23edo: Difference between revisions
Wikispaces>Nickname2 **Imported revision 583021901 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 597549152 - 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>2016-10-31 09:19:52 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>597549152</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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[[image:Ciclo Icositrifonía.png width="491" height="490" link="Harmony of 23edo"]] | [[image:Ciclo Icositrifonía.png width="491" height="490" link="Harmony of 23edo"]] | ||
|| <span style="color: #660000;">[[Degree]]</span> || [[Cent]]s value | || <span style="color: #660000;">[[Degree]]</span> || [[Cent]]s value coarse, fine | ||
DMS value ||= Approximate | DMS value ||= Approximate | ||
Ratios* ||= Armodue | Ratios* ||= Armodue | ||
Notation || Notes || | Notation || Notes || | ||
|| 0 || 0 ||= 1/1 ||= 1 || || | || 0 || 0 ||= 1/1 ||= 1 || || | ||
|| 1 || 52.1739 | || 1 || 52.1739, 62.6087 | ||
15°39'8" ||= 33/32, 34/33 ||= 2b || || | 15°39'8" ||= 33/32, 34/33 ||= 2b || || | ||
|| 2 || 104.3478 | || 2 || [[tel/104.3478|104.3478]], 125.2174 | ||
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 || 156.5217 | || 3 || [[tel/156.5217|156.5217]], 187.8261 | ||
47°57'23" ||= 11/10, 12/11, 35/32 ||= 2 || || | 47°57'23" ||= 11/10, 12/11, 35/32 ||= 2 || || | ||
|| 4· || 208. | || 4· || 208.69565, 250.4348 | ||
62°36'31" ||= 9/8, 44/39 ||= 3b || || | 62°36'31" ||= 9/8, 44/39 ||= 3b || || | ||
|| 5 || 260.8696 | || 5 || [[tel/260.8696|260.8696]], 313.0435 | ||
78°15'39" ||= 7/6, 15/13, 29/25 ||= 2# || || | 78°15'39" ||= 7/6, 15/13, 29/25 ||= 2# || || | ||
|| 6 || 313.0435 | || 6 || [[tel/313.0435|313.0435]], 375.6522 | ||
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· || 365.2174 | || 7· || [[tel/365.2174|365.2174]], 438.2681 | ||
109°33'55" ||= 16/13, 21/17, 26/21 ||= 4b || || | 109°33'55" ||= 16/13, 21/17, 26/21 ||= 4b || || | ||
|| 8 || 417.3913 | || 8 || [[tel/417.3913|417.3913]], 500.8696 | ||
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 || 469.5652 | || 9 || [[tel/469.5652|469.5652]], 563.4783 | ||
140°52'10" ||= 21/16, 17/13 ||= 4 || || | 140°52'10" ||= 21/16, 17/13 ||= 4 || || | ||
|| 10· || | || 10· || 578.7391. 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 | || 11 || 573.913, 688.69565 | ||
172°10'26" ||= 7/5, 32/23, 46/33 ||= 6b || || | 172°10'26" ||= 7/5, 32/23, 46/33 ||= 6b || || | ||
|| 12 || 626.087 | || 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· || 678.2609 | || 13· || [[tel/678.2609|678.2609]], 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 || 730.4348 | || 14 || [[tel/730.4348|730.4348]], 876.5217 | ||
219°7'50" ||= 32/21, 26/17 ||= 7b || || | 219°7'50" ||= 32/21, 26/17 ||= 7b || || | ||
|| 15 || 782.6087 | || 15 || [[tel/782.6087|782.6087]], 939.1304 | ||
234°46'57" ||= 11/7, 52/33 ||= 6# || || | 234°46'57" ||= 11/7, 52/33 ||= 6# || || | ||
|| 16· || 834.7826 | || 16· || [[tel/834.7826|834.7826]], 1001.7391 | ||
251°26'5" ||= 13/8, 34/21, 21/13 ||= 7 || || | 251°26'5" ||= 13/8, 34/21, 21/13 ||= 7 || || | ||
|| 17 || 886.9565 | || 17 || [[tel/886.9565|886.9565]], 1064.3478 | ||
266°5'13" ||= 5/3 ||= 8b || || | 266°5'13" ||= 5/3 ||= 8b || || | ||
|| 18 || 939.1304 | || 18 || [[tel/939.1304|939.1304]], 1126.9565 | ||
282°44'21" ||= 12/7, 26/15, 50/29 ||= 7# || || | 282°44'21" ||= 12/7, 26/15, 50/29 ||= 7# || || | ||
|| 19· || 991. | || 19· || 991.30435, 1189.5652 | ||
297°23'29" ||= 16/9, 39/22 ||= 8 || || | 297°23'29" ||= 16/9, 39/22 ||= 8 || || | ||
|| 20 || 1043.4783 | || 20 || 1043.4783, 1252.1739 | ||
313°2'37" ||= 11/6, 20/11, 64/35 ||= 9b || || | 313°2'37" ||= 11/6, 20/11, 64/35 ||= 9b || || | ||
|| 21 || 1095.6522 | || 21 || 1095.6522, 1314.7926 | ||
