58edo: Difference between revisions

Revision as of 12:20, 13 July 2012

IMPORTED REVISION FROM WIKISPACES

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This revision was by author genewardsmith and made on 2012-07-13 12:20:08 UTC.

The original revision id was 353000566.

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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 [[edo|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 [[Harry Partch related scales|Genesis scale]] of [[Harry Partch]]. It supports [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[Hemifamity temperaments#Mystery|mystery]], [[Hemifamity temperaments#Buzzard|buzzard]] and [[Starling temperaments#Thuja|thuja]] [[Regular Temperaments|temperament]]s, and supplies the [[optimal patent val]] for 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank three temperaments [[Starling family#Thrush|thrush]], [[Starling family#Thrush-Bluebird|bluebird]], [[Starling family#Aplonis|aplonis]] and [[Breed family#Jove, aka Wonder-Jofur|jofur]].

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. 58 = 2*29, and 58 shares the same excellent fifth with [[29edo]].

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

==Intervals== 
|| degree of 58edo || cents value || ratios || associated temperament ||
|| 0 || 0.00 || 1/1 ||   ||
|| 1 || 20.69 || 56/55, 64/63, 81/80, 128/125 ||   ||
|| 2 || 41.38 || 36/35, 49/48, 50/49, 55/54 ||   ||
|| 3 || 62.07 || 25/24, 26/25, 27/26, 28/27, 33/32 ||   ||
|| 4 || 82.76 || 21/20, 22/21 ||   ||
|| 5 || 103.45 || 16/15, 17/16, 18/17 ||   ||
|| 6 || 124.14 || 14/13, 15/14, 27/25 ||   ||
|| 7 || 144.83 || 12/11, 13/12 ||   ||
|| 8 || 165.52 || 11/10 ||   ||
|| 9 || 186.21 || 10/9 ||   ||
|| 10 || 206.9 || 9/8, 17/15 ||   ||
|| 11 || 227.59 || 8/7 ||   ||
|| 12 || 248.28 || 15/13 ||   ||
|| 13 || 268.97 || 7/6 ||   ||
|| 14 || 289.66 || 13/11, 20/17 ||   ||
|| 15 || 310.34 || 6/5 || Myna ||
|| 16 || 331.03 || 17/14 ||   ||
|| 17 || 351.72 || 11/9, 16/13 ||   ||
|| 18 || 372.41 || 21/17 ||   ||
|| 19 || 393.1 || 5/4 ||   ||
|| 20 || 413.79 || 14/11 ||   ||
|| 21 || 434.48 || 9/7 ||   ||
|| 22 || 455.17 || 13/10, 17/13, 22/17 ||   ||
|| 23 || 475.86 || 21/16 ||   ||
|| 24 || 496.55 || 4/3 ||   ||
|| 25 || 517.24 || 27/20 ||   ||
|| 26 || 537.93 || 15/11 ||   ||
|| 27 || 558.62 || 11/8, 18/13 ||   ||
|| 28 || 579.31 || 7/5 ||   ||
|| 29 || 600 || 17/12, 24/17 ||   ||
|| 30 || 620.69 || 10/7 ||   ||
|| 31 || 641.38 || 13/9, 16/11 ||   ||
|| 32 || 662.07 || 22/15 ||   ||
|| 33 || 682.76 || 40/27 ||   ||
|| 34 || 703.45 || 3/2 ||   ||
|| 35 || 724.14 || 32/21 ||   ||
|| 36 || 744.83 || 20/13, 26/17, 17/11 ||   ||
|| 37 || 765.52 || 14/9 ||   ||
|| 38 || 786.21 || 11/7 ||   ||
|| 39 || 806.9 || 8/5 ||   ||
|| 40 || 827.59 ||   ||   ||
|| 41 || 848.28 || 13/8, 18/11 ||   ||
|| 42 || 868.97 ||   ||   ||
|| 43 || 889.66 ||   ||   ||
|| 44 || 910.34 ||   ||   ||
|| 45 || 931.03 ||   ||   ||
|| 46 || 951.72 ||   ||   ||
|| 47 || 972.41 || 7/4 ||   ||
|| 48 || 993.1 || 16/9 ||   ||
|| 49 || 1013.79 || 9/5 ||   ||
|| 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 <a class="wiki_link" href="/octave">octave</a> 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 <a class="wiki_link" href="/edo">equal temperament</a> 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="/Harry%20Partch%20related%20scales">Genesis scale</a> of <a class="wiki_link" href="/Harry%20Partch">Harry Partch</a>. It supports <a class="wiki_link" href="/hemififths">hemififths</a>, <a class="wiki_link" href="/myna">myna</a>, <a class="wiki_link" href="/diaschismic">diaschismic</a>, <a class="wiki_link" href="/harry">harry</a>, <a class="wiki_link" href="/Hemifamity%20temperaments#Mystery">mystery</a>, <a class="wiki_link" href="/Hemifamity%20temperaments#Buzzard">buzzard</a> and <a class="wiki_link" href="/Starling%20temperaments#Thuja">thuja</a> <a class="wiki_link" href="/Regular%20Temperaments">temperament</a>s, and supplies the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank three temperaments <a class="wiki_link" href="/Starling%20family#Thrush">thrush</a>, <a class="wiki_link" href="/Starling%20family#Thrush-Bluebird">bluebird</a>, <a class="wiki_link" href="/Starling%20family#Aplonis">aplonis</a> and <a class="wiki_link" href="/Breed%20family#Jove, aka Wonder-Jofur">jofur</a>.<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. 58 = 2*29, and 58 shares the same excellent fifth with <a class="wiki_link" href="/29edo">29edo</a>.<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 58edo<br />
</td>
        <td>cents value<br />
</td>
        <td>ratios<br />
</td>
        <td>associated temperament<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0.00<br />
</td>
        <td>1/1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>20.69<br />
</td>
        <td>56/55, 64/63, 81/80, 128/125<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>41.38<br />
</td>
        <td>36/35, 49/48, 50/49, 55/54<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>62.07<br />
</td>
        <td>25/24, 26/25, 27/26, 28/27, 33/32<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>82.76<br />
</td>
        <td>21/20, 22/21<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>103.45<br />
</td>
