas' Comma || Leipziger Komma || | |||
|| 64827/64000 || | -9 3 -3 4 > || 22.23 || Squalentine || || || | |||
|| 875/864 || | -5 -3 3 1 > || 21.90 || Keema || || || | |||
|| 126/125 || | 1 2 -3 1 > || 13.79 || Septimal Semicomma || Starling Comma || || | |||
|| 4000/3969 || | 5 -4 3 -2 > || 13.47 || Octagar || || || | |||
|| 1029/1024 || | -10 1 0 3 > || 8.43 || Gamelisma || || || | |||
|| 6144/6125 || | 11 1 -3 -2 > || 5.36 || Porwell || || || | |||
|| 250047/250000 || | -4 6 -6 3 > || 0.33 || Landscape Comma || || || | |||
|| 100/99 || | 2 -2 2 0 -1 > || 17.40 || Ptolemisma || || || | |||
|| 121/120 || | -3 -1 -1 0 2 > || 14.37 || Biyatisma || || || | |||
|| 176/175 || | 4 0 -2 -1 1 > || 9.86 || Valinorsma || || || | |||
|| 65536/65219 || | 16 0 0 -2 -3 > || 8.39 || Orgonisma || || || | |||
|| 385/384 || | -7 -1 1 1 1 > || 4.50 || Keenanisma || || || | |||
|| 441/440 || | -3 2 -1 2 -1 > || 3.93 || Werckisma || || || | |||
|| 4000/3993 || | 5 -1 3 0 -3 > || 3.03 || Wizardharry || || || | |||
|| 3025/3024 || | -4 -3 2 -1 2 > || 0.57 || Lehmerisma || || ||</pre></div> | |||
<h4>Original HTML content:</h4> | <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>30edo</title></head><body>The <em>30 equal division</em> divides the octave into 30 equal steps of precisely 40 cents each. Its <a class="wiki_link" href="/patent%20val">patent val</a> is a doubled version of the patent val for <a class="wiki_link" href="/15edo">15edo</a> through the 11-limit, so 30 can be viewed as a <a class="wiki_link" href="/contorted">contorted</a> version of 15. However, 5\30 is 200 cents, which is a good (and familiar) approximation for 9/8, and hence 30 can be viewed inconsistently, as having a 9' at 95\30 as well as a 9 at 96\30. <br /> | <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>30edo</title></head><body>The <em>30 equal division</em> divides the octave into 30 equal steps of precisely 40 cents each. Its <a class="wiki_link" href="/patent%20val">patent val</a> is a doubled version of the patent val for <a class="wiki_link" href="/15edo">15edo</a> through the 11-limit, so 30 can be viewed as a <a class="wiki_link" href="/contorted">contorted</a> version of 15. However, 5\30 is 200 cents, which is a good (and familiar) approximation for 9/8, and hence 30 can be viewed inconsistently, as having a 9' at 95\30 as well as a 9 at 96\30.<br /> | ||
<br /> | <br /> | ||
Instead of the 18\30 fifth of 720 cents, 30 also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30 is used for pelogic, 5\30 can again be used inconsistently as a 9/8.<br /> | Instead of the 18\30 fifth of 720 cents, 30 also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30 is used for pelogic, 5\30 can again be used inconsistently as a 9/8.<br /> | ||
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Below is a plot of the Z function around 30:<br /> | Below is a plot of the Z function around 30:<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:326:&lt;img src=&quot;/file/view/plot30.png/220060356/plot30.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/plot30.png/220060356/plot30.png" alt="plot30.png" title="plot30.png" /><!-- ws:end:WikiTextLocalImageRule:326 --><br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:0 -->Commas</h1> | |||
30 EDO tempers out the following commas. (Note: This assumes the val &lt; 30 48 70 84 104 111 |.)<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>Comma<br /> | |||
</th> | |||
<th>Monzo<br /> | |||
</th> | |||
<th>Value (Cents)<br /> | |||
</th> | |||
<th>Name 1<br /> | |||
</th> | |||
<th>Name 2<br /> | |||
</th> | |||
<th>Name 3<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>256/243<br /> | |||
</td> | |||
<td>| 8 -5 &gt;<br /> | |||
</td> | |||
<td>90.22<br /> | |||
</td> | |||
<td>Limma<br /> | |||
</td> | |||
<td>Pythagorean Minor 2nd<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>250/243<br /> | |||
</td> | |||
<td>| 1 -5 3 &gt;<br /> | |||
</td> | |||
<td>49.17<br /> | |||
</td> | |||
