114edo: Difference between revisions

Revision as of 15:36, 8 August 2016

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author JosephRuhf and made on 2016-08-08 15:36:12 UTC.

The original revision id was 588922354.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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:&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>
 

<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>

114edo: Difference between revisions

Revision as of 15:36, 8 August 2016

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

Navigation menu

Search