        <td>16/15, 17/16, 18/17<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>124.14<br />
</td>
        <td>14/13, 15/14, 27/25<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>144.83<br />
</td>
        <td>12/11, 13/12<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>165.52<br />
</td>
        <td>11/10<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>186.21<br />
</td>
        <td>10/9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>206.9<br />
</td>
        <td>9/8, 17/15<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>227.59<br />
</td>
        <td>8/7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>248.28<br />
</td>
        <td>15/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>268.97<br />
</td>
        <td>7/6<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>289.66<br />
</td>
        <td>13/11, 20/17<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>310.34<br />
</td>
        <td>6/5<br />
</td>
        <td>Myna<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>331.03<br />
</td>
        <td>17/14<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>351.72<br />
</td>
        <td>11/9, 16/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>372.41<br />
</td>
        <td>21/17<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>393.1<br />
</td>
        <td>5/4<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>413.79<br />
</td>
        <td>14/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>434.48<br />
</td>
        <td>9/7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>455.17<br />
</td>
        <td>13/10, 17/13, 22/17<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>475.86<br />
</td>
        <td>21/16<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>496.55<br />
</td>
        <td>4/3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>517.24<br />
</td>
        <td>27/20<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>537.93<br />
</td>
        <td>15/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>558.62<br />
</td>
        <td>11/8, 18/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>579.31<br />
</td>
        <td>7/5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>600<br />
</td>
        <td>17/12, 24/17<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>620.69<br />
</td>
        <td>10/7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>641.38<br />
</td>
        <td>13/9, 16/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>662.07<br />
</td>
        <td>22/15<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>682.76<br />
</td>
        <td>40/27<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>703.45<br />
</td>
        <td>3/2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>724.14<br />
</td>
        <td>32/21<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>744.83<br />
</td>
        <td>20/13, 26/17, 17/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>765.52<br />
</td>
        <td>14/9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>786.21<br />
</td>
        <td>11/7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>806.9<br />
</td>
        <td>8/5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>827.59<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>848.28<br />
</td>
        <td>13/8, 18/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>868.97<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>889.66<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>910.34<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>931.03<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>951.72<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>972.41<br />
</td>
        <td>7/4<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>993.1<br />
</td>
        <td>16/9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>1013.79<br />
</td>
        <td>9/5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>1034.48<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>1055.17<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>1075.86<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>1096.55<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>1117.24<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>1137.93<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>56<br />
</td>
        <td>1158.62<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>57<br />
</td>
        <td>1179.31<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-07-13 12:16:01 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-07-13 12:20:08 UTC</tt>.<br>
-: The original revision id was <tt>353000072</tt>.<br>
+: The original revision id was <tt>353000566</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>
 <h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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 [[edo|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 [[Harry Partch related scales|Genesis scale]] of [[Harry Partch]]. It supports [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[Hemifamity temperaments#Mystery|mystery]], [[Hemifamity temperaments#Buzzard|buzzard]] and [[Starling temperaments#Thuja|thuja]] [[Regular Temperaments|temperament]]s, and supplies the [[optimal patent val]] for 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank three temperaments [[thrush]], [[bluebird]], [[aplonis]] and [[jofur]].
