62edo: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 597445174 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 601616670 - Original comment: ** |
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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:JosephRuhf|JosephRuhf]] and made on <tt>2016-10 | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-07 10:09:40 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>601616670</tt>.<br> | ||
: The revision comment was: <tt></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> | 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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62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for [[31 comma temperaments#Gallium|gallium]], [[Starling temperaments#Valentine%20temperament-Semivalentine|semivalentine]] and [[Meantone family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone|hemimeantone]] temperaments. | 62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for [[31 comma temperaments#Gallium|gallium]], [[Starling temperaments#Valentine%20temperament-Semivalentine|semivalentine]] and [[Meantone family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone|hemimeantone]] temperaments. | ||
Using the 35\62 generator, which leads to the < | Using the 35\62 generator, which leads to the <62 97 143/1 173| val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively <62 97 143/1 172| supports hornbostel. | ||
===**62-EDO Intervals**=== | ===**62-EDO Intervals**=== | ||
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|| 11 || 212.90323 || 3b || · || | || 11 || 212.90323 || 3b || · || | ||
|| 12 || 232.25806 || 2◊3 || || | || 12 || 232.25806 || 2◊3 || || | ||
|| 13 || | || 13 || 251.6129/1 || 2# || || | ||
|| 14 || 270.96774 || 3v || || | || 14 || 270.96774 || 3v || || | ||
|| 15 || 290.32258 || 3⌐ || || | || 15 || 290.32258 || 3⌐ || || | ||
|| 16 || 309.67742 || 3 || || | || 16 || 309.67742 || 3 || || | ||
|| 17 || 329.03226 || 3Ɨ || || | || 17 || 329.03226 || 3Ɨ || || | ||
|| 18 || | || 18 || 348.3871/1 || 3‡ || || | ||
|| 19 || 367.74194 || 4b || · || | || 19 || 367.74194 || 4b || · || | ||
|| 20 || 387.09677 || 3◊4 || || | || 20 || 387.09677 || 3◊4 || || | ||
| Line 67: | Line 67: | ||
|| 42 || 812.90323 || 7⌐ || || | || 42 || 812.90323 || 7⌐ || || | ||
|| 43 || 832.25806 || 7 || · || | || 43 || 832.25806 || 7 || · || | ||
|| 44 || | || 44 || 851.6129/1 || 7Ɨ || || | ||
|| 45 || 870.96774 || 7‡ || || | || 45 || 870.96774 || 7‡ || || | ||
|| 46 || 890.32258 || 8b || || | || 46 || 890.32258 || 8b || || | ||
|| 47 || 909.67742 || 7◊8 || || | || 47 || 909.67742 || 7◊8 || || | ||
|| 48 || 929.03226 || 7# || || | || 48 || 929.03226 || 7# || || | ||
|| 49 || | || 49 || 948.3871/1 || 8v || || | ||
|| 50 || 967.74194 || 8⌐ || || | || 50 || 967.74194 || 8⌐ || || | ||
|| 51 || 987.09677 || 8 || · || | || 51 || 987.09677 || 8 || · || | ||
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62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for <a class="wiki_link" href="/31%20comma%20temperaments#Gallium">gallium</a>, <a class="wiki_link" href="/Starling%20temperaments#Valentine%20temperament-Semivalentine">semivalentine</a> and <a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone">hemimeantone</a> temperaments.<br /> | 62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for <a class="wiki_link" href="/31%20comma%20temperaments#Gallium">gallium</a>, <a class="wiki_link" href="/Starling%20temperaments#Valentine%20temperament-Semivalentine">semivalentine</a> and <a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone">hemimeantone</a> temperaments.<br /> | ||
<br /> | <br /> | ||
Using the 35\62 generator, which leads to the &lt | Using the 35\62 generator, which leads to the &lt;62 97 143/1 173| val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively &lt;62 97 143/1 172| supports hornbostel.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x62 tone equal temperament--62-EDO Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 --><strong>62-EDO Intervals</strong></h3> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x62 tone equal temperament--62-EDO Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 --><strong>62-EDO Intervals</strong></h3> | ||
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<td>13<br /> | <td>13<br /> | ||
</td> | </td> | ||
<td | <td>251.6129/1<br /> | ||
</td> | </td> | ||
<td>2#<br /> | <td>2#<br /> | ||
| Line 297: | Line 297: | ||
<td>18<br /> | <td>18<br /> | ||
</td> | </td> | ||
<td | <td>348.3871/1<br /> | ||
</td> | </td> | ||
<td>3‡<br /> | <td>3‡<br /> | ||
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<td>44<br /> | <td>44<br /> | ||
</td> | </td> | ||
<td | <td>851.6129/1<br /> | ||
</td> | </td> | ||
<td>7Ɨ<br /> | <td>7Ɨ<br /> | ||
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<td>49<br /> | <td>49<br /> | ||
</td> | </td> | ||
<td | <td>948.3871/1<br /> | ||
</td> | </td> | ||
<td>8v<br /> | <td>8v<br /> | ||