Xenharmonic Wiki

57edo

Revision as of 17:47, 29 December 2016 by Wikispaces>xenwolf (**Imported revision 602901438 - Original comment: **)

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=<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]] || Size ([[cent|Cents]]) ||
||=  0 ||>    0.0000 ||
||=  1 ||>   21.0526 ||
||=  2 ||>   42.1053 ||
||=  3 ||>   63.1579 ||
||=  4 ||>   84.2105 ||
||=  5 ||>  105.2632 ||
||=  6 ||>  126.3158 ||
||=  7 ||>  147.3684 ||
||=  8 ||>  168.4211 ||
||=  9 ||>  189.4737 ||
||= 10 ||>  210.5263 ||
||= 11 ||>  231.5789 ||
||= 12 ||>  252.6316 ||
||= 13 ||>  273.6842 ||
||= 14 ||>  294.7368 ||
||= 15 ||>  315.7895 ||
||= 16 ||>  336.8421 ||
||= 17 ||>  357.8947 ||
||= 18 ||>  378.9474 ||
||= 19 ||>  400.0000 ||
||= 20 ||>  421.0526 ||
||= 21 ||>  442.1053 ||
||= 22 ||>  463.1579 ||
||= 23 ||>  484.2105 ||
||= 24 ||>  505.2632 ||
||= 25 ||>  526.3158 ||
||= 26 ||>  547.3684 ||
||= 27 ||>  568.4211 ||
||= 28 ||>  589.4737 ||
||= 29 ||>  610.5263 ||
||= 30 ||>  631.5789 ||
||= 31 ||>  652.6316 ||
||= 32 ||>  673.6842 ||
||= 33 ||>  694.7368 ||
||= 34 ||>  715.7895 ||
||= 35 ||>  736.8421 ||
||= 36 ||>  757.8947 ||
||= 37 ||>  778.9474 ||
||= 38 ||>  800.0000 ||
||= 39 ||>  821.0526 ||
||= 40 ||>  842.1053 ||
||= 41 ||>  863.1579 ||
||= 42 ||>  884.2105 ||
||= 43 ||>  905.2632 ||
||= 44 ||>  926.3158 ||
||= 45 ||>  947.3684 ||
||= 46 ||>  968.4211 ||
||= 47 ||>  989.4737 ||
||= 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 ||
||= 57 ||> 1200.0000 ||

__**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><br />
</td>
        <td>Size (<a class="wiki_link" href="/cent">Cents</a>)<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">0<br />
</td>
        <td style="text-align: right;">0.0000<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1<br />
</td>
        <td style="text-align: right;">21.0526<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2<br />
</td>
        <td style="text-align: right;">42.1053<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3<br />
</td>
        <td style="text-align: right;">63.1579<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4<br />
</td>
        <td style="text-align: right;">84.2105<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">5<br />
</td>
        <td style="text-align: right;">105.2632<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6<br />
</td>
        <td style="text-align: right;">126.3158<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">7<br />
</td>
        <td style="text-align: right;">147.3684<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">8<br />
</td>
        <td style="text-align: right;">168.4211<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">9<br />
</td>
        <td style="text-align: right;">189.4737<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">10<br />
</td>
        <td style="text-align: right;">210.5263<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">11<br />
</td>
        <td style="text-align: right;">231.5789<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">12<br />
</td>
        <td style="text-align: right;">252.6316<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">13<br />
</td>
        <td style="text-align: right;">273.6842<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">14<br />
</td>
        <td style="text-align: right;">294.7368<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">15<br />
</td>
        <td style="text-align: right;">315.7895<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">16<br />
</td>
        <td style="text-align: right;">336.8421<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">17<br />
</td>
        <td style="text-align: right;">357.8947<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">18<br />
</td>
        <td style="text-align: right;">378.9474<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">19<br />
</td>
        <td style="text-align: right;">400.0000<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">20<br />
</td>
        <td style="text-align: right;">421.0526<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">21<br />
</td>
        <td style="text-align: right;">442.1053<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">22<br />
</td>
        <td style="text-align: right;">463.1579<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">23<br />
</td>
        <td style="text-align: right;">484.2105<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">24<br />
</td>
        <td style="text-align: right;">505.2632<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">25<br />
</td>
        <td style="text-align: right;">526.3158<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">26<br />
</td>
        <td style="text-align: right;">547.3684<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">27<br />
</td>
        <td style="text-align: right;">568.4211<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">28<br />
</td>
        <td style="text-align: right;">589.4737<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">29<br />
</td>
        <td style="text-align: right;">610.5263<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">30<br />
</td>
        <td style="text-align: right;">631.5789<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">31<br />
</td>
        <td style="text-align: right;">652.6316<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">32<br />
</td>
        <td style="text-align: right;">673.6842<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">33<br />
</td>
        <td style="text-align: right;">694.7368<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">34<br />
</td>
        <td style="text-align: right;">715.7895<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">35<br />
</td>
        <td style="text-align: right;">736.8421<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">36<br />
</td>
        <td style="text-align: right;">757.8947<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">37<br />
</td>
        <td style="text-align: right;">778.9474<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">38<br />
</td>
        <td style="text-align: right;">800.0000<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">39<br />
</td>
        <td style="text-align: right;">821.0526<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">40<br />
</td>
        <td style="text-align: right;">842.1053<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">41<br />
</td>
        <td style="text-align: right;">863.1579<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">42<br />
</td>
        <td style="text-align: right;">884.2105<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">43<br />
</td>
        <td style="text-align: right;">905.2632<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">44<br />
</td>
        <td style="text-align: right;">926.3158<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">45<br />
</td>
        <td style="text-align: right;">947.3684<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">46<br />
</td>
        <td style="text-align: right;">968.4211<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">47<br />
</td>
        <td style="text-align: right;">989.4737<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">48<br />
</td>
        <td style="text-align: right;">1010.5263<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">49<br />
</td>
        <td style="text-align: right;">1031.5789<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">50<br />
</td>
        <td style="text-align: right;">1052.6316<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">51<br />
</td>
        <td style="text-align: right;">1073.6842<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">52<br />
</td>
        <td style="text-align: right;">1094.7368<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">53<br />
</td>
        <td style="text-align: right;">1115.7895<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">54<br />
</td>
        <td style="text-align: right;">1136.8421<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">55<br />
</td>
        <td style="text-align: right;">1157.8947<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">56<br />
</td>
        <td style="text-align: right;">1178.9474<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">57<br />
</td>
        <td style="text-align: right;">1200.0000<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>
Retrieved from "https://en.xen.wiki/index.php?title=57edo&oldid=9416"