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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 [[edo|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 [[Harry Partch related scales|Genesis scale]] of [[Harry Partch]]. It supports [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[Hemifamity temperaments#Mystery|mystery]], [[Hemifamity temperaments#Buzzard|buzzard]] and [[Starling temperaments#Thuja|thuja]] [[Regular Temperaments|temperament]]s, and supplies the [[optimal patent val]] for 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank three temperaments [[Starling family#Thrush|thrush]], [[Starling family#Thrush-Bluebird|bluebird]], [[Starling family#Aplonis|aplonis]] and [[Breed family#Jove, aka Wonder-Jofur|jofur]].
 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. 58 = 2*29, and 58 shares the same excellent fifth with [[29edo]].
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 <h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;58edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;58 equal temperament&lt;/em&gt;, often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; 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 &lt;a class="wiki_link" href="/11-limit"&gt;11&lt;/a&gt;, &lt;a class="wiki_link" href="/13-limit"&gt;13&lt;/a&gt; and &lt;a class="wiki_link" href="/17-limit"&gt;17-limit&lt;/a&gt;s. It is the smallest &lt;a class="wiki_link" href="/edo"&gt;equal temperament&lt;/a&gt; which is &lt;a class="wiki_link" href="/consistent"&gt;consistent&lt;/a&gt; through the 17-limit, and is also the first et to map the entire 11-limit &lt;a class="wiki_link" href="/tonality%20diamond"&gt;tonality diamond&lt;/a&gt; to distinct scale steps, and hence the first et which can define a version of the famous 43-note &lt;a class="wiki_link" href="/Harry%20Partch%20related%20scales"&gt;Genesis scale&lt;/a&gt; of &lt;a class="wiki_link" href="/Harry%20Partch"&gt;Harry Partch&lt;/a&gt;. It supports &lt;a class="wiki_link" href="/hemififths"&gt;hemififths&lt;/a&gt;, &lt;a class="wiki_link" href="/myna"&gt;myna&lt;/a&gt;, &lt;a class="wiki_link" href="/diaschismic"&gt;diaschismic&lt;/a&gt;, &lt;a class="wiki_link" href="/harry"&gt;harry&lt;/a&gt;, &lt;a class="wiki_link" href="/Hemifamity%20temperaments#Mystery"&gt;mystery&lt;/a&gt;, &lt;a class="wiki_link" href="/Hemifamity%20temperaments#Buzzard"&gt;buzzard&lt;/a&gt; and &lt;a class="wiki_link" href="/Starling%20temperaments#Thuja"&gt;thuja&lt;/a&gt; &lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;temperament&lt;/a&gt;s, and supplies the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank three temperaments &lt;a class="wiki_link" href="/thrush"&gt;thrush&lt;/a&gt;, &lt;a class="wiki_link" href="/bluebird"&gt;bluebird&lt;/a&gt;, &lt;a class="wiki_link" href="/aplonis"&gt;aplonis&lt;/a&gt; and &lt;a class="wiki_link" href="/jofur"&gt;jofur&lt;/a&gt;.&lt;br /&gt;
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;58edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;58 equal temperament&lt;/em&gt;, often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; 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 &lt;a class="wiki_link" href="/11-limit"&gt;11&lt;/a&gt;, &lt;a class="wiki_link" href="/13-limit"&gt;13&lt;/a&gt; and &lt;a class="wiki_link" href="/17-limit"&gt;17-limit&lt;/a&gt;s. It is the smallest &lt;a class="wiki_link" href="/edo"&gt;equal temperament&lt;/a&gt; which is &lt;a class="wiki_link" href="/consistent"&gt;consistent&lt;/a&gt; through the 17-limit, and is also the first et to map the entire 11-limit &lt;a class="wiki_link" href="/tonality%20diamond"&gt;tonality diamond&lt;/a&gt; to distinct scale steps, and hence the first et which can define a version of the famous 43-note &lt;a class="wiki_link" href="/Harry%20Partch%20related%20scales"&gt;Genesis scale&lt;/a&gt; of &lt;a class="wiki_link" href="/Harry%20Partch"&gt;Harry Partch&lt;/a&gt;. It supports &lt;a class="wiki_link" href="/hemififths"&gt;hemififths&lt;/a&gt;, &lt;a class="wiki_link" href="/myna"&gt;myna&lt;/a&gt;, &lt;a class="wiki_link" href="/diaschismic"&gt;diaschismic&lt;/a&gt;, &lt;a class="wiki_link" href="/harry"&gt;harry&lt;/a&gt;, &lt;a class="wiki_link" href="/Hemifamity%20temperaments#Mystery"&gt;mystery&lt;/a&gt;, &lt;a class="wiki_link" href="/Hemifamity%20temperaments#Buzzard"&gt;buzzard&lt;/a&gt; and &lt;a class="wiki_link" href="/Starling%20temperaments#Thuja"&gt;thuja&lt;/a&gt; &lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;temperament&lt;/a&gt;s, and supplies the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank three temperaments &lt;a class="wiki_link" href="/Starling%20family#Thrush"&gt;thrush&lt;/a&gt;, &lt;a class="wiki_link" href="/Starling%20family#Thrush-Bluebird"&gt;bluebird&lt;/a&gt;, &lt;a class="wiki_link" href="/Starling%20family#Aplonis"&gt;aplonis&lt;/a&gt; and &lt;a class="wiki_link" href="/Breed%20family#Jove, aka Wonder-Jofur"&gt;jofur&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 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. 58 = 2*29, and 58 shares the same excellent fifth with &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;.&lt;br /&gt;

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