43edo: Difference between revisions

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Wikispaces>genewardsmith
**Imported revision 312141768 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 312142276 - Original comment: **
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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>2012-03-18 15:19:59 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-03-18 15:21:58 UTC</tt>.<br>
: The original revision id was <tt>312141768</tt>.<br>
: The original revision id was <tt>312142276</tt>.<br>
: The revision comment was: <tt></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>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
Line 20: Line 20:
|| Degrees of 43-EDO || Cents value ||
|| Degrees of 43-EDO || Cents value ||
|| 0 || 0 ||
|| 0 || 0 ||
|| 1 || 27,907 ||
|| 1 || 27.907 ||
|| 2 || 55,814 ||
|| 2 || 55.814 ||
|| 3 || 83,721 ||
|| 3 || 83.721 ||
|| 4 || 111,628 ||
|| 4 || 111.628 ||
|| 5 || 139,535 ||
|| 5 || 139.535 ||
|| 6 || 167,442 ||
|| 6 || 167.442 ||
|| 7 || 195,349 ||
|| 7 || 195.349 ||
|| 8 || 223,256 ||
|| 8 || 223.256 ||
|| 9 || 251,163 ||
|| 9 || 251.163 ||
|| 10 || 279,07 ||
|| 10 || 279.07 ||
|| 11 || 306,977 ||
|| 11 || 306.977 ||
|| 12 || 334,884 ||
|| 12 || 334.884 ||
|| 13 || 362,791 ||
|| 13 || 362.791 ||
|| 14 || 390,698 ||
|| 14 || 390.698 ||
|| 15 || 418,605 ||
|| 15 || 418.605 ||
|| 16 || 446,512 ||
|| 16 || 446.512 ||
|| 17 || 474,419 ||
|| 17 || 474.419 ||
|| 18 || 502,326 ||
|| 18 || 502.326 ||
|| 19 || 530,233 ||
|| 19 || 530.233 ||
|| 20 || 558,139 ||
|| 20 || 558.139 ||
|| 21 || 586,046 ||
|| 21 || 586.046 ||
|| 22 || 613,953 ||
|| 22 || 613.953 ||
|| 23 || 641,86 ||
|| 23 || 641.86 ||
|| 24 || 669,767 ||
|| 24 || 669.767 ||
|| 25 || 697,674 ||
|| 25 || 697.674 ||
|| 26 || 725,581 ||
|| 26 || 725.581 ||
|| 27 || 753,488 ||
|| 27 || 753.488 ||
|| 28 || 781,395 ||
|| 28 || 781.395 ||
|| 29 || 809,302 ||
|| 29 || 809.302 ||
|| 30 || 837,209 ||
|| 30 || 837.209 ||
|| 31 || 865,116 ||
|| 31 || 865.116 ||
|| 32 || 893,023 ||
|| 32 || 893.023 ||
|| 33 || 920,93 ||
|| 33 || 920.93 ||
|| 34 || 948,837 ||
|| 34 || 948.837 ||
|| 35 || 976,744 ||
|| 35 || 976.744 ||
|| 36 || 1004,651 ||
|| 36 || 1004.651 ||
|| 37 || 1032,558 ||
|| 37 || 1032.558 ||
|| 38 || 1060,465 ||
|| 38 || 1060.465 ||
|| 39 || 1088,372 ||
|| 39 || 1088.372 ||
|| 40 || 1116,279 ||
|| 40 || 1116.279 ||
|| 41 || 1144,186 ||
|| 41 || 1144.186 ||
|| 42 || 1172,093 ||
|| 42 || 1172.093 ||




