23edo: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 601443654 - Original comment: ** |
Wikispaces>TallKite **Imported revision 602739272 - 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:TallKite|TallKite]] and made on <tt>2016-12-22 04:54:55 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>602739272</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 | ||= <span style="color: #660000;">[[Degree]]</span> ||= [[Cent]]s ||= Approximate | ||
Ratios* ||= Armodue | Ratios* ||= Armodue | ||
Notation || Notes || | Notation || Notes || | ||
|| 0 || 0 ||= 1/1 ||= 1 || || | ||= 0 ||= 0 ||= 1/1 ||= 1 || || | ||
|| 1 || 52. | ||= 1 ||= 52.174 ||= 33/32, 34/33 ||= 2b || || | ||
||= 2 ||= 104.348 ||= 17/16, 16/15, 18/17 ||= 1# || Less than 1-cent off 17/16 || | |||
|| 2 || 104. | ||= 3 ||= 156.522 ||= 11/10, 12/11, 35/32 ||= 2 || || | ||
||= 4· ||= 208.696 ||= 9/8, 44/39 ||= 3b || || | |||
|| 3 || 156. | ||= 5 ||= 260.870 ||= 7/6, 15/13, 29/25 ||= 2# || || | ||
||= 6 ||= 313.043 ||= 6/5 ||= 3 || Much better at approximating 6/5 than 12-EDO || | |||
|| 4· || 208. | ||= 7· ||= 365.217 ||= 16/13, 21/17, 26/21 ||= 4b || || | ||
||= 8 ||= 417.391 ||= 14/11, 33/26 ||= 3# || Practically just approximation of 14/11 || | |||
|| 5 || 260. | ||= 9 ||= 469.565 ||= 21/16, 17/13 ||= 4 || || | ||
||= 10· ||= 521.739 ||= 23/17, 88/65, 256/189 ||= 5 || || | |||
|| 6 || 313. | ||= 11 ||= 573.913 ||= 7/5, 32/23, 46/33 ||= 6b || || | ||
||= 12 ||= 626.087 ||= 10/7, 23/16, 33/23 ||= 5# || || | |||
|| 7· || 365. | ||= 13· ||= 678.261 ||= 34/23, 65/44, 189/128 ||= 6 || Great generator for Hornbostel temperament. || | ||
||= 14 ||= 730.435 ||= 32/21, 26/17 ||= 7b || || | |||
|| 8 || 417. | ||= 15 ||= 782.609 ||= 11/7, 52/33 ||= 6# || || | ||
||= 16· ||= 834.783 ||= 13/8, 34/21, 21/13 ||= 7 || || | |||
|| 9 || | ||= 17 ||= 886.957 ||= 5/3 ||= 8b || || | ||
||= 18 ||= 939.130 ||= 12/7, 26/15, 50/29 ||= 7# || || | |||
|| 10· || 521. | ||= 19· ||= 991.304 ||= 16/9, 39/22 ||= 8 || || | ||
||= 20 ||= 1043.478 ||= 11/6, 20/11, 64/35 ||= 9b || || | |||
|| 11 || 573.913 | ||= 21 ||= 1095.652 ||= 15/8, 17/9, 32/17 ||= 8# || || | ||
||= 22 ||= 1147.826 ||= 33/17, 64/33 ||= 9 || || | |||
|| 12 || 626.087 | ||= 23·· ||= 1200 ||= 2/1 ||= 1 || || | ||
|| 13· || 678. | |||
|| 14 || 730. | |||
|| 15 || 782. | |||
|| 16· || 834. | |||
|| 17 || 886. | |||
|| 18 || 939. | |||
|| 19· || 991. | |||
|| 20 || 1043. | |||
|| 21 || 1095. | |||
|| 22 || 1147. | |||
|| 23·· || 1200 | |||
*based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible. | *based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible. | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td><span style="color: #660000;"><a class="wiki_link" href="/Degree">Degree</a></span><br /> | <td style="text-align: center;"><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 | <td style="text-align: center;"><a class="wiki_link" href="/Cent">Cent</a>s<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Approximate<br /> | <td style="text-align: center;">Approximate<br /> | ||
Line 270: | Line 245: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>0<br /> | <td style="text-align: center;">0<br /> | ||
</td> | </td> | ||
<td>0<br /> | <td style="text-align: center;">0<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1/1<br /> | <td style="text-align: center;">1/1<br /> | ||
Line 282: | Line 257: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>1<br /> | <td style="text-align: center;">1<br /> | ||
</td> | </td> | ||
<td>52. | <td style="text-align: center;">52.174<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">33/32, 34/33<br /> | <td style="text-align: center;">33/32, 34/33<br /> | ||
Line 295: | Line 269: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>2<br /> | <td style="text-align: center;">2<br /> | ||
</td> | </td> | ||
<td>104. | <td style="text-align: center;">104.348<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">17/16, 16/15, 18/17<br /> | <td style="text-align: center;">17/16, 16/15, 18/17<br /> | ||
Line 308: | Line 281: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>3<br /> | <td style="text-align: center;">3<br /> | ||
</td> | </td> | ||
<td>156. | <td style="text-align: center;">156.522<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">11/10, 12/11, 35/32<br /> | <td style="text-align: center;">11/10, 12/11, 35/32<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>4·<br /> | <td style="text-align: center;">4·<br /> | ||
</td> | </td> | ||
<td>208. | <td style="text-align: center;">208.696<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">9/8, 44/39<br /> | <td style="text-align: center;">9/8, 44/39<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>5<br /> | <td style="text-align: center;">5<br /> | ||
</td> | </td> | ||
<td>260. | <td style="text-align: center;">260.870<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">7/6, 15/13, 29/25<br /> | <td style="text-align: center;">7/6, 15/13, 29/25<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>6<br /> | <td style="text-align: center;">6<br /> | ||
</td> | </td> | ||
<td>313. | <td style="text-align: center;">313.043<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">6/5<br /> | <td style="text-align: center;">6/5<br /> | ||
