57edo: Difference between revisions

Revision as of 12:53, 19 March 2011

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This revision was by author genewardsmith and made on 2011-03-19 12:53:38 UTC.

The original revision id was 211993418.

The revision comment was:

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=<span style="color: #006118;">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.

[[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 ||

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;">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.<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>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>

</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>2011-03-18 18:48:57 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-19 12:53:38 UTC</tt>.<br>
-: The original revision id was <tt>211901286</tt>.<br>
+: The original revision id was <tt>211993418</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 8: / Line 8: @@
 <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">=&lt;span style="color: #006118;"&gt;57 tone equal temperament&lt;/span&gt;=
-//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]].
+//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&amp;57 temperament.
 [[5-limit]] [[comma]]s: 81/80, 3125/3072
@@ Line 78: / Line 78: @@
 <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;57edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x57 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #006118;"&gt;57 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
   &lt;br /&gt;
-&lt;em&gt;57edo&lt;/em&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 57 parts of size 21.053. It can be used to tune &lt;a class="wiki_link" href="/mothra%20temperament"&gt;mothra temperament&lt;/a&gt;, and is an excellent tuning for the 2.5/3.7.11.13.17.19 &lt;a class="wiki_link" href="/just%20intonation%20subgroup"&gt;just intonation subgroup&lt;/a&gt;.&lt;br /&gt;
+&lt;em&gt;57edo&lt;/em&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 57 parts of size 21.053. It can be used to tune &lt;a class="wiki_link" href="/mothra%20temperament"&gt;mothra temperament&lt;/a&gt;, and is an excellent tuning for the 2.5/3.7.11.13.17.19 &lt;a class="wiki_link" href="/just%20intonation%20subgroup"&gt;just intonation subgroup&lt;/a&gt;. One way to describe 57 is that it has a &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; 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 &lt;a class="wiki_link" href="/19-limit"&gt;19-limit&lt;/a&gt; 46&amp;amp;57 temperament.&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;s: 81/80, 3125/3072&lt;br /&gt;

57edo: Difference between revisions

Revision as of 12:53, 19 March 2011

IMPORTED REVISION FROM WIKISPACES

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