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         &lt;td&gt;83,721&lt;br /&gt;
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         &lt;td&gt;167,442&lt;br /&gt;
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         &lt;td&gt;7&lt;br /&gt;
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         &lt;td&gt;195,349&lt;br /&gt;
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         &lt;td&gt;8&lt;br /&gt;
         &lt;td&gt;8&lt;br /&gt;
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         &lt;td&gt;223,256&lt;br /&gt;
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         &lt;td&gt;9&lt;br /&gt;
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         &lt;td&gt;251,163&lt;br /&gt;
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         &lt;td&gt;10&lt;br /&gt;
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         &lt;td&gt;279,07&lt;br /&gt;
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         &lt;td&gt;11&lt;br /&gt;
         &lt;td&gt;11&lt;br /&gt;
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         &lt;td&gt;306,977&lt;br /&gt;
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         &lt;td&gt;12&lt;br /&gt;
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         &lt;td&gt;334,884&lt;br /&gt;
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         &lt;td&gt;13&lt;br /&gt;
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         &lt;td&gt;362,791&lt;br /&gt;
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         &lt;td&gt;14&lt;br /&gt;
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         &lt;td&gt;390,698&lt;br /&gt;
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         &lt;td&gt;15&lt;br /&gt;
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         &lt;td&gt;418,605&lt;br /&gt;
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         &lt;td&gt;16&lt;br /&gt;
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         &lt;td&gt;446,512&lt;br /&gt;
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         &lt;td&gt;17&lt;br /&gt;
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         &lt;td&gt;18&lt;br /&gt;
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         &lt;td&gt;502,326&lt;br /&gt;
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         &lt;td&gt;19&lt;br /&gt;
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         &lt;td&gt;530,233&lt;br /&gt;
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         &lt;td&gt;20&lt;br /&gt;
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         &lt;td&gt;558,139&lt;br /&gt;
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         &lt;td&gt;21&lt;br /&gt;
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         &lt;td&gt;586,046&lt;br /&gt;
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         &lt;td&gt;22&lt;br /&gt;
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         &lt;td&gt;613,953&lt;br /&gt;
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         &lt;td&gt;23&lt;br /&gt;
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         &lt;td&gt;641,86&lt;br /&gt;
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         &lt;td&gt;24&lt;br /&gt;
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         &lt;td&gt;669,767&lt;br /&gt;
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         &lt;td&gt;25&lt;br /&gt;
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         &lt;td&gt;26&lt;br /&gt;
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         &lt;td&gt;725,581&lt;br /&gt;
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         &lt;td&gt;27&lt;br /&gt;
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         &lt;td&gt;753,488&lt;br /&gt;
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         &lt;td&gt;28&lt;br /&gt;
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         &lt;td&gt;781,395&lt;br /&gt;
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     &lt;/tr&gt;
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         &lt;td&gt;29&lt;br /&gt;
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         &lt;td&gt;809,302&lt;br /&gt;
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     &lt;/tr&gt;
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         &lt;td&gt;30&lt;br /&gt;
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         &lt;td&gt;837,209&lt;br /&gt;
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     &lt;/tr&gt;
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         &lt;td&gt;31&lt;br /&gt;
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         &lt;td&gt;865,116&lt;br /&gt;
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     &lt;/tr&gt;
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         &lt;td&gt;32&lt;br /&gt;
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         &lt;td&gt;893,023&lt;br /&gt;
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         &lt;td&gt;33&lt;br /&gt;
         &lt;td&gt;33&lt;br /&gt;
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         &lt;td&gt;920,93&lt;br /&gt;
         &lt;td&gt;920.93&lt;br /&gt;
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     &lt;/tr&gt;
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         &lt;td&gt;34&lt;br /&gt;
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         &lt;td&gt;948,837&lt;br /&gt;
         &lt;td&gt;948.837&lt;br /&gt;
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         &lt;td&gt;35&lt;br /&gt;
         &lt;td&gt;35&lt;br /&gt;
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&lt;/td&gt;
         &lt;td&gt;976,744&lt;br /&gt;
         &lt;td&gt;976.744&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
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         &lt;td&gt;36&lt;br /&gt;
         &lt;td&gt;36&lt;br /&gt;
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&lt;/td&gt;
         &lt;td&gt;1004,651&lt;br /&gt;
         &lt;td&gt;1004.651&lt;br /&gt;
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     &lt;/tr&gt;
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         &lt;td&gt;37&lt;br /&gt;
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         &lt;td&gt;1032,558&lt;br /&gt;
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         &lt;td&gt;38&lt;br /&gt;
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         &lt;td&gt;1060,465&lt;br /&gt;
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         &lt;td&gt;39&lt;br /&gt;
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         &lt;td&gt;1088,372&lt;br /&gt;
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         &lt;td&gt;40&lt;br /&gt;
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     &lt;/tr&gt;
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         &lt;td&gt;41&lt;br /&gt;
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&lt;/td&gt;
         &lt;td&gt;1144,186&lt;br /&gt;
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         &lt;td&gt;42&lt;br /&gt;
         &lt;td&gt;42&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;1172,093&lt;br /&gt;
         &lt;td&gt;1172.093&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;

Revision as of 15:21, 18 March 2012

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2012-03-18 15:21:58 UTC.
The original revision id was 312142276.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

