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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-03-05 20:34:53 UTC</tt>.<br>
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| : The original revision id was <tt>543142144</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <h4>Original Wikitext content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">This scale coincidentally turns out to be 16 equal divisions of a stretched octave (1217.25 cents) and a tritave twin of the Armodue/Hornbostel flat third-tone system (6th=1065.095 cents, squared=2130.19 cents=228.235 cents, cubed=1293.33 cents, fourth power=2358.425 cents=456.47 cents).
| |
| ||~ Degree ||~ cents ||~ Armodue name ||
| |
| || 1\25 || 76.08 || 1#/2bb ||
| |
| || 2\25 || 152.16 || 1x/2b ||
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| || 3\25 || 228.235 || 2 ||
| |
| || 4\25 || 304.31 || 2#/3bb ||
| |
| || 5\25 || 380.39 || 2x/3b ||
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| || 6\25 || 456.47 || 3 ||
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| || 7\25 || 532.55 || 3#/4b ||
| |
| || 8\25 || 608.625 || 4 ||
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| || 9\25 || 684.70 || 4#/5bb ||
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| || 10\25 || 760.78 || 4x/5b ||
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| || 11\25 || 836.86 || 5 ||
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| || 12\25 || 912.94 || 5#/6bb ||
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| || 13\25 || 989.02 || 5x/6b ||
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| || 14\25 || 1065.095 || 6 ||
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| || 15\25 || 1141.17 || 6#/7bb ||
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| || 16\25 || 1217.25 || 6x/7b ||
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| || 17\25 || 1293.33 || 7 ||
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| || 18\25 || 1369.41 || 7#/8b ||
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| || 19\25 || 1445.485 || 8 ||
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| || 20\25 || 1521.56 || 8#/9bb ||
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| || 21\25 || 1597.64 || 8x/9b ||
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| || 22\25 || 1673.72 || 9 ||
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| || 23\25 || 1749.80 || 9#/1bb ||
| |
| || 24\25 || 1825.88 || 9x/1b ||
| |
| || 25\25 || 1901.955 || 1 ||</pre></div>
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| <h4>Original HTML content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>25edt</title></head><body>This scale coincidentally turns out to be 16 equal divisions of a stretched octave (1217.25 cents) and a tritave twin of the Armodue/Hornbostel flat third-tone system (6th=1065.095 cents, squared=2130.19 cents=228.235 cents, cubed=1293.33 cents, fourth power=2358.425 cents=456.47 cents).<br />
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|
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|
| | == Theory == |
| | 25edt corresponds to 15.7732…[[edo]], or 16 equal divisions of a stretched octave (1217.25{{c}}) and a tritave twin of the Armodue/Hornbostel flat third-tone system: |
| | * 6th = 1065.095{{c}} |
| | * squared = 2130.19{{c}} → 228.235{{c}} |
| | * cubed = 1293.33{{c}} |
| | * fourth power = 2358.425{{c}} → 456.47{{c}} |
|
| |
|
| <table class="wiki_table"> | | It can be used as a tuning for [[mavila]] and has an antidiatonic ([[2L 5s]]) scale which approximates [[Pelog]] tunings in Indonesian gamelan music. |
| <tr>
| |
| <th>Degree<br />
| |
| </th>
| |
| <th>cents<br />
| |
| </th>
| |
| <th>Armodue name<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1\25<br />
| |
| </td>
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| <td>76.08<br />
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| </td>
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| <td>1#/2bb<br />
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| </td>
| |
| </tr>
| |
| <tr>
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| <td>2\25<br />
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| </td>
| |
| <td>152.16<br />
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| </td>
| |
| <td>1x/2b<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>3\25<br />
| |
| </td>
| |
| <td>228.235<br />
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| </td>
| |
| <td>2<br />
| |
| </td>
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| </tr>
| |
| <tr>
| |
| <td>4\25<br />
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| </td>
| |
| <td>304.31<br />
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| </td>
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| <td>2#/3bb<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>5\25<br />
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| </td>
| |
| <td>380.39<br />
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| </td>
| |
| <td>2x/3b<br />
| |
| </td>
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| </tr>
| |
| <tr>
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| <td>6\25<br />
| |
| </td>
| |
| <td>456.47<br />
| |
| </td>
| |
| <td>3<br />
| |
| </td>
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| </tr>
| |
| <tr>
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| <td>7\25<br />
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| </td>
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| <td>532.55<br />
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| </td>
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| <td>3#/4b<br />
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| </td>
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| </tr>
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| <tr>
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| <td>8\25<br />
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| </td>
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| <td>608.625<br />
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| </td>
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| <td>4<br />
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| </td>
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| </tr>
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| <tr>
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| <td>9\25<br />
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| </td>
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| <td>684.70<br />
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| </td>
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| <td>4#/5bb<br />
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| </td>
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| </tr>
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| <tr>
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| <td>10\25<br />
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| </td>
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| <td>760.78<br />
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| </td>
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| <td>4x/5b<br />
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| </td>
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| </tr>
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| <tr>
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| <td>11\25<br />
