20edo: Difference between revisions
Wikispaces>PiotrGrochowski **Imported revision 589259408 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 597506976 - 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>2016-10-30 18:26:31 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>597506976</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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=Properties= | =Properties= | ||
==Intervals== | ==Intervals== | ||
|| **Degree** || **Cents** | || **Degree** || **Cents coarse/fine** | ||
**DMS** ||= **Approximate** | **DMS** ||= **Approximate** | ||
**Ratios** ||= **Nearest** | **Ratios** ||= **Nearest** | ||
**Harmonic** || | **Harmonic** || | ||
|| 0 || 0 ||= 1/1 ||= 1 || | || 0 || 0 ||= 1/1 ||= 1 || | ||
|| 1 || 60 | || 1 || 60, 72 | ||
18° ||= 29/28 ||= 33 || | 18° ||= 29/28 ||= 33 || | ||
|| 2 || 120 | || 2 || 120, 144 | ||
36° ||= 14/13, 15/14 ||= 69 || | 36° ||= 14/13, 15/14 ||= 69 || | ||
|| 3 || 180 | || 3 || 180, 216 | ||
54° ||= 10/9 ||= 71 || | 54° ||= 10/9 ||= 71 || | ||
|| 4 || 240 | || 4 || 240, 288 | ||
72° ||= 8/7, 15/13 ||= 37 || | 72° ||= 8/7, 15/13 ||= 37 || | ||
|| 5 || 300 | || 5 || 300, 360 | ||
90° ||= 13/11, 19/16 ||= 19 || | 90° ||= 13/11, 19/16 ||= 19 || | ||
|| 6 || 360 | || 6 || 360, 432 | ||
108° ||= 16/13, 5/4 ||= 79 || | 108° ||= 16/13, 5/4 ||= 79 || | ||
|| 7 || 420 | || 7 || 420, 504 | ||
126° ||= [[14_11|14/11]], [[51_40|51/40]] ||= 41 || | 126° ||= [[14_11|14/11]], [[51_40|51/40]] ||= 41 || | ||
|| 8 || 480 | || 8 || 480, 576 | ||
144° ||= 25/19, 4/3 ||= 21 || | 144° ||= 25/19, 4/3 ||= 21 || | ||
|| 9 || 540 | || 9 || 540, 648 | ||
162° ||= 15/11, 11/8 ||= 11 || | 162° ||= 15/11, 11/8 ||= 11 || | ||
|| 10 || 600 | || 10 || 600, 720 | ||
180° ||= 7/5 ||= 91 || | 180° ||= 7/5 ||= 91 || | ||
|| 11 || 660 | || 11 || 660, 792 | ||
198° ||= 22/15, 16/11 ||= 47 || | 198° ||= 22/15, 16/11 ||= 47 || | ||
|| 12 || 720 | || 12 || 720, 864 | ||
216° ||= 38/25, 3/2 ||= 97 || | 216° ||= 38/25, 3/2 ||= 97 || | ||
|| 13 || 780 | || 13 || 780, 936 | ||
234° ||= 11/7, 25/16 ||= 25 || | 234° ||= 11/7, 25/16 ||= 25 || | ||
|| 14 || 840 | || 14 || 840, 1008 | ||
252° ||= 13/8, 8/5 ||= 13 || | 252° ||= 13/8, 8/5 ||= 13 || | ||
|| 15 || 900 | || 15 || 900, 1080 | ||
270° ||= 22/13, 32/19 ||= 27 || | 270° ||= 22/13, 32/19 ||= 27 || | ||
|| 16 || 960 | || 16 || 960, 1152 | ||
288° ||= 7/4, 26/15 ||= 7 || | 288° ||= 7/4, 26/15 ||= 7 || | ||
|| 17 || 1020 | || 17 || 1020, 1224 | ||
306° ||= 9/5 ||= 115 || | 306° ||= 9/5 ||= 115 || | ||
|| 18 || 1080 | || 18 || 1080, 1296 | ||
324° ||= 15/8, 13/7 ||= 15 || | 324° ||= 15/8, 13/7 ||= 15 || | ||
|| 19 || 1140 | || 19 || 1140, 1368 | ||
342° ||= 56/29 ||= 31 || | 342° ||= 56/29 ||= 31 || | ||
|| 20 || 1200 | || 20 || 1200, 1440 | ||
360° ||= 2/1 ||= 2 || | 360° ||= 2/1 ||= 2 || | ||
==Modes== | ==Modes== | ||
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==Commas== | ==Commas== | ||
20 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] < 20 32 46 56 69 74 |.) | 20 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] < [[tel:20 32 46 56 69 74|20 32 46 56 69 74]] |.) | ||
||~ 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 ||= || | ||
||= 16875/16384 ||< | -14 3 4 > ||> 51.12 ||= Negri Comma ||= Double Augmentation Diesis || || | ||= 16875/16384 ||< | -14 3 4 > ||> 51.12 ||= Negri Comma ||= Double Augmentation Diesis || || | ||
||= 9931568/9752117 ||< | -25 7 6 > ||> 31.57 ||= Ampersand's Comma ||= ||= || | ||= [[tel:9931568/9752117|9931568/9752117]] ||< | -25 7 6 > ||> 31.57 ||= Ampersand's Comma ||= ||= || | ||
||= 2048/2025 ||< | 11 -4 -2 > ||> 19.55 ||= Diaschisma ||= ||= || | ||= 2048/2025 ||< | 11 -4 -2 > ||> 19.55 ||= Diaschisma ||= ||= || | ||
