114edo
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author JosephRuhf and made on 2016-08-08 15:36:12 UTC.
- The original revision id was 588922354.
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Original Wikitext content:
**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. ===Period of 19-limit Shrutar=== ||~ Degree ||~ Cents || || 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 ||
Original HTML content:
<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 />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h3> --><h3 id="toc0"><a name="x--Period of 19-limit Shrutar"></a><!-- ws:end:WikiTextHeadingRule:0 -->Period of 19-limit Shrutar</h3>
<table class="wiki_table">
<tr>
<th>Degree<br />
</th>
<th>Cents<br />
</th>
</tr>
<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 />
</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 />
</td>
<td>315.78947<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>336.842105<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>357.89474<br />
</td>
</tr>
<tr>
<td>35<br />
</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 />
</td>
<td>421.05263<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>442.10526<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>463.157895<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>473.68421<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<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>