58edo: Difference between revisions

Revision as of 08:36, 13 July 2012

IMPORTED REVISION FROM WIKISPACES

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This revision was by author phylingual and made on 2012-07-13 08:36:00 UTC.

The original revision id was 352968254.

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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 [[Genesis scale]] of [[Harry Partch]]. It supports [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[mystery]], [[buzzard]] and [[thuja]] [[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]].

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="/Genesis%20scale">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="/mystery">mystery</a>, <a class="wiki_link" href="/buzzard">buzzard</a> and <a class="wiki_link" href="/thuja">thuja</a> <a class="wiki_link" href="/temperament">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="/thrush">thrush</a>, <a class="wiki_link" href="/bluebird">bluebird</a>, <a class="wiki_link" href="/aplonis">aplonis</a> and <a class="wiki_link" href="/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:guest|guest]] and made on <tt>2012-02-26 23:53:52 UTC</tt>.<br>
+: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-07-13 08:36:00 UTC</tt>.<br>
-: The original revision id was <tt>305358568</tt>.<br>
+: The original revision id was <tt>352968254</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>
@@ Line 16: / Line 16: @@
 ==Intervals==
-|| degree of 58edo || cents value || associated temperament ||
+|| degree of 58edo || cents value || ratios || associated temperament ||
-|| 0 || 0.00 ||   ||
+|| 0 || 0.00 || 1/1 ||   ||
-|| 1 || 20.69 ||   ||
+|| 1 || 20.69 || 56/55, 64/63, 81/80, 128/125 ||   ||
-|| 2 || 41.38 ||   ||
+|| 2 || 41.38 || 36/35, 49/48, 50/49, 55/54 ||   ||
-|| 3 || 62.07 ||   ||
+|| 3 || 62.07 || 25/24, 26/25, 27/26, 28/27, 33/32 ||   ||
-|| 4 || 82.76 ||   ||
+|| 4 || 82.76 || 21/20, 22/21 ||   ||
-|| 5 || 103.45 ||   ||
+|| 5 || 103.45 || 16/15, 17/16, 18/17 ||   ||
-|| 6 || 124.14 ||   ||
+|| 6 || 124.14 || 14/13, 15/14, 27/25 ||   ||
-|| 7 || 144.83 ||   ||
+|| 7 || 144.83 || 12/11, 13/12 ||   ||
-|| 8 || 165.52 ||   ||
+|| 8 || 165.52 || 11/10 ||   ||
-|| 9 || 186.21 ||   ||
+|| 9 || 186.21 || 10/9 ||   ||
-|| 10 || 206.9 ||   ||
+|| 10 || 206.9 || 9/8, 17/15 ||   ||
-|| 11 || 227.59 ||   ||
+|| 11 || 227.59 || 8/7 ||   ||
-|| 12 || 248.28 ||   ||
+|| 12 || 248.28 || 15/13 ||   ||
-|| 13 || 268.97 ||   ||
+|| 13 || 268.97 || 7/6 ||   ||
-|| 14 || 289.66 ||   ||
+|| 14 || 289.66 || 13/11, 20/17 ||   ||
-|| 15 || 310.34 ||   ||
+|| 15 || 310.34 || 6/5 || Myna ||
-|| 16 || 331.03 ||   ||
+|| 16 || 331.03 || 17/14 ||   ||
-|| 17 || 351.72 ||   ||
+|| 17 || 351.72 || 11/9, 16/13 ||   ||
-|| 18 || 372.41 ||   ||
+|| 18 || 372.41 || 21/17 ||   ||
-|| 19 || 393.1 ||   ||
+|| 19 || 393.1 || 5/4 ||   ||
-|| 20 || 413.79 ||   ||
+|| 20 || 413.79 || 14/11 ||   ||
-|| 21 || 434.48 ||   ||
+|| 21 || 434.48 || 9/7 ||   ||
-|| 22 || 455.17 ||   ||
+|| 22 || 455.17 || 13/10, 17/13, 22/17 ||   ||
-|| 23 || 475.86 ||   ||
+|| 23 || 475.86 || 21/16 ||   ||
-|| 24 || 496.55 ||   ||
+|| 24 || 496.55 || 4/3 ||   ||
-|| 25 || 517.24 ||   ||
+|| 25 || 517.24 || 27/20 ||   ||
-|| 26 || 537.93 ||   ||
+|| 26 || 537.93 || 15/11 ||   ||
-|| 27 || 558.62 ||   ||
+|| 27 || 558.62 || 11/8, 18/13 ||   ||
-|| 28 || 579.31 ||   ||
+|| 28 || 579.31 || 7/5 ||   ||
-|| 29 || 600 ||   ||
+|| 29 || 600 || 17/12, 24/17 ||   ||
-|| 30 || 620.69 ||   ||
+|| 30 || 620.69 || 10/7 ||   ||
-|| 31 || 641.38 ||   ||
+|| 31 || 641.38 || 13/9, 16/11 ||   ||
-|| 32 || 662.07 ||   ||
+|| 32 || 662.07 || 22/15 ||   ||
-|| 33 || 682.76 ||   ||
+|| 33 || 682.76 || 40/27 ||   ||
-|| 34 || 703.45 ||   ||
+|| 34 || 703.45 || 3/2 ||   ||
-|| 35 || 724.14 ||   ||
+|| 35 || 724.14 || 32/21 ||   ||
-|| 36 || 744.83 ||   ||
+|| 36 || 744.83 || 20/13, 26/17, 17/11 ||   ||
-|| 37 || 765.52 ||   ||
+|| 37 || 765.52 || 14/9 ||   ||
-|| 38 || 786.21 ||   ||
+|| 38 || 786.21 || 11/7 ||   ||
-|| 39 || 806.9 ||   ||
+|| 39 || 806.9 || 8/5 ||   ||
-|| 40 || 827.59 ||   ||
+|| 40 || 827.59 ||   ||   ||
-|| 41 || 848.28 ||   ||
+|| 41 || 848.28 || 13/8, 18/11 ||   ||
-|| 42 || 868.97 ||   ||
+|| 42 || 868.97 ||   ||   ||
-|| 43 || 889.66 ||   ||
+|| 43 || 889.66 ||   ||   ||
-|| 44 || 910.34 ||   ||
+|| 44 || 910.34 ||   ||   ||
-|| 45 || 931.03 ||   ||
+|| 45 || 931.03 ||   ||   ||
-|| 46 || 951.72 ||   ||
+|| 46 || 951.72 ||   ||   ||
-|| 47 || 972.41 ||   ||
+|| 47 || 972.41 || 7/4 ||   ||
-|| 48 || 993.1 ||   ||
+|| 48 || 993.1 || 16/9 ||   ||
-|| 49 || 1013.79 ||   ||
+|| 49 || 1013.79 || 9/5 ||   ||
-|| 50 || 1034.48 ||   ||
+|| 50 || 1034.48 ||   ||   ||
-|| 51 || 1055.17 ||   ||
+|| 51 || 1055.17 ||   ||   ||
-|| 52 || 1075.86 ||   ||
+|| 52 || 1075.86 ||   ||   ||
-|| 53 || 1096.55 ||   ||
+|| 53 || 1096.55 ||   ||   ||
-|| 54 || 1117.24 ||   ||
+|| 54 || 1117.24 ||   ||   ||
-|| 55 || 1137.93 ||   ||
+|| 55 || 1137.93 ||   ||   ||
-|| 56 || 1158.62 ||   ||
+|| 56 || 1158.62 ||   ||   ||
-|| 57 || 1179.31 ||   ||</pre></div>
