10edo: Difference between revisions
Wikispaces>PiotrGrochowski **Imported revision 591535472 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 597475228 - 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 07:03:59 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>597475228</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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=[[media type="custom" key="10886138"]]= | =[[media type="custom" key="10886138"]]= | ||
=Intervals= | =Intervals= | ||
|| Degree || Cents | || Degree || Cents (coarse and fine) | ||
DMS || Approximate | DMS || Approximate | ||
Ratios* || Additional Ratios of 3, 5 and 9 || Name || | Ratios* || Additional Ratios of 3, 5 and 9 || Name || | ||
|| 0 || 0 | || 0 || 0, 0° || 1/1 || 256/243, 50/49, 25/24 || unison || | ||
0° || 1/1 || 256/243, 50/49, 25/24 || unison || | || 1 || 120, 144 | ||
|| 1 || 120 | |||
36° || 16/15, 15/14, 13/14 || 10/9, 13/12, 81/80 || small neutral second/large minor second || | 36° || 16/15, 15/14, 13/14 || 10/9, 13/12, 81/80 || small neutral second/large minor second || | ||
|| 2 || 240 | || 2 || 240, 288, 72° || 8/7, 15/13, 144/125 || 9/8, 7/6 || second/third || | ||
72° || 8/7, 15/13, 144/125 || 9/8, 7/6 || second/third || | || 3 || 360, 432, 108° || 16/13 || 5/4 || large neutral third || | ||
|| 3 || 360 | || 4 || 480, 576, 144° || 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth || | ||
108° || 16/13 || 5/4 || large neutral third || | || 5 || 600, 720 | ||
|| 4 || 480 | |||
144° || 64/49, 169/128 || 4/3, 9/7, 13/10 || smaller fourth || | |||
|| 5 || 600 | |||
180° || 91/64, 128/91, 169/120, 240/169 || 7/5, 10/7, 13/9, 18/13 || tritone || | 180° || 91/64, 128/91, 169/120, 240/169 || 7/5, 10/7, 13/9, 18/13 || tritone || | ||
|| 6 || 720 | || 6 || 720, 864, 216° || 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth || | ||
216° || 49/32, 256/169 || 3/2, 14/9, 20/13 || bigger fifth || | || 7 || 840, 1008, 252° || 13/8 || 8/5 || neutral sixth || | ||
|| 7 || 840 | || 8 || 960, 1152, 288° || 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh || | ||
252° || 13/8 || 8/5 || neutral sixth || | || 9 || 1080, 1296, 324° || 15/8, 28/15, 13/7 || 9/5, 24/13, 160/81 || small major 7th || | ||
|| 8 || 960 | || 10 || 1200, 1440, 360° || 2/1 || 243/128, 49/25, 48/25 || octave || | ||
288° || 7/4, 26/15, 125/72 || 16/9, 12/7 || sixth/seventh || | |||
|| 9 || 1080 | |||
324° || 15/8, 28/15, 13/7 || 9/5, 24/13, 160/81 || small major 7th || | |||
|| 10 || 1200 | |||
360° || 2/1 || 243/128, 49/25, 48/25 || octave || | |||
*based on treating 10-EDO as a 2.7.13.15 subgroup temperament. | *based on treating 10-EDO as a 2.7.13.15 subgroup temperament. | ||
adding the ratios of 3, 5 and 9 introduces greater [[error]] while giving several more harmonic identities to the 10-EDO intervals. | adding the ratios of 3, 5 and 9 introduces greater [[error]] while giving several more harmonic identities to the 10-EDO intervals. | ||
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<td>Degree<br /> | <td>Degree<br /> | ||
</td> | </td> | ||
<td>Cents<br /> | <td>Cents (coarse and fine)<br /> | ||
DMS<br /> | DMS<br /> | ||
</td> | </td> | ||
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<td>0<br /> | <td>0<br /> | ||
</td> | </td> | ||
<td>0 | <td>0, 0°<br /> | ||
0°<br /> | |||
</td> | </td> | ||
<td>1/1<br /> | <td>1/1<br /> | ||
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<td>1<br /> | <td>1<br /> | ||
</td> | </td> | ||
<td>120<br /> | <td>120, 144<br /> | ||
36°<br /> | 36°<br /> | ||
</td> | </td> | ||
| Line 173: | Line 163: | ||
<td>2<br /> | <td>2<br /> | ||
</td> | </td> | ||
<td>240 | <td>240, 288, 72°<br /> | ||
72°<br /> | |||
</td> | </td> | ||
<td>8/7, 15/13, 144/125<br /> | <td>8/7, 15/13, 144/125<br /> | ||
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<td>3<br /> | <td>3<br /> | ||
</td> | </td> | ||
<td>360 | <td>360, 432, 108°<br /> | ||
108°<br /> | |||
</td> | </td> | ||
<td>16/13<br /> | <td>16/13<br /> | ||
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<td>4<br /> | <td>4<br /> | ||
</td> | </td> | ||
<td>480 | <td>480, 576, 144°<br /> | ||
144°<br /> | |||
</td> | </td> | ||
<td>64/49, 169/128<br /> | <td>64/49, 169/128<br /> | ||
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<td>5<br /> | <td>5<br /> | ||
</td> | </td> | ||
<td>600<br /> | <td>600, 720<br /> | ||
180°<br /> | 180°<br /> | ||
</td> | </td> | ||
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<td>6<br /> | <td>6<br /> | ||
</td> | </td> | ||
<td>720 | <td>720, 864, 216°<br /> | ||
216°<br /> | |||
</td> | </td> | ||
<td>49/32, 256/169<br /> | <td>49/32, 256/169<br /> | ||
| Line 238: | Line 224: | ||
<td>7<br /> | <td>7<br /> | ||
</td> | </td> | ||
<td>840 | <td>840, 1008, 252°<br /> | ||
252°<br /> | |||
</td> | </td> | ||
<td>13/8<br /> | <td>13/8<br /> | ||
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<td>8<br /> | <td>8<br /> | ||
</td> | </td> | ||
<td>960 | <td>960, 1152, 288°<br /> | ||
288°<br /> | |||
</td> | </td> | ||
<td>7/4, 26/15, 125/72<br /> | <td>7/4, 26/15, 125/72<br /> | ||
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<td>9<br /> | <td>9<br /> | ||
</td> | </td> | ||
<td>1080 | <td>1080, 1296, 324°<br /> | ||
324°<br /> | |||
</td> | </td> | ||
<td>15/8, 28/15, 13/7<br /> | <td>15/8, 28/15, 13/7<br /> | ||
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<td>10<br /> | <td>10<br /> | ||
</td> | </td> | ||
<td>1200 | <td>1200, 1440, 360°<br /> | ||
360°<br /> | |||
</td> | </td> | ||
<td>2/1<br /> | <td>2/1<br /> | ||