328°41'44" ||= 15/8, 17/9, 32/17 ||= 8# || || | 328°41'44" ||= 15/8, 17/9, 32/17 ||= 8# || || | ||
|| 22 || 1147.8261 | || 22 || 1147.8261, 1377.3913 | ||
344°40'52" ||= 33/17, 64/33 ||= 9 || || | 344°40'52" ||= 33/17, 64/33 ||= 9 || || | ||
|| 23·· || 1200 | || 23·· || 1200, 1440 | ||
360° ||= 2/1 ||= 1 || || | 360° ||= 2/1 ||= 1 || || | ||
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=Commas= | =Commas= | ||
23 EDO tempers out the following commas. (Note: This assumes the val < 23 36 53 65 80 85 |.) Also note the discussion above, where there are some commas mentioned that are not in the standard comma list (e.g., 28/27). | 23 EDO tempers out the following commas. (Note: This assumes the val < [[tel/23 36 53 65 80 85|23 36 53 65 80 85]] |.) 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 || | ||
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<td><span style="color: #660000;"><a class="wiki_link" href="/Degree">Degree</a></span><br /> | <td><span style="color: #660000;"><a class="wiki_link" href="/Degree">Degree</a></span><br /> | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/Cent">Cent</a>s value<br /> | <td><a class="wiki_link" href="/Cent">Cent</a>s value coarse, fine<br /> | ||
DMS value<br /> | DMS value<br /> | ||
</td> | </td> | ||
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<td>1<br /> | <td>1<br /> | ||
</td> | </td> | ||
<td>52.1739<br /> | <td>52.1739, 62.6087<br /> | ||
15°39'8&quot;<br /> | 15°39'8&quot;<br /> | ||
</td> | </td> | ||
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<td>2<br /> | <td>2<br /> | ||
</td> | </td> | ||
<td>104.3478<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/104.3478">104.3478</a>, 125.2174<br /> | ||
31°18'16&quot;<br /> | 31°18'16&quot;<br /> | ||
</td> | </td> | ||
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<td>3<br /> | <td>3<br /> | ||
</td> | </td> | ||
<td>156.5217<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/156.5217">156.5217</a>, 187.8261<br /> | ||
47°57'23&quot;<br /> | 47°57'23&quot;<br /> | ||
</td> | </td> | ||
Line 312: | Line 312: | ||
<td>4·<br /> | <td>4·<br /> | ||
</td> | </td> | ||
<td>208. | <td>208.69565, 250.4348<br /> | ||
62°36'31&quot;<br /> | 62°36'31&quot;<br /> | ||
</td> | </td> | ||
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<td>5<br /> | <td>5<br /> | ||
</td> | </td> | ||
<td>260.8696<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/260.8696">260.8696</a>, 313.0435<br /> | ||
78°15'39&quot;<br /> | 78°15'39&quot;<br /> | ||
</td> | </td> | ||
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<td>6<br /> | <td>6<br /> | ||
</td> | </td> | ||
<td>313.0435<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/313.0435">313.0435</a>, 375.6522<br /> | ||
93°54'47&quot;<br /> | 93°54'47&quot;<br /> | ||
</td> | </td> | ||
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<td>7·<br /> | <td>7·<br /> | ||
</td> | </td> | ||
<td>365.2174<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/365.2174">365.2174</a>, 438.2681<br /> | ||
109°33'55&quot;<br /> | 109°33'55&quot;<br /> | ||
</td> | </td> | ||
Line 364: | Line 364: | ||
<td>8<br /> | <td>8<br /> | ||
</td> | </td> | ||
<td>417.3913<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/417.3913">417.3913</a>, 500.8696<br /> | ||
125°13'3*<br /> | 125°13'3*<br /> | ||
</td> | </td> | ||
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<td>9<br /> | <td>9<br /> | ||
</td> | </td> | ||
<td>469.5652<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/469.5652">469.5652</a>, 563.4783<br /> | ||
140°52'10&quot;<br /> | 140°52'10&quot;<br /> | ||
</td> | </td> | ||
Line 390: | Line 390: | ||
<td>10·<br /> | <td>10·<br /> | ||
</td> | </td> | ||
