57edo
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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 || || 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 || || 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 || || 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 || __**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:<h1> --><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&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:<h2> --><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<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>126.3158<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>147.3684<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>168.4211<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>189.4737<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>210.5263<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>231.5789<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>252.6316<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>273.6842<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>294.7368<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>315.7895<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>336.8421<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>357.8947<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>378.9474<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>400<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>421.0526<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>442.1053<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>463.1579<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>484.2105<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>505.2632<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>526.3158<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>547.3684<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>568.4211<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>589.4737<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>610.5263<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>631.5789<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>652.6316<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>673.6842<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>694.7368<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>715.7895<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>736.8421<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>757.8947<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>778.9474<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>800<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>821.0526<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>842.1053<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>863.1579<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>884.2105<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>905.2632<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>926.3158<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>947.3684<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>968.4211<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>989.4737<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>