||= 525/512 ||< | -9 1 2 1 > ||> 43.41 ||= Avicennma ||= Avicenna's Enharmonic Diesis || || | ||= 525/512 ||< | -9 1 2 1 > ||> 43.41 ||= Avicennma ||= Avicenna's Enharmonic Diesis || || | ||
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||= 686/675 ||< | 1 -3 -2 3 > ||> 27.99 ||= Senga ||= ||= || | ||= 686/675 ||< | 1 -3 -2 3 > ||> 27.99 ||= Senga ||= ||= || | ||
||= 64/63 ||< | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma || | ||= 64/63 ||< | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma ||= Leipziger Komma || | ||
||= 9859966/9733137 ||< | -10 7 8 -7 > ||> 22.41 ||= Blackjackisma ||= ||= || | ||= [[tel:9859966/9733137|9859966/9733137]] ||< | -10 7 8 -7 > ||> 22.41 ||= Blackjackisma ||= ||= || | ||
||= 1029/1024 ||< | -10 1 0 3 > ||> 8.43 ||= Gamelisma ||= ||= || | ||= 1029/1024 ||< | -10 1 0 3 > ||> 8.43 ||= Gamelisma ||= ||= || | ||
||= 225/224 ||< | -5 2 2 -1 > ||> 7.71 ||= Septimal Kleisma ||= Marvel Comma ||= || | ||= 225/224 ||< | -5 2 2 -1 > ||> 7.71 ||= Septimal Kleisma ||= Marvel Comma ||= || | ||
||= 16875/16807 ||< | 0 3 4 -5 > ||> 6.99 ||= Mirkwai ||= ||= || | ||= 16875/16807 ||< | 0 3 4 -5 > ||> 6.99 ||= Mirkwai ||= ||= || | ||
||= 6772805/6751042 ||< | 11 -10 -10 10 > ||> 5.57 ||= Linus ||= ||= || | ||= [[tel:6772805/6751042|6772805/6751042]] ||< | [[tel:11 -10 -10 10|11 -10 -10 10]] > ||> 5.57 ||= Linus ||= ||= || | ||
||= 2401/2400 ||< | -5 -1 -2 4 > ||> 0.72 ||= Breedsma ||= ||= || | ||= 2401/2400 ||< | -5 -1 -2 4 > ||> 0.72 ||= Breedsma ||= ||= || | ||
||= 121/120 ||< | -3 -1 -1 0 2 > ||> 14.37 ||= Biyatisma ||= ||= || | ||= 121/120 ||< | -3 -1 -1 0 2 > ||> 14.37 ||= Biyatisma ||= ||= || | ||
| Line 132: | Line 132: | ||
<td><strong>Degree</strong><br /> | <td><strong>Degree</strong><br /> | ||
</td> | </td> | ||
<td><strong>Cents</strong><br /> | <td><strong>Cents coarse/fine</strong><br /> | ||
<strong>DMS</strong><br /> | <strong>DMS</strong><br /> | ||
</td> | </td> | ||
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<td>1<br /> | <td>1<br /> | ||
</td> | </td> | ||
<td>60<br /> | <td>60, 72<br /> | ||
18°<br /> | 18°<br /> | ||
</td> | </td> | ||
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<td>2<br /> | <td>2<br /> | ||
</td> | </td> | ||
<td>120<br /> | <td>120, 144<br /> | ||
36°<br /> | 36°<br /> | ||
</td> | </td> | ||
| Line 177: | Line 177: | ||
<td>3<br /> | <td>3<br /> | ||
</td> | </td> | ||
<td>180<br /> | <td>180, 216<br /> | ||
54°<br /> | 54°<br /> | ||
</td> | </td> | ||
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<td>4<br /> | <td>4<br /> | ||
</td> | </td> | ||
<td>240<br /> | <td>240, 288<br /> | ||
72°<br /> | 72°<br /> | ||
</td> | </td> | ||
| Line 199: | Line 199: | ||
<td>5<br /> | <td>5<br /> | ||
</td> | </td> | ||
<td>300<br /> | <td>300, 360<br /> | ||
90°<br /> | 90°<br /> | ||
</td> | </td> | ||
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<td>6<br /> | <td>6<br /> | ||
</td> | </td> | ||
<td>360<br /> | <td>360, 432<br /> | ||
108°<br /> | 108°<br /> | ||
</td> | </td> | ||
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<td>7<br /> | <td>7<br /> | ||
</td> | </td> | ||
<td>420<br /> | <td>420, 504<br /> | ||
126°<br /> | 126°<br /> | ||
</td> | </td> | ||
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<td>8<br /> | <td>8<br /> | ||
</td> | </td> | ||
<td>480<br /> | <td>480, 576<br /> | ||
144°<br /> | 144°<br /> | ||
</td> | </td> | ||
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<td>9<br /> | <td>9<br /> | ||
</td> | </td> | ||
<td>540<br /> | <td>540, 648<br /> | ||
162°<br /> | 162°<br /> | ||
</td> | </td> | ||
