23edo: Difference between revisions
Wikispaces>TallKite **Imported revision 599953430 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 601443654 - 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: | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-05 14:16:45 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>601443654</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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|| 1 || 52.1739, 62.6087 | || 1 || 52.1739, 62.6087 | ||
15°39'8" ||= 33/32, 34/33 ||= 2b || || | 15°39'8" ||= 33/32, 34/33 ||= 2b || || | ||
|| 2 || | || 2 || 104.3478/1, 125.2174/1 | ||
31°18'16" ||= 17/16, 16/15, 18/17 ||= 1# || Less than 1-cent off 17/16 || | 31°18'16" ||= 17/16, 16/15, 18/17 ||= 1# || Less than 1-cent off 17/16 || | ||
|| 3 || | || 3 || 156.5217/1, 187.8261/1 | ||
47°57'23" ||= 11/10, 12/11, 35/32 ||= 2 || || | 47°57'23" ||= 11/10, 12/11, 35/32 ||= 2 || || | ||
|| 4· || 208.69565, 250.4348 | || 4· || 208.69565, 250.4348/1 | ||
62°36'31" ||= 9/8, 44/39 ||= 3b || || | 62°36'31" ||= 9/8, 44/39 ||= 3b || || | ||
|| 5 || | || 5 || 260.8696/1, 313.0435/1 | ||
78°15'39" ||= 7/6, 15/13, 29/25 ||= 2# || || | 78°15'39" ||= 7/6, 15/13, 29/25 ||= 2# || || | ||
|| 6 || | || 6 || 313.0435/1, 375.6522/1 | ||
93°54'47" ||= 6/5 ||= 3 || Much better at approximating 6/5 than 12-EDO || | 93°54'47" ||= 6/5 ||= 3 || Much better at approximating 6/5 than 12-EDO || | ||
|| 7· || | || 7· || 365.2174/1, 438.2681/1 | ||
109°33'55" ||= 16/13, 21/17, 26/21 ||= 4b || || | 109°33'55" ||= 16/13, 21/17, 26/21 ||= 4b || || | ||
|| 8 || | || 8 || 417.3913/1, 500.8696/1 | ||
125°13'3* ||= 14/11, 33/26 ||= 3# || Practically just approximation of 14/11 || | 125°13'3* ||= 14/11, 33/26 ||= 3# || Practically just approximation of 14/11 || | ||
|| 9 || [[tel/469.5652|469.5652]], 563.4783 | || 9 || [[tel/469.5652|469.5652]], [[tel/563.4783|563.4783]] | ||
140°52'10" ||= 21/16, 17/13 ||= 4 || || | 140°52'10" ||= 21/16, 17/13 ||= 4 || || | ||
|| 10· || | || 10· || 521.7391/1. 626.087 | ||
156°31'18" ||= 23/17, 88/65, 256/189 ||= 5 || || | 156°31'18" ||= 23/17, 88/65, 256/189 ||= 5 || || | ||
|| 11 || 573.913, 688.69565 | || 11 || 573.913, 688.69565 | ||
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|| 12 || 626.087, 751.30435 | || 12 || 626.087, 751.30435 | ||
187°49'34" ||= 10/7, 23/16, 33/23 ||= 5# || || | 187°49'34" ||= 10/7, 23/16, 33/23 ||= 5# || || | ||
|| 13· || | || 13· || 678.2609/1, 813.913 | ||
204°28'42" ||= 34/23, 65/44, 189/128 ||= 6 || Great generator for Hornbostel temperament. || | 204°28'42" ||= 34/23, 65/44, 189/128 ||= 6 || Great generator for Hornbostel temperament. || | ||
|| 14 || | || 14 || 730.4348/1, 876.5217/1 | ||
219°7'50" ||= 32/21, 26/17 ||= 7b || || | 219°7'50" ||= 32/21, 26/17 ||= 7b || || | ||
|| 15 || | || 15 || 782.6087/1, 939.1304/1 | ||
234°46'57" ||= 11/7, 52/33 ||= 6# || || | 234°46'57" ||= 11/7, 52/33 ||= 6# || || | ||
|| 16· || | || 16· || 834.7826/1, 1001.7391 | ||
251°26'5" ||= 13/8, 34/21, 21/13 ||= 7 || || | 251°26'5" ||= 13/8, 34/21, 21/13 ||= 7 || || | ||
|| 17 || | || 17 || 886.9565/1, 1064.3478 | ||
266°5'13" ||= 5/3 ||= 8b || || | 266°5'13" ||= 5/3 ||= 8b || || | ||
|| 18 || | || 18 || 939.1304/1, 1126.9565 | ||
282°44'21" ||= 12/7, 26/15, 50/29 ||= 7# || || | 282°44'21" ||= 12/7, 26/15, 50/29 ||= 7# || || | ||
|| 19· || 991.30435, 1189.5652 | || 19· || 991.30435, 1189.5652 | ||
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=Commas= | =Commas= | ||
23 EDO tempers out the following commas. (Note: This assumes the val < | 23 EDO tempers out the following commas. (Note: This assumes the val < 23 36 53 65 80 85/1 |.) Also note the discussion above, where there are some commas mentioned that are not in the standard comma list (e.g., 28/27). | ||
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | ||
