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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>2016-08-08 15:36:12 UTC</tt>.<br>
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| : The original revision id was <tt>588922354</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">**114edo** is the [[equal division of the octave]] into 114 parts, each of 10.52632 [[cent]]s. In the [[5-limit]] it [[tempering out|tempers out]] 2048/2025, in the [[7-limit]] 245/243, in the [[11-limit]] 121/120 and 176/175, in the [[13-limit]] 196/195 and 325/324, in the [[17-limit]] 136/135 and 154/153, in the [[19-limit]] 286/285 and 343/342. These commas make for 114edo being an excellent tuning for [[Diaschismic family|shrutar temperament]]; it is in fact the [[optimal patent val]] for [[shrutar]] in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.
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| ===Period of 19-limit Shrutar=== | | == Theory == |
| ||~ Degree ||~ Cents ||
| | In the [[5-limit]] the equal temperament [[tempering out|tempers out]] 2048/2025 ([[diaschisma]]), in the [[7-limit]] [[245/243]], in the [[11-limit]] [[121/120]], [[176/175]] and notably the [[quartisma]], in the [[13-limit]] [[196/195]] and [[325/324]], in the [[17-limit]] [[136/135]] and [[154/153]], in the [[19-limit]] [[286/285]] and [[343/342]]. These commas make for 114edo being an excellent tuning for the [[shrutar]] temperament; it is in fact the [[optimal patent val]] for shrutar in the 11-, 13-, 17-, and 19-limit, as well as the rank-3 [[bisector]] temperament. |
| || 2 || 21.05263 ||
| |
| || 3 || 31.57895 ||
| |
| || 5 || 52.63158 ||
| |
| || 7 || 73.68421 ||
| |
| || 8 || 84.21053 ||
| |
| || 10 || 105.26316 ||
| |
| || 12 || 126.31579 ||
| |
| || 13 || 136.842105 ||
| |
| || 15 || 157.89474 ||
| |
| || 17 || 178.94737 ||
| |
| || 18 || 189.47369 ||
| |
| || 20 || 210.52632 ||
| |
| || 22 || 231.57895 ||
| |
| || 23 || 242.10526 ||
| |
| || 25 || 263.157895 ||
| |
| || 27 || 284.21053 ||
| |
| || 29 || 305.26316 ||
| |
| || 30 || 315.78947 ||
| |
| || 32 || 336.842105 ||
| |
| || 34 || 357.89474 ||
| |
| || 35 || 368.42105 ||
| |
| || 37 || 389.47368 ||
| |
| || 39 || 410.52632 ||
| |
| || 40 || 421.05263 ||
| |
| || 42 || 442.10526 ||
| |
| || 44 || 463.157895 ||
| |
| || 45 || 473.68421 ||
| |
| || 47 || 494.73684 ||
| |
| || 49 || 515.78947 ||
| |
| || 50 || 526.31579 ||
| |
| || 52 || 547.36842 ||
| |
| || 54 || 568.42105 ||
| |
| || 55 || 578.94737 ||</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>114edo</title></head><body><strong>114edo</strong> is the <a class="wiki_link" href="/equal%20division%20of%20the%20octave">equal division of the octave</a> into 114 parts, each of 10.52632 <a class="wiki_link" href="/cent">cent</a>s. In the <a class="wiki_link" href="/5-limit">5-limit</a> it <a class="wiki_link" href="/tempering%20out">tempers out</a> 2048/2025, in the <a class="wiki_link" href="/7-limit">7-limit</a> 245/243, in the <a class="wiki_link" href="/11-limit">11-limit</a> 121/120 and 176/175, in the <a class="wiki_link" href="/13-limit">13-limit</a> 196/195 and 325/324, in the <a class="wiki_link" href="/17-limit">17-limit</a> 136/135 and 154/153, in the <a class="wiki_link" href="/19-limit">19-limit</a> 286/285 and 343/342. These commas make for 114edo being an excellent tuning for <a class="wiki_link" href="/Diaschismic%20family">shrutar temperament</a>; it is in fact the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for <a class="wiki_link" href="/shrutar">shrutar</a> in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.<br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--Period of 19-limit Shrutar"></a><!-- ws:end:WikiTextHeadingRule:0 -->Period of 19-limit Shrutar</h3>
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| <table class="wiki_table">
| | === Odd harmonics === |
| <tr>
| | {{Harmonics in equal|114}} |
| <th>Degree<br />
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| </th>
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| <th>Cents<br />
| |
| </th>
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| </tr>
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| <tr>
| |
| <td>2<br />
| |
| </td>
| |
| <td>21.05263<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3<br />
| |
| </td>
| |
| <td>31.57895<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5<br />
| |
| </td>
| |
| <td>52.63158<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7<br />
| |
| </td>
| |
| <td>73.68421<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8<br />
| |
| </td>
| |
| <td>84.21053<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10<br />
| |
| </td>
| |
| <td>105.26316<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12<br />
| |
| </td>
| |
| <td>126.31579<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13<br />
| |
| </td>
| |
| <td>136.842105<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15<br />
| |
| </td>
| |
| <td>157.89474<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17<br />
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| </td>
| |
| <td>178.94737<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18<br />
| |
| </td>
| |
| <td>189.47369<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20<br />
| |
| </td>
| |
| <td>210.52632<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22<br />
| |
| </td>
| |
| <td>231.57895<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23<br />
| |
| </td>
| |
| <td>242.10526<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25<br />
| |
| </td>
| |
| <td>263.157895<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27<br />
| |
| </td>
| |
| <td>284.21053<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>29<br />
| |
| </td>
| |
| <td>305.26316<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>30<br />
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| </td>
| |
| <td>315.78947<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32<br />
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| </td>
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| <td>336.842105<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34<br />
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| </td>
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| <td>357.89474<br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>35<br />
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| </td>
| |
| <td>368.42105<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>37<br />
| |
| </td>
| |
| <td>389.47368<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>39<br />
| |
| </td>
| |
| <td>410.52632<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>40<br />
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| </td>
| |
| <td>421.05263<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>42<br />
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| </td>
| |
| <td>442.10526<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>44<br />
| |
| </td>
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| <td>463.157895<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>45<br />
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| </td>
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| <td>473.68421<br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47<br />
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| </td>
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| <td>494.73684<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>49<br />
| |
| </td>
| |
| <td>515.78947<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>50<br />
| |
| </td>
| |
| <td>526.31579<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>52<br />
| |
| </td>
| |
| <td>547.36842<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>54<br />
| |
| </td>
| |
| <td>568.42105<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>55<br />
| |
| </td>
| |
| <td>578.94737<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div>
| | === Subsets and supersets === |
| | Since 114 factors into {{factorization|114}}, 114 edo has subset edos {{EDOs| 2, 3, 6, 19, 38, and 57 }}. |
| | |
| | == Intervals == |
| | {{Interval table}} |
| | |
| | [[Category:Shrutar]] |
| | [[Category:Bisector]] |