25edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 576286773 - Original comment: link to file description (accessibility)** |
Wikispaces>JosephRuhf **Imported revision 597589954 - 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 16:08:48 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>597589954</tt>.<br> | ||
: The revision comment was: <tt> | : 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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
Line 28: | Line 28: | ||
Ratios* ||= Armodue | Ratios* ||= Armodue | ||
Notation || | Notation || | ||
|| 0 || 0 ||= 1/1 ||= 1 || | || 0 || 0 | ||
|| 1 || 48 | 0° ||= 1/1 ||= 1 || | ||
|| 1 || 48, //57.6// | |||
14°24' ||= 33/32, 39/38, 34/33 ||= 1# || | 14°24' ||= 33/32, 39/38, 34/33 ||= 1# || | ||
|| 2 || 96 | || 2 || 96, //115.2// | ||
28°48' ||= 17/16, 20/19, 18/17 ||= 2b || | 28°48' ||= 17/16, 20/19, 18/17 ||= 2b || | ||
|| 3 || 144 | || 3 || 144, //172.8// | ||
43°12' ||= 12/11, 38/35 ||= 2 || | 43°12' ||= 12/11, 38/35 ||= 2 || | ||
|| 4 || 192 | || 4 || 192, //230.4// | ||
57°36' ||= 9/8, 10/9, 19/17 ||= 2# || | 57°36' ||= 9/8, 10/9, 19/17 ||= 2# || | ||
|| 5· || 240 | || 5· || 240, 288 | ||
72° ||= 8/7 ||= 3b || | 72° ||= 8/7 ||= 3b || | ||
|| 6 || 288 | || 6 || 288, //345.6// | ||
86°24' ||= 19/16, 20/17 ||= 3 || | 86°24' ||= 19/16, 20/17 ||= 3 || | ||
|| 7 || 336 ||= 39/32, 17/14, 40/33 ||= 3# || | || 7 || 336, //403.2// | ||
|| 8· || 384 | 100°48' ||= 39/32, 17/14, 40/33 ||= 3# || | ||
|| 8· || 384, //460.8// | |||
|| 9 || 432 | 115°12' ||= 5/4 ||= 4b || | ||
|| 9 || 432, //518.4// | |||
|| 10 || 480 | 129°36' ||= 9/7, 32/25, 50/39 ||= 4 || | ||
|| 10 || 480, 576 | |||
144° ||= 33/25, 25/19 ||= 4#/5b || | 144° ||= 33/25, 25/19 ||= 4#/5b || | ||
|| 11· || 528 | || 11· || 528, //633.6// | ||
158°24' ||= 31/21, 34/25 ||= 5 || | 158°24' ||= 31/21, 34/25 ||= 5 || | ||
|| 12 || 576 | || 12 || 576, //691.2// | ||
172°48' ||= 7/5, 39/28 ||= 5# || | 172°48' ||= 7/5, 39/28 ||= 5# || | ||
|| 13 || 624 | || 13 || 624, //748.8// | ||
187°12' ||= 10/7, 56/39 ||= 6b || | 187°12' ||= 10/7, 56/39 ||= 6b || | ||
|| 14· || 672 | || 14· || 672, //806.4// | ||
201°36' ||= 42/31, 25/17 ||= 6 || | 201°36' ||= 42/31, 25/17 ||= 6 || | ||
|| 15 || 720 | || 15 || 720, 864 | ||
216° ||= 50/33, 38/25 ||= 6# || | 216° ||= 50/33, 38/25 ||= 6# || | ||
|| 16 || 768 | || 16 || 768, //921.6// | ||
230°24' ||= 14/9, 25/16, 39/25 ||= 7b || | 230°24' ||= 14/9, 25/16, 39/25 ||= 7b || | ||
|| 17· || 816 | || 17· || 816, //979.2// | ||
244°48' ||= 8/5 ||= 7 || | 244°48' ||= 8/5 ||= 7 || | ||
|| 18 || 864 | || 18 || 864, //1036.8// | ||
259°12' ||= 64/39, 28/17, 33/20 ||= 7# || | 259°12' ||= 64/39, 28/17, 33/20 ||= 7# || | ||
|| 19 || 912 | || 19 || 912, //1094.4// | ||
273°36' ||= 32/19, 17/10 ||= 8b || | 273°36' ||= 32/19, 17/10 ||= 8b || | ||
|| 20· || 960 | || 20· || 960, 1152 | ||
288° ||= 7/4 ||= 8 || | 288° ||= 7/4 ||= 8 || | ||
|| 21 || 1008 | || 21 || 1008, //1209.6// | ||
302°14' ||= 16/9, 9/5, 34/19 ||= 8# || | 302°14' ||= 16/9, 9/5, 34/19 ||= 8# || | ||
|| 22 || 1056 | || 22 || 1056, //1267.2// | ||
316°48' ||= 11/6, 35/19 ||= 9b || | 316°48' ||= 11/6, 35/19 ||= 9b || | ||
|| 23 || 1104 | || 23 || 1104, //1324.8// | ||
331°12' ||= 32/17, 17/9, 19/10 ||= 9 || | 331°12' ||= 32/17, 17/9, 19/10 ||= 9 || | ||
|| 24 || 1152 | || 24 || 1152, //1382.4// | ||
345°36' ||= 33/17, 64/33, 76/39 ||= 9#/1b || | 345°36' ||= 33/17, 64/33, 76/39 ||= 9#/1b || | ||
|| 25 || 1200 | || 25 || 1200, 1440 | ||
360° ||= 2/1 ||= 1 || | 360° ||= 2/1 ||= 1 || | ||
