57edo: Difference between revisions

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Wikispaces>JosephRuhf
**Imported revision 586818343 - Original comment: **
Wikispaces>JosephRuhf
**Imported revision 601607792 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-07-12 11:25:21 UTC</tt>.<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-07 08:48:32 UTC</tt>.<br>
: The original revision id was <tt>586818343</tt>.<br>
: The original revision id was <tt>601607792</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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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Revision as of 08:48, 7 December 2016

IMPORTED REVISION FROM WIKISPACES

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

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Original Wikitext content:

=<span style="color: #006118; font-family: 'Times New Roman',Times,serif; font-size: 113%;">57 tone equal temperament</span>= 

//57edo// divides the [[octave]] into 57 parts of size 21.053. It can be used to tune [[mothra temperament]], and is an excellent tuning for the 2.5/3.7.11.13.17.19 [[just intonation subgroup]]. One way to describe 57 is that it has a [[5-limit]] part consisting of three versions of 19, plus a no-threes no-fives part which is much more accurate. A good generator to exploit the 2.5/3.7.11.13.17.19 aspect of 57 is the approximate 11/8, which is 26\57. This gives the [[19-limit]] 46&57 temperament [[Sensipent family|Heinz]].

[[5-limit]] [[comma]]s: 81/80, 3125/3072

[[7-limit]] commas: 81/80, 3125/3072, 1029/1024

[[11-limit]] commas: 99/98, 385/384, 441/440, 625/616

==Intervals== 
|| [[Degree]]s of 57-EDO || [[Cent]]s value ||
|| 0 || 0 ||
|| 1 || 21.0526 ||
|| 2 || 42.1053 ||
|| 3 || 63.1579 ||
|| 4 || 84.2105 ||
|| 5 || 105.2632/1 ||
|| 6 || 126.3158/1 ||
|| 7 || 147.3684/1 ||
|| 8 || 168.4211/1 ||
|| 9 || 189.4737/1 ||
|| 10 || 210.5263/1 ||
|| 11 || 231.5789/1 ||
|| 12 || 252.6316/1 ||
|| 13 || 273.6842/1 ||
|| 14 || 294.7368/1 ||
|| 15 || 315.7895/1 ||
|| 16 || 336.8421/1 ||
|| 17 || 357.8947/1 ||
|| 18 || 378.9474/1 ||
|| 19 || 400 ||
|| 20 || 421.0526/1 ||
|| 21 || 442.1053/1 ||
|| 22 || 463.1579/1 ||
|| 23 || 484.2105/1 ||
|| 24 || 505.2632/1 ||
|| 25 || 526.3158/1 ||
|| 26 || 547.3684/1 ||
|| 27 || 568.4211/1 ||
|| 28 || 589.4737/1 ||
|| 29 || 610.5263/1 ||
|| 30 || 631.5789/1 ||
|| 31 || 652.6316/1 ||
|| 32 || 673.6842/1 ||
|| 33 || 694.7368/1 ||
|| 34 || 715.7895/1 ||
|| 35 || 736.8421/1 ||
|| 36 || 757.8947/1 ||
|| 37 || 778.9474/1 ||
|| 38 || 800 ||
|| 39 || 821.0526/1 ||
|| 40 || 842.1053/1 ||
|| 41 || 863.1579/1 ||
|| 42 || 884.2105/1 ||
|| 43 || 905.2632/1 ||
|| 44 || 926.3158/1 ||
|| 45 || 947.3684/1 ||
|| 46 || 968.4211/1 ||
|| 47 || 989.4737/1 ||
|| 48 || 1010.5263 ||
|| 49 || 1031.5789 ||
|| 50 || 1052.6316 ||
|| 51 || 1073.6842 ||
|| 52 || 1094.7368 ||
|| 53 || 1115.7895 ||
|| 54 || 1136.8421 ||
|| 55 || 1157.8947 ||
|| 56 || 1178.9474 ||

__**Modes of** **57edo**__
2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 - 3MOS of type 18L 21s (augene)

Original HTML content:

<html><head><title>57edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x57 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #006118; font-family: 'Times New Roman',Times,serif; font-size: 113%;">57 tone equal temperament</span></h1>
 <br />
<em>57edo</em> divides the <a class="wiki_link" href="/octave">octave</a> into 57 parts of size 21.053. It can be used to tune <a class="wiki_link" href="/mothra%20temperament">mothra temperament</a>, and is an excellent tuning for the 2.5/3.7.11.13.17.19 <a class="wiki_link" href="/just%20intonation%20subgroup">just intonation subgroup</a>. One way to describe 57 is that it has a <a class="wiki_link" href="/5-limit">5-limit</a> part consisting of three versions of 19, plus a no-threes no-fives part which is much more accurate. A good generator to exploit the 2.5/3.7.11.13.17.19 aspect of 57 is the approximate 11/8, which is 26\57. This gives the <a class="wiki_link" href="/19-limit">19-limit</a> 46&amp;57 temperament <a class="wiki_link" href="/Sensipent%20family">Heinz</a>.<br />
<br />
<a class="wiki_link" href="/5-limit">5-limit</a> <a class="wiki_link" href="/comma">comma</a>s: 81/80, 3125/3072<br />
<br />
<a class="wiki_link" href="/7-limit">7-limit</a> commas: 81/80, 3125/3072, 1029/1024<br />
<br />
<a class="wiki_link" href="/11-limit">11-limit</a> commas: 99/98, 385/384, 441/440, 625/616<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x57 tone equal temperament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2>
 

<table class="wiki_table">
    <tr>
        <td><a class="wiki_link" href="/Degree">Degree</a>s of 57-EDO<br />
</td>
        <td><a class="wiki_link" href="/Cent">Cent</a>s value<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>21.0526<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>42.1053<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>63.1579<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>84.2105<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>105.2632/1<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>126.3158/1<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>147.3684/1<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>168.4211/1<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>189.4737/1<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>210.5263/1<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>231.5789/1<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>252.6316/1<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>273.6842/1<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>294.7368/1<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>315.7895/1<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>336.8421/1<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>357.8947/1<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>378.9474/1<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>400<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>421.0526/1<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>442.1053/1<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>463.1579/1<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>484.2105/1<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>505.2632/1<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>526.3158/1<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>547.3684/1<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>568.4211/1<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>589.4737/1<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>610.5263/1<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>631.5789/1<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>652.6316/1<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>673.6842/1<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>694.7368/1<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>715.7895/1<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>736.8421/1<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>757.8947/1<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>778.9474/1<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>800<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>821.0526/1<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>842.1053/1<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>863.1579/1<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>884.2105/1<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>905.2632/1<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>926.3158/1<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>947.3684/1<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>968.4211/1<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>989.4737/1<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>1010.5263<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>1031.5789<br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>1052.6316<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>1073.6842<br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>1094.7368<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>1115.7895<br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>1136.8421<br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>1157.8947<br />
</td>
    </tr>
    <tr>
        <td>56<br />
</td>
        <td>1178.9474<br />
</td>
    </tr>
</table>

<br />
<u><strong>Modes of</strong> <strong>57edo</strong></u><br />
2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 - 3MOS of type 18L 21s (augene)</body></html>