<td>Maximal Diesis<br /> | |||
</td> | |||
<td>Porcupine Comma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>128/125<br /> | |||
</td> | |||
<td>| 7 0 -3 &gt;<br /> | |||
</td> | |||
<td>41.06<br /> | |||
</td> | |||
<td>Diesis<br /> | |||
</td> | |||
<td>Augmented Comma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>15625/15552<br /> | |||
</td> | |||
<td>| -6 -5 6 &gt;<br /> | |||
</td> | |||
<td>8.11<br /> | |||
</td> | |||
<td>Kleisma<br /> | |||
</td> | |||
<td>Semicomma Majeur<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1029/1000<br /> | |||
</td> | |||
<td>| -3 1 -3 3 &gt;<br /> | |||
</td> | |||
<td>49.49<br /> | |||
</td> | |||
<td>Keega<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>49/48<br /> | |||
</td> | |||
<td>| -4 -1 0 2 &gt;<br /> | |||
</td> | |||
<td>35.70<br /> | |||
</td> | |||
<td>Slendro Diesis<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>64/63<br /> | |||
</td> | |||
<td>| 6 -2 0 -1 &gt;<br /> | |||
</td> | |||
<td>27.26<br /> | |||
</td> | |||
<td>Septimal Comma<br /> | |||
</td> | |||
<td>Archytas' Comma<br /> | |||
</td> | |||
<td>Leipziger Komma<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>64827/64000<br /> | |||
</td> | |||
<td>| -9 3 -3 4 &gt;<br /> | |||
</td> | |||
<td>22.23<br /> | |||
</td> | |||
<td>Squalentine<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>875/864<br /> | |||
</td> | |||
<td>| -5 -3 3 1 &gt;<br /> | |||
</td> | |||
<td>21.90<br /> | |||
</td> | |||
<td>Keema<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>126/125<br /> | |||
</td> | |||
<td>| 1 2 -3 1 &gt;<br /> | |||
</td> | |||
<td>13.79<br /> | |||
</td> | |||
<td>Septimal Semicomma<br /> | |||
</td> | |||
<td>Starling Comma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4000/3969<br /> | |||
</td> | |||
<td>| 5 -4 3 -2 &gt;<br /> | |||
</td> | |||
<td>13.47<br /> | |||
</td> | |||
<td>Octagar<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1029/1024<br /> | |||
</td> | |||
<td>| -10 1 0 3 &gt;<br /> | |||
</td> | |||
<td>8.43<br /> | |||
</td> | |||
<td>Gamelisma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6144/6125<br /> | |||
</td> | |||
<td>| 11 1 -3 -2 &gt;<br /> | |||
</td> | |||
<td>5.36<br /> | |||
</td> | |||
<td>Porwell<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>250047/250000<br /> | |||
</td> | |||
<td>| -4 6 -6 3 &gt;<br /> | |||
</td> | |||
<td>0.33<br /> | |||
</td> | |||
<td>Landscape Comma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>100/99<br /> | |||
</td> | |||
<td>| 2 -2 2 0 -1 &gt;<br /> | |||
</td> | |||
<td>17.40<br /> | |||
</td> | |||
<td>Ptolemisma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>121/120<br /> | |||
</td> | |||
<td>| -3 -1 -1 0 2 &gt;<br /> | |||
</td> | |||
<td>14.37<br /> | |||
</td> | |||
<td>Biyatisma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>176/175<br /> | |||
</td> | |||
<td>| 4 0 -2 -1 1 &gt;<br /> | |||
</td> | |||
<td>9.86<br /> | |||
</td> | |||
<td>Valinorsma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>65536/65219<br /> | |||
</td> | |||
<td>| 16 0 0 -2 -3 &gt;<br /> | |||
</td> | |||
<td>8.39<br /> | |||
</td> | |||
<td>Orgonisma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>385/384<br /> | |||
</td> | |||
<td>| -7 -1 1 1 1 &gt;<br /> | |||
</td> | |||
<td>4.50<br /> | |||
</td> | |||
<td>Keenanisma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>441/440<br /> | |||
</td> | |||
<td>| -3 2 -1 2 -1 &gt;<br /> | |||
</td> | |||
<td>3.93<br /> | |||
</td> | |||
<td>Werckisma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4000/3993<br /> | |||
</td> | |||
<td>| 5 -1 3 0 -3 &gt;<br /> | |||
</td> | |||
<td>3.03<br /> | |||
</td> | |||
<td>Wizardharry<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3025/3024<br /> | |||
</td> | |||
<td>| -4 -3 2 -1 2 &gt;<br /> | |||
</td> | |||
<td>0.57<br /> | |||
</td> | |||
<td>Lehmerisma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
</table> | |||
</body></html></pre></div> | |||