||= 135/128 ||< | -7 3 1 > ||> 92.18 ||= Major Chroma ||= Major Limma ||= Pelogic Comma || | ||= 135/128 ||< | -7 3 1 > ||> 92.18 ||= Major Chroma ||= Major Limma ||= Pelogic Comma || | ||
| Line 297: | Line 297: | ||
<td>2<br /> | <td>2<br /> | ||
</td> | </td> | ||
<td> | <td>104.3478/1, 125.2174/1<br /> | ||
31°18'16&quot;<br /> | 31°18'16&quot;<br /> | ||
</td> | </td> | ||
| Line 310: | Line 310: | ||
<td>3<br /> | <td>3<br /> | ||
</td> | </td> | ||
<td> | <td>156.5217/1, 187.8261/1<br /> | ||
47°57'23&quot;<br /> | 47°57'23&quot;<br /> | ||
</td> | </td> | ||
| Line 323: | Line 323: | ||
<td>4·<br /> | <td>4·<br /> | ||
</td> | </td> | ||
<td>208.69565, 250.4348<br /> | <td>208.69565, 250.4348/1<br /> | ||
62°36'31&quot;<br /> | 62°36'31&quot;<br /> | ||
</td> | </td> | ||
| Line 336: | Line 336: | ||
<td>5<br /> | <td>5<br /> | ||
</td> | </td> | ||
<td> | <td>260.8696/1, 313.0435/1<br /> | ||
78°15'39&quot;<br /> | 78°15'39&quot;<br /> | ||
</td> | </td> | ||
| Line 349: | Line 349: | ||
<td>6<br /> | <td>6<br /> | ||
</td> | </td> | ||
<td> | <td>313.0435/1, 375.6522/1<br /> | ||
93°54'47&quot;<br /> | 93°54'47&quot;<br /> | ||
</td> | </td> | ||
| Line 362: | Line 362: | ||
<td>7·<br /> | <td>7·<br /> | ||
</td> | </td> | ||
<td> | <td>365.2174/1, 438.2681/1<br /> | ||
109°33'55&quot;<br /> | 109°33'55&quot;<br /> | ||
</td> | </td> | ||
| Line 375: | Line 375: | ||
<td>8<br /> | <td>8<br /> | ||
</td> | </td> | ||
<td> | <td>417.3913/1, 500.8696/1<br /> | ||
125°13'3*<br /> | 125°13'3*<br /> | ||
</td> | </td> | ||
| Line 388: | Line 388: | ||
<td>9<br /> | <td>9<br /> | ||
</td> | </td> | ||
<td><a class="wiki_link" href="http://tel.wikispaces.com/469.5652">469.5652</a>, 563.4783<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/469.5652">469.5652</a>, <a class="wiki_link" href="http://tel.wikispaces.com/563.4783">563.4783</a><br /> | ||
140°52'10&quot;<br /> | 140°52'10&quot;<br /> | ||
</td> | </td> | ||
| Line 401: | Line 401: | ||
<td>10·<br /> | <td>10·<br /> | ||
</td> | </td> | ||
<td> | <td>521.7391/1. 626.087<br /> | ||
156°31'18&quot;<br /> | 156°31'18&quot;<br /> | ||
</td> | </td> | ||
| Line 440: | Line 440: | ||
<td>13·<br /> | <td>13·<br /> | ||
</td> | </td> | ||
<td | <td>678.2609/1, 813.913<br /> | ||
204°28'42&quot;<br /> | 204°28'42&quot;<br /> | ||
</td> | </td> | ||
| Line 453: | Line 453: | ||
<td>14<br /> | <td>14<br /> | ||
</td> | </td> | ||
<td> | <td>730.4348/1, 876.5217/1<br /> | ||
219°7'50&quot;<br /> | 219°7'50&quot;<br /> | ||
</td> | </td> | ||
| Line 466: | Line 466: | ||
<td>15<br /> | <td>15<br /> | ||
</td> | </td> | ||
<td> | <td>782.6087/1, 939.1304/1<br /> | ||
234°46'57&quot;<br /> | 234°46'57&quot;<br /> | ||
</td> | </td> | ||
| Line 479: | Line 479: | ||
<td>16·<br /> | <td>16·<br /> | ||
</td> | </td> | ||
<td | <td>834.7826/1, 1001.7391<br /> | ||
251°26'5&quot;<br /> | 251°26'5&quot;<br /> | ||
</td> | </td> | ||
| Line 492: | Line 492: | ||
<td>17<br /> | <td>17<br /> | ||
</td> | </td> | ||
<td | <td>886.9565/1, 1064.3478<br /> | ||
266°5'13&quot;<br /> | 266°5'13&quot;<br /> | ||
</td> | </td> | ||
| Line 505: | Line 505: | ||
<td>18<br /> | <td>18<br /> | ||
</td> | </td> | ||
<td | <td>939.1304/1, 1126.9565<br /> | ||
282°44'21&quot;<br /> | 282°44'21&quot;<br /> | ||
</td> | </td> | ||
| Line 649: | Line 649: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc4"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:10 -->Commas</h1> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc4"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:10 -->Commas</h1> | ||
23 EDO tempers out the following commas. (Note: This assumes the val &lt | 23 EDO tempers out the following commas. (Note: This assumes the val &lt; 23 36 53 65 80 85/1 |.) Also note the discussion above, where there are some commas mentioned that are not in the standard comma list (e.g., 28/27).<br /> | ||