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<td>10<br /> | <td>10<br /> | ||
</td> | </td> | ||
<td>600<br /> | <td>600, 720<br /> | ||
180°<br /> | 180°<br /> | ||
</td> | </td> | ||
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<td>11<br /> | <td>11<br /> | ||
</td> | </td> | ||
<td>660<br /> | <td>660, 792<br /> | ||
198°<br /> | 198°<br /> | ||
</td> | </td> | ||
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<td>12<br /> | <td>12<br /> | ||
</td> | </td> | ||
<td>720<br /> | <td>720, 864<br /> | ||
216°<br /> | 216°<br /> | ||
</td> | </td> | ||
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<td>13<br /> | <td>13<br /> | ||
</td> | </td> | ||
<td>780<br /> | <td>780, 936<br /> | ||
234°<br /> | 234°<br /> | ||
</td> | </td> | ||
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<td>14<br /> | <td>14<br /> | ||
</td> | </td> | ||
<td>840<br /> | <td>840, 1008<br /> | ||
252°<br /> | 252°<br /> | ||
</td> | </td> | ||
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<td>15<br /> | <td>15<br /> | ||
</td> | </td> | ||
<td>900<br /> | <td>900, 1080<br /> | ||
270°<br /> | 270°<br /> | ||
</td> | </td> | ||
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<td>16<br /> | <td>16<br /> | ||
</td> | </td> | ||
<td>960<br /> | <td>960, 1152<br /> | ||
288°<br /> | 288°<br /> | ||
</td> | </td> | ||
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<td>17<br /> | <td>17<br /> | ||
</td> | </td> | ||
<td>1020<br /> | <td>1020, 1224<br /> | ||
306°<br /> | 306°<br /> | ||
</td> | </td> | ||
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<td>18<br /> | <td>18<br /> | ||
</td> | </td> | ||
<td>1080<br /> | <td>1080, 1296<br /> | ||
324°<br /> | 324°<br /> | ||
</td> | </td> | ||
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<td>19<br /> | <td>19<br /> | ||
</td> | </td> | ||
<td>1140<br /> | <td>1140, 1368<br /> | ||
342°<br /> | 342°<br /> | ||
</td> | </td> | ||
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<td>20<br /> | <td>20<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;h2&gt; --><h2 id="toc5"><a name="Properties-Commas"></a><!-- ws:end:WikiTextHeadingRule:10 -->Commas</h2> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Properties-Commas"></a><!-- ws:end:WikiTextHeadingRule:10 -->Commas</h2> | ||
20 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="/val">val</a> &lt; 20 32 46 56 69 74 |.)<br /> | 20 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="/val">val</a> &lt; <a class="wiki_link" href="http://tel.wikispaces.com/20%2032%2046%2056%2069%2074">20 32 46 56 69 74</a> |.)<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;">9931568/9752117<br /> | <td style="text-align: center;">[[tel:9931568/9752117|9931568/9752117]]<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">| -25 7 6 &gt;<br /> | <td style="text-align: left;">| -25 7 6 &gt;<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;">9859966/9733137<br /> | <td style="text-align: center;">[[tel:9859966/9733137|9859966/9733137]]<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">| -10 7 8 -7 &gt;<br /> | <td style="text-align: left;">| -10 7 8 -7 &gt;<br /> | ||
| Line 698: | Line 698: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;">6772805/6751042<br /> | <td style="text-align: center;">[[tel:6772805/6751042|6772805/6751042]]<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">| 11 -10 -10 10 &gt;<br /> | <td style="text-align: left;">| <a class="wiki_link" href="http://tel.wikispaces.com/11%20-10%20-10%2010">11 -10 -10 10</a> &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: right;">5.57<br /> | <td style="text-align: right;">5.57<br /> | ||