<td> | <td>578.7391. 626.087<br /> | ||
156°31'18&quot;<br /> | 156°31'18&quot;<br /> | ||
</td> | </td> | ||
Line 403: | Line 403: | ||
<td>11<br /> | <td>11<br /> | ||
</td> | </td> | ||
<td>573.913<br /> | <td>573.913, 688.69565<br /> | ||
172°10'26&quot;<br /> | 172°10'26&quot;<br /> | ||
</td> | </td> | ||
Line 416: | Line 416: | ||
<td>12<br /> | <td>12<br /> | ||
</td> | </td> | ||
<td>626.087<br /> | <td>626.087, 751.30435<br /> | ||
187°49'34&quot;<br /> | 187°49'34&quot;<br /> | ||
</td> | </td> | ||
Line 429: | Line 429: | ||
<td>13·<br /> | <td>13·<br /> | ||
</td> | </td> | ||
<td>678.2609<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/678.2609">678.2609</a>, 813.913<br /> | ||
204°28'42&quot;<br /> | 204°28'42&quot;<br /> | ||
</td> | </td> | ||
Line 442: | Line 442: | ||
<td>14<br /> | <td>14<br /> | ||
</td> | </td> | ||
<td>730.4348<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/730.4348">730.4348</a>, 876.5217<br /> | ||
219°7'50&quot;<br /> | 219°7'50&quot;<br /> | ||
</td> | </td> | ||
Line 455: | Line 455: | ||
<td>15<br /> | <td>15<br /> | ||
</td> | </td> | ||
<td>782.6087<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/782.6087">782.6087</a>, 939.1304<br /> | ||
234°46'57&quot;<br /> | 234°46'57&quot;<br /> | ||
</td> | </td> | ||
Line 468: | Line 468: | ||
<td>16·<br /> | <td>16·<br /> | ||
</td> | </td> | ||
<td>834.7826<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/834.7826">834.7826</a>, 1001.7391<br /> | ||
251°26'5&quot;<br /> | 251°26'5&quot;<br /> | ||
</td> | </td> | ||
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<td>17<br /> | <td>17<br /> | ||
</td> | </td> | ||
<td>886.9565<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/886.9565">886.9565</a>, 1064.3478<br /> | ||
266°5'13&quot;<br /> | 266°5'13&quot;<br /> | ||
</td> | </td> | ||
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<td>18<br /> | <td>18<br /> | ||
</td> | </td> | ||
<td>939.1304<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/939.1304">939.1304</a>, 1126.9565<br /> | ||
282°44'21&quot;<br /> | 282°44'21&quot;<br /> | ||
</td> | </td> | ||
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<td>19·<br /> | <td>19·<br /> | ||
</td> | </td> | ||
<td>991. | <td>991.30435, 1189.5652<br /> | ||
297°23'29&quot;<br /> | 297°23'29&quot;<br /> | ||
</td> | </td> | ||
Line 520: | Line 520: | ||
<td>20<br /> | <td>20<br /> | ||
</td> | </td> | ||
<td>1043.4783<br /> | <td>1043.4783, 1252.1739<br /> | ||
313°2'37&quot;<br /> | 313°2'37&quot;<br /> | ||
</td> | </td> | ||
Line 533: | Line 533: | ||
<td>21<br /> | <td>21<br /> | ||
</td> | </td> | ||
<td>1095.6522<br /> | <td>1095.6522, 1314.7926<br /> | ||
328°41'44&quot;<br /> | 328°41'44&quot;<br /> | ||
</td> | </td> | ||
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<td>22<br /> | <td>22<br /> | ||
</td> | </td> | ||
<td>1147.8261<br /> | <td>1147.8261, 1377.3913<br /> | ||
344°40'52&quot;<br /> | 344°40'52&quot;<br /> | ||
</td> | </td> | ||
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<td>23··<br /> | <td>23··<br /> | ||
</td> | </td> | ||
<td>1200<br /> | <td>1200, 1440<br /> | ||
360°<br /> | 360°<br /> | ||
</td> | </td> | ||
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<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 36 53 65 80 85 |.) Also note the discussion above, where there are some commas mentioned that are not in the standard comma list (e.g., 28/27).<br /> | 23 EDO tempers out the following commas. (Note: This assumes the val &lt; <a class="wiki_link" href="http://tel.wikispaces.com/23%2036%2053%2065%2080%2085">23 36 53 65 80 85</a> |.) Also note the discussion above, where there are some commas mentioned that are not in the standard comma list (e.g., 28/27).<br /> | ||