+|| 57 || 1179.31 ||   ||   ||</pre></div>
 <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="/Genesis%20scale"&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="/mystery"&gt;mystery&lt;/a&gt;, &lt;a class="wiki_link" href="/buzzard"&gt;buzzard&lt;/a&gt; and &lt;a class="wiki_link" href="/thuja"&gt;thuja&lt;/a&gt; &lt;a class="wiki_link" href="/temperament"&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;
@@ Line 93: / Line 93: @@
 &lt;/td&gt;
          &lt;td&gt;cents value&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;ratios&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;associated temperament&lt;br /&gt;
@@ Line 101: / Line 103: @@
 &lt;/td&gt;
          &lt;td&gt;0.00&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1/1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 109: / Line 113: @@
 &lt;/td&gt;
          &lt;td&gt;20.69&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;56/55, 64/63, 81/80, 128/125&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 117: / Line 123: @@
 &lt;/td&gt;
          &lt;td&gt;41.38&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;36/35, 49/48, 50/49, 55/54&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 125: / Line 133: @@
 &lt;/td&gt;
          &lt;td&gt;62.07&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;25/24, 26/25, 27/26, 28/27, 33/32&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 133: / Line 143: @@
 &lt;/td&gt;
          &lt;td&gt;82.76&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21/20, 22/21&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 141: / Line 153: @@
 &lt;/td&gt;
          &lt;td&gt;103.45&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;16/15, 17/16, 18/17&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 149: / Line 163: @@
 &lt;/td&gt;
          &lt;td&gt;124.14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14/13, 15/14, 27/25&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 157: / Line 173: @@
 &lt;/td&gt;
          &lt;td&gt;144.83&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;12/11, 13/12&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 165: / Line 183: @@
 &lt;/td&gt;
          &lt;td&gt;165.52&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11/10&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 173: / Line 193: @@
 &lt;/td&gt;
          &lt;td&gt;186.21&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;10/9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 181: / Line 203: @@
 &lt;/td&gt;
          &lt;td&gt;206.9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9/8, 17/15&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 189: / Line 213: @@
 &lt;/td&gt;
          &lt;td&gt;227.59&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8/7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 197: / Line 223: @@
 &lt;/td&gt;
          &lt;td&gt;248.28&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;15/13&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 205: / Line 233: @@
 &lt;/td&gt;
          &lt;td&gt;268.97&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7/6&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 213: / Line 243: @@
 &lt;/td&gt;
          &lt;td&gt;289.66&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13/11, 20/17&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 222: / Line 254: @@
          &lt;td&gt;310.34&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;6/5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Myna&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 229: / Line 263: @@
 &lt;/td&gt;
          &lt;td&gt;331.03&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;17/14&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 237: / Line 273: @@
 &lt;/td&gt;
          &lt;td&gt;351.72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11/9, 16/13&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 245: / Line 283: @@
 &lt;/td&gt;
          &lt;td&gt;372.41&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21/17&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 253: / Line 293: @@
 &lt;/td&gt;
          &lt;td&gt;393.1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5/4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 261: / Line 303: @@
 &lt;/td&gt;
          &lt;td&gt;413.79&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14/11&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 269: / Line 313: @@
 &lt;/td&gt;
          &lt;td&gt;434.48&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9/7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 277: / Line 323: @@
 &lt;/td&gt;
          &lt;td&gt;455.17&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13/10, 17/13, 22/17&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 285: / Line 333: @@
 &lt;/td&gt;
          &lt;td&gt;475.86&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21/16&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 293: / Line 343: @@
 &lt;/td&gt;
          &lt;td&gt;496.55&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4/3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 301: / Line 353: @@
