58edo

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This revision was by author Andrew_Heathwaite and made on 2011-08-21 17:56:22 UTC.
The original revision id was 247462201.
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Original Wikitext content:

The //58 equal temperament//, often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the octave into 58 equally-sized steps. Each step represents a frequency ratio of 20.69 cents. It tempers out 2048/2025, 126/125, 1728/1715, 144/143, 176/175, 896/891, 243/242, 5120/5103, 351/350, 364/363, 441/440, and 540/539, and is a strong system in the [[11-limit|11]], [[13-limit|13]] and [[17-limit]]s. It is the smallest equal temperament which is [[consistent]] through the 17-limit, and is also the first et to map the entire 11-limit [[tonality diamond]] to distinct scale steps, and hence the first et which can define a version of the famous 43-note [[Genesis scale]] of [[Harry Partch]]. It supports hemififths, myna, diaschismic, harry, mystery and buzzard [[temperament]]s.

While the 17th harmonic is a cent and a half cent flat, the harmonics below it are all a little sharp, giving it the sound of a sharp system.

=Scales= 
[[hemif7]]
[[hemif10]]
[[hemif17]]

==Intervals== 
|| degree of 59edo || cents value || associated temperament ||
|| 0 || 0.00 ||   ||
|| 1 || 20.69 ||   ||
|| 2 || 41.38 ||   ||
|| 3 || 62.07 ||   ||
|| 4 || 82.76 ||   ||
|| 5 || 103.45 ||   ||
|| 6 || 124.14 ||   ||
|| 7 || 144.83 ||   ||
|| 8 || 165.52 ||   ||
|| 9 || 186.21 ||   ||
|| 10 || 206.9 ||   ||
|| 11 || 227.59 ||   ||
|| 12 || 248.28 ||   ||
|| 13 || 268.97 ||   ||
|| 14 || 289.66 ||   ||
|| 15 || 310.34 ||   ||
|| 16 || 331.03 ||   ||
|| 17 || 351.72 ||   ||
|| 18 || 372.41 ||   ||
|| 19 || 393.1 ||   ||
|| 20 || 413.79 ||   ||
|| 21 || 434.48 ||   ||
|| 22 || 455.17 ||   ||
|| 23 || 475.86 ||   ||
|| 24 || 496.55 ||   ||
|| 25 || 517.24 ||   ||
|| 26 || 537.93 ||   ||
|| 27 || 558.62 ||   ||
|| 28 || 579.31 ||   ||
|| 29 || 600 ||   ||
|| 30 || 620.69 ||   ||
|| 31 || 641.38 ||   ||
|| 32 || 662.07 ||   ||
|| 33 || 682.76 ||   ||
|| 34 || 703.45 ||   ||
|| 35 || 724.14 ||   ||
|| 36 || 744.83 ||   ||
|| 37 || 765.52 ||   ||
|| 38 || 786.21 ||   ||
|| 39 || 806.9 ||   ||
|| 40 || 827.59 ||   ||
|| 41 || 848.28 ||   ||
|| 42 || 868.97 ||   ||
|| 43 || 889.66 ||   ||
|| 44 || 910.34 ||   ||
|| 45 || 931.03 ||   ||
|| 46 || 951.72 ||   ||
|| 47 || 972.41 ||   ||
|| 48 || 993.1 ||   ||
|| 49 || 1013.79 ||   ||
|| 50 || 1034.48 ||   ||
|| 51 || 1055.17 ||   ||
|| 52 || 1075.86 ||   ||
|| 53 || 1096.55 ||   ||
|| 54 || 1117.24 ||   ||
|| 55 || 1137.93 ||   ||
|| 56 || 1158.62 ||   ||
|| 57 || 1179.31 ||   ||

Original HTML content:

<html><head><title>58edo</title></head><body>The <em>58 equal temperament</em>, often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the octave into 58 equally-sized steps. Each step represents a frequency ratio of 20.69 cents. It tempers out 2048/2025, 126/125, 1728/1715, 144/143, 176/175, 896/891, 243/242, 5120/5103, 351/350, 364/363, 441/440, and 540/539, and is a strong system in the <a class="wiki_link" href="/11-limit">11</a>, <a class="wiki_link" href="/13-limit">13</a> and <a class="wiki_link" href="/17-limit">17-limit</a>s. It is the smallest equal temperament which is <a class="wiki_link" href="/consistent">consistent</a> through the 17-limit, and is also the first et to map the entire 11-limit <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a> to distinct scale steps, and hence the first et which can define a version of the famous 43-note <a class="wiki_link" href="/Genesis%20scale">Genesis scale</a> of <a class="wiki_link" href="/Harry%20Partch">Harry Partch</a>. It supports hemififths, myna, diaschismic, harry, mystery and buzzard <a class="wiki_link" href="/temperament">temperament</a>s.<br />
<br />
While the 17th harmonic is a cent and a half cent flat, the harmonics below it are all a little sharp, giving it the sound of a sharp system.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:0 -->Scales</h1>
 <a class="wiki_link" href="/hemif7">hemif7</a><br />
<a class="wiki_link" href="/hemif10">hemif10</a><br />
<a class="wiki_link" href="/hemif17">hemif17</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Scales-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2>
 

<table class="wiki_table">
    <tr>
        <td>degree of 59edo<br />
</td>
        <td>cents value<br />
</td>
        <td>associated temperament<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0.00<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>20.69<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>41.38<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>62.07<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>82.76<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>103.45<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>124.14<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>144.83<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>165.52<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>186.21<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>206.9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>227.59<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>248.28<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>268.97<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>289.66<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>310.34<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>331.03<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>351.72<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>372.41<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>393.1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>413.79<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>434.48<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>455.17<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>475.86<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>496.55<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>517.24<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>537.93<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>558.62<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>579.31<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>600<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>620.69<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>641.38<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>662.07<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>682.76<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>703.45<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>724.14<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>744.83<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>765.52<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>786.21<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>806.9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>827.59<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>848.28<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>868.97<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>889.66<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>910.34<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>931.03<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>951.72<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>972.41<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>993.1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>1013.79<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>1034.48<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>1055.17<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>1075.86<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>1096.55<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>1117.24<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>1137.93<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>56<br />
</td>
        <td>1158.62<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>57<br />
</td>
        <td>1179.31<br />
</td>
        <td><br />
</td>
    </tr>
</table>

</body></html>
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