*based on treating 25-EDO as a 2.9.5.7.33.39.17.19 subgroup; other approaches are possible. | *based on treating 25-EDO as a 2.9.5.7.33.39.17.19 subgroup; other approaches are possible. | ||
Line 90: | Line 92: | ||
=Commas= | =Commas= | ||
25 EDO tempers out the following commas. (Note: This assumes the val < 25 40 58 70 86 93 |.) | 25 EDO tempers out the following commas. (Note: This assumes the val < [[tel/25 40 58 70 86 93|25 40 58 70 86 93]] |.) | ||
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | ||
||= 256/243 ||< | 8 -5 > ||> 90.22 ||= Limma ||= Pythagorean Minor 2nd ||= || | ||= 256/243 ||< | 8 -5 > ||> 90.22 ||= Limma ||= Pythagorean Minor 2nd ||= || | ||
||= 3125/3072 ||< | -10 -1 5 > ||> 29.61 ||= Small Diesis ||= Magic Comma ||= || | ||= 3125/3072 ||< | -10 -1 5 > ||> 29.61 ||= Small Diesis ||= Magic Comma ||= || | ||
||= 6719816/6714445 ||< | 38 -2 -15 > ||> 1.38 ||= Hemithirds Comma ||= ||= || | ||= [[tel:6719816/6714445|6719816/6714445]] ||< | 38 -2 -15 > ||> 1.38 ||= Hemithirds Comma ||= ||= || | ||
||= 16807/16384 || | -14 0 0 5 > ||> 44.13 || || || || | ||= 16807/16384 || | -14 0 0 5 > ||> 44.13 || || || || | ||
||= 49/48 ||< | -4 -1 0 2 > ||> 35.70 ||= Slendro Diesis ||= ||= || | ||= 49/48 ||< | -4 -1 0 2 > ||> 35.70 ||= Slendro Diesis ||= ||= || | ||
Line 150: | Line 152: | ||
</td> | </td> | ||
<td>0<br /> | <td>0<br /> | ||
0°<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">1/1<br /> | <td style="text-align: center;">1/1<br /> | ||
Line 159: | Line 162: | ||
<td>1<br /> | <td>1<br /> | ||
</td> | </td> | ||
<td>48<br /> | <td>48, <em>57.6</em><br /> | ||
14°24'<br /> | 14°24'<br /> | ||
</td> | </td> | ||
Line 170: | Line 173: | ||
<td>2<br /> | <td>2<br /> | ||
</td> | </td> | ||
<td>96<br /> | <td>96, <em>115.2</em><br /> | ||
28°48'<br /> | 28°48'<br /> | ||
</td> | </td> | ||
Line 181: | Line 184: | ||
<td>3<br /> | <td>3<br /> | ||
</td> | </td> | ||
<td>144<br /> | <td>144, <em>172.8</em><br /> | ||
43°12'<br /> | 43°12'<br /> | ||
</td> | </td> | ||
Line 192: | Line 195: | ||
<td>4<br /> | <td>4<br /> | ||
</td> | </td> | ||
<td>192<br /> | <td>192, <em>230.4</em><br /> | ||
57°36'<br /> | 57°36'<br /> | ||
</td> | </td> | ||
Line 203: | Line 206: | ||
<td>5·<br /> | <td>5·<br /> | ||
</td> | </td> | ||
<td>240<br /> | <td>240, 288<br /> | ||
72°<br /> | 72°<br /> | ||
</td> | </td> | ||
Line 214: | Line 217: | ||
<td>6<br /> | <td>6<br /> | ||
</td> | </td> | ||
<td>288<br /> | <td>288, <em>345.6</em><br /> | ||
86°24'<br /> | 86°24'<br /> | ||
</td> | </td> | ||
Line 225: | Line 228: | ||
<td>7<br /> | <td>7<br /> | ||
</td> | </td> | ||
<td>336<br /> | <td>336, <em>403.2</em><br /> | ||
100°48'<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">39/32, 17/14, 40/33<br /> | <td style="text-align: center;">39/32, 17/14, 40/33<br /> | ||
Line 235: | Line 239: | ||
<td>8·<br /> | <td>8·<br /> | ||
</td> | </td> | ||
<td>384<br /> | <td>384, <em>460.8</em><br /> | ||
115°12'<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">5/4<br /> | <td style="text-align: center;">5/4<br /> | ||
Line 246: | Line 250: | ||
<td>9<br /> | <td>9<br /> | ||
</td> | </td> | ||
<td>432<br /> | <td>432, <em>518.4</em><br /> | ||
129°36'<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">9/7, 32/25, 50/39<br /> | <td style="text-align: center;">9/7, 32/25, 50/39<br /> | ||
Line 257: | Line 261: | ||
<td>10<br /> | <td>10<br /> | ||
</td> | </td> | ||
<td>480<br /> | <td>480, 576<br /> | ||
144°<br /> | 144°<br /> | ||
</td> | </td> | ||
Line 268: | Line 272: | ||