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| </td>
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| <td>836.86<br />
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| </td>
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| <td>5<br />
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| </td>
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| </tr>
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| <tr>
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| <td>12\25<br />
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| </td>
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| <td>912.94<br />
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| </td>
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| <td>5#/6bb<br />
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| </td>
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| </tr>
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| <tr>
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| <td>13\25<br />
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| </td>
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| <td>989.02<br />
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| </td>
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| <td>5x/6b<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>14\25<br />
| |
| </td>
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| <td>1065.095<br />
| |
| </td>
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| <td>6<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>15\25<br />
| |
| </td>
| |
| <td>1141.17<br />
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| </td>
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| <td>6#/7bb<br />
| |
| </td>
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| </tr>
| |
| <tr>
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| <td>16\25<br />
| |
| </td>
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| <td>1217.25<br />
| |
| </td>
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| <td>6x/7b<br />
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| </td>
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| </tr>
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| <tr>
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| <td>17\25<br />
| |
| </td>
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| <td>1293.33<br />
| |
| </td>
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| <td>7<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>18\25<br />
| |
| </td>
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| <td>1369.41<br />
| |
| </td>
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| <td>7#/8b<br />
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| </td>
| |
| </tr>
| |
| <tr>
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| <td>19\25<br />
| |
| </td>
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| <td>1445.485<br />
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| </td>
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| <td>8<br />
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| </td>
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| </tr>
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| <tr>
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| <td>20\25<br />
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| </td>
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| <td>1521.56<br />
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| </td>
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| <td>8#/9bb<br />
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| </td>
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| </tr>
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| <tr>
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| <td>21\25<br />
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| </td>
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| <td>1597.64<br />
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| </td>
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| <td>8x/9b<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>22\25<br />
| |
| </td>
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| <td>1673.72<br />
| |
| </td>
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| <td>9<br />
| |
| </td>
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| </tr>
| |
| <tr>
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| <td>23\25<br />
| |
| </td>
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| <td>1749.80<br />
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| </td>
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| <td>9#/1bb<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>24\25<br />
| |
| </td>
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| <td>1825.88<br />
| |
| </td>
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| <td>9x/1b<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td>25\25<br />
| |
| </td>
| |
| <td>1901.955<br />
| |
| </td>
| |
| <td>1<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div>
| | === Harmonics === |
| | {{Harmonics in equal|25|3|1|intervals=integer|columns=11}} |
| | {{Harmonics in equal|25|3|1|intervals=integer|columns=11|start=12|collapsed=true|title=Approximation of harmonics in 25edt (continued)}} |
| | |
| | === Subsets and supersets === |
| | Since 25 factors into primes as 5<sup>2</sup>, 25edt contains [[5edt]] as its only nontrivial subset edt. |
| | |
| | == Intervals == |
| | {| class="wikitable center-1 right-2 right-3" |
| | |- |
| | ! # |
| | ! [[Cent]]s |
| | ! [[Hekt]]s |
| | ! Armodue name |
| | |- |
| | | 0 |
| | | 0.0 |
| | | 0.0 |
| | | 1 |
| | |- |
| | | 1 |
| | | 76.1 |
| | | 52.0 |
| | | 1#/2bb |
| | |- |
| | | 2 |
| | | 152.2 |
| | | 104.0 |
| | | 1x/2b |
| | |- |
| | | 3 |
| | | 228.2 |
| | | 156.0 |
| | | 2 |
| | |- |
| | | 4 |
| | | 304.3 |
| | | 208.0 |
| | | 2#/3bb |
| | |- |
| | | 5 |
| | | 380.4 |
| | | 260.0 |
| | | 2x/3b |
| | |- |
| | | 6 |
| | | 456.5 |
| | | 312.0 |
| | | 3 |
| | |- |
| | | 7 |
| | | 532.5 |
| | | 364.0 |
| | | 3#/4b |
| | |- |
| | | 8 |
| | | 608.6 |
| | | 416.0 |
| | | 4 |
| | |- |
| | | 9 |
| | | 684.7 |
| | | 468.0 |
| | | 4#/5bb |
| | |- |
| | | 10 |
| | | 760.8 |
| | | 520.0 |
| | | 4x/5b |
| | |- |
| | | 11 |
| | | 836.9 |
| | | 572.0 |
| | | 5 |
| | |- |
| | | 12 |
| | | 912.9 |
| | | 624.0 |
| | | 5#/6bb |
| | |- |
| | | 13 |
| | | 989.0 |
| | | 676.0 |
| | | 5x/6b |
| | |- |
| | | 14 |
| | | 1065.1 |
| | | 728.0 |
| | | 6 |
| | |- |
| | | 15 |
| | | 1141.2 |
| | | 780.0 |
| | | 6#/7bb |
| | |- |
| | | 16 |
| | | 1217.3 |
| | | 832.0 |
| | | 6x/7b |
| | |- |
| | | 17 |
| | | 1293.3 |
| | | 884.0 |
| | | 7 |
| | |- |
| | | 18 |
| | | 1369.4 |
| | | 936.0 |
| | | 7#/8b |
| | |- |
| | | 19 |
| | | 1445.5 |
| | | 988.0 |
| | | 8 |
| | |- |
| | | 20 |
| | | 1521.6 |
| | | 1040.0 |
| | | 8#/9bb |
| | |- |
| | | 21 |
| | | 1597.6 |
| | | 1092.0 |
| | | 8x/9b |
| | |- |
| | | 22 |
| | | 1673.7 |
| | | 1144.0 |
| | | 9 |
| | |- |
| | | 23 |
| | | 1749.8 |
| | | 1196.0 |
| | | 9#/1bb |
| | |- |
| | | 24 |
| | | 1825.9 |
| | | 1248.0 |
| | | 9x/1b |
| | |- |
| | | 25 |
| | | 1902.0 |
| | | 1300.0 |
| | | 1 |
| | |} |
| | |
| | == See also == |
| | * [[16edo]] – relative edo |
| | * [[41ed6]] – relative ed6 |
| | * [[57ed12]] – relative ed12 |
| | |
| | {{Todo|expand}} |
| | [[Category:Armodue]] |