30edo
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author jdfreivald and made on 2011-05-31 22:36:59 UTC.
- The original revision id was 233352062.
- The revision comment was: Added comma list.
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Original Wikitext content:
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. Below is a plot of the Z function around 30: [[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 || || ||
Original HTML content:
<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 />
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 />
<br />
Below is a plot of the Z function around 30:<br />
<br />
<!-- ws:start:WikiTextLocalImageRule:326:<img src="/file/view/plot30.png/220060356/plot30.png" alt="" title="" /> --><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:<h1> --><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 < 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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><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 ><br />
</td>
<td>0.57<br />
</td>
<td>Lehmerisma<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
</table>
</body></html>