<td>11·<br /> | <td>11·<br /> | ||
</td> | </td> | ||
<td>528<br /> | <td>528, <em>633.6</em><br /> | ||
158°24'<br /> | 158°24'<br /> | ||
</td> | </td> | ||
Line 279: | Line 283: | ||
<td>12<br /> | <td>12<br /> | ||
</td> | </td> | ||
<td>576<br /> | <td>576, <em>691.2</em><br /> | ||
172°48'<br /> | 172°48'<br /> | ||
</td> | </td> | ||
Line 290: | Line 294: | ||
<td>13<br /> | <td>13<br /> | ||
</td> | </td> | ||
<td>624<br /> | <td>624, <em>748.8</em><br /> | ||
187°12'<br /> | 187°12'<br /> | ||
</td> | </td> | ||
Line 301: | Line 305: | ||
<td>14·<br /> | <td>14·<br /> | ||
</td> | </td> | ||
<td>672<br /> | <td>672, <em>806.4</em><br /> | ||
201°36'<br /> | 201°36'<br /> | ||
</td> | </td> | ||
Line 312: | Line 316: | ||
<td>15<br /> | <td>15<br /> | ||
</td> | </td> | ||
<td>720<br /> | <td>720, 864<br /> | ||
216°<br /> | 216°<br /> | ||
</td> | </td> | ||
Line 323: | Line 327: | ||
<td>16<br /> | <td>16<br /> | ||
</td> | </td> | ||
<td>768<br /> | <td>768, <em>921.6</em><br /> | ||
230°24'<br /> | 230°24'<br /> | ||
</td> | </td> | ||
Line 334: | Line 338: | ||
<td>17·<br /> | <td>17·<br /> | ||
</td> | </td> | ||
<td>816<br /> | <td>816, <em>979.2</em><br /> | ||
244°48'<br /> | 244°48'<br /> | ||
</td> | </td> | ||
Line 345: | Line 349: | ||
<td>18<br /> | <td>18<br /> | ||
</td> | </td> | ||
<td>864<br /> | <td>864, <em>1036.8</em><br /> | ||
259°12'<br /> | 259°12'<br /> | ||
</td> | </td> | ||
Line 356: | Line 360: | ||
<td>19<br /> | <td>19<br /> | ||
</td> | </td> | ||
<td>912<br /> | <td>912, <em>1094.4</em><br /> | ||
273°36'<br /> | 273°36'<br /> | ||
</td> | </td> | ||
Line 367: | Line 371: | ||
<td>20·<br /> | <td>20·<br /> | ||
</td> | </td> | ||
<td>960<br /> | <td>960, 1152<br /> | ||
288°<br /> | 288°<br /> | ||
</td> | </td> | ||
Line 378: | Line 382: | ||
<td>21<br /> | <td>21<br /> | ||
</td> | </td> | ||
<td>1008<br /> | <td>1008, <em>1209.6</em><br /> | ||
302°14'<br /> | 302°14'<br /> | ||
</td> | </td> | ||
Line 389: | Line 393: | ||
<td>22<br /> | <td>22<br /> | ||
</td> | </td> | ||
<td>1056<br /> | <td>1056, <em>1267.2</em><br /> | ||
316°48'<br /> | 316°48'<br /> | ||
</td> | </td> | ||
Line 400: | Line 404: | ||
<td>23<br /> | <td>23<br /> | ||
</td> | </td> | ||
<td>1104<br /> | <td>1104, <em>1324.8</em><br /> | ||
331°12'<br /> | 331°12'<br /> | ||
</td> | </td> | ||
Line 411: | Line 415: | ||
<td>24<br /> | <td>24<br /> | ||
</td> | </td> | ||
<td>1152<br /> | <td>1152, <em>1382.4</em><br /> | ||
345°36'<br /> | 345°36'<br /> | ||
</td> | </td> | ||
Line 422: | Line 426: | ||
<td>25<br /> | <td>25<br /> | ||
</td> | </td> | ||
<td>1200<br /> | <td>1200, 1440<br /> | ||
360°<br /> | 360°<br /> | ||
</td> | </td> | ||
Line 444: | Line 448: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc4"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:11 -->Commas</h1> | <!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc4"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:11 -->Commas</h1> | ||
25 EDO tempers out the following commas. (Note: This assumes the val &lt; 25 40 58 70 86 93 |.)<br /> | 25 EDO tempers out the following commas. (Note: This assumes the val &lt; <a class="wiki_link" href="http://tel.wikispaces.com/25%2040%2058%2070%2086%2093">25 40 58 70 86 93</a> |.)<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;">6719816/6714445<br /> | <td style="text-align: center;">[[tel:6719816/6714445|6719816/6714445]]<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">| 38 -2 -15 &gt;<br /> | <td style="text-align: left;">| 38 -2 -15 &gt;<br /> |