 &lt;/td&gt;
          &lt;td&gt;517.24&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;27/20&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 309: / Line 363: @@
 &lt;/td&gt;
          &lt;td&gt;537.93&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;15/11&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 317: / Line 373: @@
 &lt;/td&gt;
          &lt;td&gt;558.62&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11/8, 18/13&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 325: / Line 383: @@
 &lt;/td&gt;
          &lt;td&gt;579.31&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7/5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 333: / Line 393: @@
 &lt;/td&gt;
          &lt;td&gt;600&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;17/12, 24/17&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 341: / Line 403: @@
 &lt;/td&gt;
          &lt;td&gt;620.69&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;10/7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 349: / Line 413: @@
 &lt;/td&gt;
          &lt;td&gt;641.38&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13/9, 16/11&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 357: / Line 423: @@
 &lt;/td&gt;
          &lt;td&gt;662.07&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;22/15&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 365: / Line 433: @@
 &lt;/td&gt;
          &lt;td&gt;682.76&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;40/27&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 373: / Line 443: @@
 &lt;/td&gt;
          &lt;td&gt;703.45&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3/2&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 381: / Line 453: @@
 &lt;/td&gt;
          &lt;td&gt;724.14&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;32/21&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 389: / Line 463: @@
 &lt;/td&gt;
          &lt;td&gt;744.83&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;20/13, 26/17, 17/11&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 397: / Line 473: @@
 &lt;/td&gt;
          &lt;td&gt;765.52&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14/9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 405: / Line 483: @@
 &lt;/td&gt;
          &lt;td&gt;786.21&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11/7&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 413: / Line 493: @@
 &lt;/td&gt;
          &lt;td&gt;806.9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8/5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 421: / Line 503: @@
 &lt;/td&gt;
          &lt;td&gt;827.59&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 429: / Line 513: @@
 &lt;/td&gt;
          &lt;td&gt;848.28&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13/8, 18/11&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 437: / Line 523: @@
 &lt;/td&gt;
          &lt;td&gt;868.97&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 445: / Line 533: @@
 &lt;/td&gt;
          &lt;td&gt;889.66&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 453: / Line 543: @@
 &lt;/td&gt;
          &lt;td&gt;910.34&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 461: / Line 553: @@
 &lt;/td&gt;
          &lt;td&gt;931.03&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 469: / Line 563: @@
 &lt;/td&gt;
          &lt;td&gt;951.72&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 477: / Line 573: @@
 &lt;/td&gt;
          &lt;td&gt;972.41&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7/4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 485: / Line 583: @@
 &lt;/td&gt;
          &lt;td&gt;993.1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;16/9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 493: / Line 593: @@
 &lt;/td&gt;
          &lt;td&gt;1013.79&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9/5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 501: / Line 603: @@
 &lt;/td&gt;
          &lt;td&gt;1034.48&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 509: / Line 613: @@
 &lt;/td&gt;
          &lt;td&gt;1055.17&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 517: / Line 623: @@
 &lt;/td&gt;
          &lt;td&gt;1075.86&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 525: / Line 633: @@
 &lt;/td&gt;
          &lt;td&gt;1096.55&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 533: / Line 643: @@
 &lt;/td&gt;
          &lt;td&gt;1117.24&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 541: / Line 653: @@
 &lt;/td&gt;
          &lt;td&gt;1137.93&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 549: / Line 663: @@
 &lt;/td&gt;
          &lt;td&gt;1158.62&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 557: / Line 673: @@
 &lt;/td&gt;
          &lt;td&gt;1179.31&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;

58edo: Difference between revisions

Revision as of 08:36, 13 July 2012

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