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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:xenwolf|xenwolf]] and made on <tt>2016-12-29 13:27:39 UTC</tt>.<br>
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| : The original revision id was <tt>602896474</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">**102edo** is the [[equal division of the octave]] into 102 steps of size 11.765 [[cent]]s each. In the [[5-limit]] it [[tempering out|tempers out]] the same [[comma]]s (2048/2025, 15625/15552, 20000/19683) as [[34edo]]. In the [[7-limit]] it tempers out 686/675 and 1029/1024; in the [[11-limit]] 385/384, 441/440 and 4000/3993; in the [[13-limit]] 91/90 and 169/168; in the [[17-limit]] 136/135 and 154/153; and in the [[19-limit]] 133/132 and 190/189. It is the [[optimal patent val]] for 13-limit [[Diaschismic family#Echidnic|echidnic temperament]], and the rank five temperament tempering out 91/90.
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| ===13-limit Echidnic===
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| || 2 || 23.529 ||
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| || 4 || 47.059 ||
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| || 7 || 82.353 ||
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| || 9 || 105.882 ||
| |
| || 11 || 129.412 ||
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| || 13 || 152.941 ||
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| || 16 || 188.235 ||
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| || 18 || 211.765 ||
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| || 20 || 235.294 ||
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| || 22 || 258.824 ||
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| || 24 || 282.353 ||
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| || 27 || 317.647 ||
| |
| || 29 || 341.176 ||
| |
| || 31 || 364.706 ||
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| || 33 || 388.235 ||
| |
| || 35 || 411.765 ||
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| || 38 || 447.059 ||
| |
| || 40 || 470.588 ||
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| || 42 || 494.117 ||
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| || 44 || 517.647 ||
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| || 47 || 552.941 ||
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| || 49 || 576.471 ||</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>102edo</title></head><body><strong>102edo</strong> is the <a class="wiki_link" href="/equal%20division%20of%20the%20octave">equal division of the octave</a> into 102 steps of size 11.765 <a class="wiki_link" href="/cent">cent</a>s each. In the <a class="wiki_link" href="/5-limit">5-limit</a> it <a class="wiki_link" href="/tempering%20out">tempers out</a> the same <a class="wiki_link" href="/comma">comma</a>s (2048/2025, 15625/15552, 20000/19683) as <a class="wiki_link" href="/34edo">34edo</a>. In the <a class="wiki_link" href="/7-limit">7-limit</a> it tempers out 686/675 and 1029/1024; in the <a class="wiki_link" href="/11-limit">11-limit</a> 385/384, 441/440 and 4000/3993; in the <a class="wiki_link" href="/13-limit">13-limit</a> 91/90 and 169/168; in the <a class="wiki_link" href="/17-limit">17-limit</a> 136/135 and 154/153; and in the <a class="wiki_link" href="/19-limit">19-limit</a> 133/132 and 190/189. It is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for 13-limit <a class="wiki_link" href="/Diaschismic%20family#Echidnic">echidnic temperament</a>, and the rank five temperament tempering out 91/90.<br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--13-limit Echidnic"></a><!-- ws:end:WikiTextHeadingRule:0 -->13-limit Echidnic</h3>
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| <table class="wiki_table">
| | == Theory == |
| <tr>
| | 102edo is [[enfactoring|enfactored]] in the [[5-limit]], where it [[tempering out|tempers out]] the same [[comma]]s ([[2048/2025]], [[15625/15552]], [[20000/19683]]) as [[34edo]]. In the [[7-limit]] it tempers out [[686/675]] and [[1029/1024]]; in the [[11-limit]] [[385/384]], [[441/440]] and [[4000/3993]]; in the [[13-limit]] [[91/90]] and [[169/168]]; in the [[17-limit]] [[136/135]] and [[154/153]]; and in the [[19-limit]] [[133/132]] and [[190/189]]. It is the [[optimal patent val]] for 13-limit [[Diaschismic family #Echidnic|echidnic]] temperament, and the rank-5 temperament tempering out 91/90. |
| <td>2<br />
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| </td>
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| <td>23.529<br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4<br />
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| </td>
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| <td>47.059<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7<br />
| |
| </td>
| |
| <td>82.353<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9<br />
| |
| </td>
| |
| <td>105.882<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11<br />
| |
| </td>
| |
| <td>129.412<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13<br />
| |
| </td>
| |
| <td>152.941<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16<br />
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| </td>
| |
| <td>188.235<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18<br />
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| </td>
| |
| <td>211.765<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20<br />
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| </td>
| |
| <td>235.294<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22<br />
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| </td>
| |
| <td>258.824<br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>24<br />
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| </td>
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| <td>282.353<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>27<br />
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| </td>
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| <td>317.647<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>29<br />
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| </td>
| |
| <td>341.176<br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>31<br />
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| </td>
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| <td>364.706<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33<br />
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| </td>
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| <td>388.235<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>35<br />
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| </td>
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| <td>411.765<br />
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| </td>
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| </tr>
| |
| <tr>
| |
| <td>38<br />
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| </td>
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| <td>447.059<br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>40<br />
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| </td>
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| <td>470.588<br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>42<br />
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| </td>
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| <td>494.117<br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>44<br />
| |
| </td>
| |
| <td>517.647<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47<br />
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| </td>
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| <td>552.941<br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>49<br />
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| </td>
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| <td>576.471<br />
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| </td>
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| </tr>
| |
| </table>
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|
| |
|
| </body></html></pre></div>
| | === Odd harmonics === |
| | {{Harmonics in equal|102}} |
| | |
| | == Intervals == |
| | {{Interval table}} |
| | |
| | [[Category:Echidnic]] |