Line 360: | Line 329: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>7·<br /> | <td style="text-align: center;">7·<br /> | ||
</td> | </td> | ||
<td>365. | <td style="text-align: center;">365.217<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">16/13, 21/17, 26/21<br /> | <td style="text-align: center;">16/13, 21/17, 26/21<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>8<br /> | <td style="text-align: center;">8<br /> | ||
</td> | </td> | ||
<td>417. | <td style="text-align: center;">417.391<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">14/11, 33/26<br /> | <td style="text-align: center;">14/11, 33/26<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>9<br /> | <td style="text-align: center;">9<br /> | ||
</td> | </td> | ||
<td | <td style="text-align: center;">469.565<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">21/16, 17/13<br /> | <td style="text-align: center;">21/16, 17/13<br /> | ||
Line 399: | Line 365: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>10·<br /> | <td style="text-align: center;">10·<br /> | ||
</td> | </td> | ||
<td>521. | <td style="text-align: center;">521.739<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">23/17, 88/65, 256/189<br /> | <td style="text-align: center;">23/17, 88/65, 256/189<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>11<br /> | <td style="text-align: center;">11<br /> | ||
</td> | </td> | ||
<td>573.913 | <td style="text-align: center;">573.913<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">7/5, 32/23, 46/33<br /> | <td style="text-align: center;">7/5, 32/23, 46/33<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>12<br /> | <td style="text-align: center;">12<br /> | ||
</td> | </td> | ||
<td>626.087 | <td style="text-align: center;">626.087<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">10/7, 23/16, 33/23<br /> | <td style="text-align: center;">10/7, 23/16, 33/23<br /> | ||
Line 438: | Line 401: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>13·<br /> | <td style="text-align: center;">13·<br /> | ||
</td> | </td> | ||
<td>678. | <td style="text-align: center;">678.261<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">34/23, 65/44, 189/128<br /> | <td style="text-align: center;">34/23, 65/44, 189/128<br /> | ||
Line 451: | Line 413: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>14<br /> | <td style="text-align: center;">14<br /> | ||
</td> | </td> | ||
<td>730. | <td style="text-align: center;">730.435<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">32/21, 26/17<br /> | <td style="text-align: center;">32/21, 26/17<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>15<br /> | <td style="text-align: center;">15<br /> | ||
</td> | </td> | ||
<td>782. | <td style="text-align: center;">782.609<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">11/7, 52/33<br /> | <td style="text-align: center;">11/7, 52/33<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>16·<br /> | <td style="text-align: center;">16·<br /> | ||
</td> | </td> | ||
<td>834. | <td style="text-align: center;">834.783<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">13/8, 34/21, 21/13<br /> | <td style="text-align: center;">13/8, 34/21, 21/13<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>17<br /> | <td style="text-align: center;">17<br /> | ||
</td> | </td> | ||
<td>886. | <td style="text-align: center;">886.957<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">5/3<br /> | <td style="text-align: center;">5/3<br /> | ||
Line 503: | Line 461: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>18<br /> | <td style="text-align: center;">18<br /> | ||
</td> | </td> | ||
<td>939. | <td style="text-align: center;">939.130<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">12/7, 26/15, 50/29<br /> | <td style="text-align: center;">12/7, 26/15, 50/29<br /> | ||
Line 516: | Line 473: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>19·<br /> | <td style="text-align: center;">19·<br /> | ||
</td> | </td> | ||
<td>991. | <td style="text-align: center;">991.304<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">16/9, 39/22<br /> | <td style="text-align: center;">16/9, 39/22<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>20<br /> | <td style="text-align: center;">20<br /> | ||
</td> | </td> | ||
<td>1043. | <td style="text-align: center;">1043.478<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">11/6, 20/11, 64/35<br /> | <td style="text-align: center;">11/6, 20/11, 64/35<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>21<br /> | <td style="text-align: center;">21<br /> | ||
</td> | </td> | ||
<td>1095. | <td style="text-align: center;">1095.652<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">15/8, 17/9, 32/17<br /> | <td style="text-align: center;">15/8, 17/9, 32/17<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>22<br /> | <td style="text-align: center;">22<br /> | ||
</td> | </td> | ||
<td>1147. | <td style="text-align: center;">1147.826<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">33/17, 64/33<br /> | <td style="text-align: center;">33/17, 64/33<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td>23··<br /> | <td style="text-align: center;">23··<br /> | ||
</td> | </td> | ||
<td>1200 | <td style="text-align: center;">1200<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">2/1<br /> | <td style="text-align: center;">2/1<br /> |