=<span style="color: #027bac; font-size: 103%;">43 tone equal temperament</span>= 
= = 
//43edo// divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, particularly 1/5 comma meantone, being a good tuning system in the 5, 7, 11, and 13-limit. The version of 11-limit meantone is the one tempering out 99/98, 176/175 and 441/440 sometimes called Huygens. 43-equal has the first good 13-limit meantone available as an equal division of the octave. The baroque, french, ironically hearing and speech impaired acoustician [[@http://en.wikipedia.org/wiki/Joseph_Sauveur|Joseph Saveur]] based his system on 43 equal tones to the octave, calling them "merides". Further information: [[http://tonalsoft.com/enc/m/meride.aspx]]

In the 13-limit, we get two versions of meantone equivalent in 43et, one, [[Meantone family#Septimal meantone-Unidecimal meantone aka Huygens-Meridetone|meridetone]], tempering out 78/77, the other, [[Meantone family#Septimal meantone-Unidecimal meantone aka Huygens-Grosstone|grosstone]], 144/143. Meridetone has generator mapping <0 1 4 10 18 27|, and grosstone <0 1 4 10 18 -16|; 43 supplies the optimal patent val for meridetone.

The 43 patent val <43 68 100 121 149 169| maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to [[Meantone family#Jerome|jerome temperament]], an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits. It also provides the optimal patent val for 11- and 13-limit [[Marvel temperaments#Amavil|amavil temperament]], which is not a meantone temperament.

43edo is the 14th [[prime numbers|prime]] edo, following [[41edo]] and coming before [[47edo]].

==Intervals== 

|| Degrees of 43-EDO || Cents value ||
|| 0 || 0 ||
|| 1 || 27.907 ||
|| 2 || 55.814 ||
|| 3 || 83.721 ||
|| 4 || 111.628 ||
|| 5 || 139.535 ||
|| 6 || 167.442 ||
|| 7 || 195.349 ||
|| 8 || 223.256 ||
|| 9 || 251.163 ||
|| 10 || 279.07 ||
|| 11 || 306.977 ||
|| 12 || 334.884 ||
|| 13 || 362.791 ||
|| 14 || 390.698 ||
|| 15 || 418.605 ||
|| 16 || 446.512 ||
|| 17 || 474.419 ||
|| 18 || 502.326 ||
|| 19 || 530.233 ||
|| 20 || 558.139 ||
|| 21 || 586.046 ||
|| 22 || 613.953 ||
|| 23 || 641.86 ||
|| 24 || 669.767 ||
|| 25 || 697.674 ||
|| 26 || 725.581 ||
|| 27 || 753.488 ||
|| 28 || 781.395 ||
|| 29 || 809.302 ||
|| 30 || 837.209 ||
|| 31 || 865.116 ||
|| 32 || 893.023 ||
|| 33 || 920.93 ||
|| 34 || 948.837 ||
|| 35 || 976.744 ||
|| 36 || 1004.651 ||
|| 37 || 1032.558 ||
|| 38 || 1060.465 ||
|| 39 || 1088.372 ||
|| 40 || 1116.279 ||
|| 41 || 1144.186 ||
|| 42 || 1172.093 ||


[[http://xenharmonic.wikispaces.com/file/view/43%20edo%20counterpoint.mid|43 edo counterpoint.mid]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Kosmorsky/43%20edo%20counterpoint.mp3|mp3]] Peter Kosmorsky (late 2011)

Original HTML content:

<html><head><title>43edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x43 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #027bac; font-size: 103%;">43 tone equal temperament</span></h1>
 <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><!-- ws:end:WikiTextHeadingRule:2 --> </h1>
 <em>43edo</em> divides the octave into 43 equal parts of 27.907 cents each. It is strongly associated with meantone temperament, particularly 1/5 comma meantone, being a good tuning system in the 5, 7, 11, and 13-limit. The version of 11-limit meantone is the one tempering out 99/98, 176/175 and 441/440 sometimes called Huygens. 43-equal has the first good 13-limit meantone available as an equal division of the octave. The baroque, french, ironically hearing and speech impaired acoustician <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Joseph_Sauveur" rel="nofollow" target="_blank">Joseph Saveur</a> based his system on 43 equal tones to the octave, calling them &quot;merides&quot;. Further information: <a class="wiki_link_ext" href="http://tonalsoft.com/enc/m/meride.aspx" rel="nofollow">http://tonalsoft.com/enc/m/meride.aspx</a><br />
<br />
In the 13-limit, we get two versions of meantone equivalent in 43et, one, <a class="wiki_link" href="/Meantone%20family#Septimal meantone-Unidecimal meantone aka Huygens-Meridetone">meridetone</a>, tempering out 78/77, the other, <a class="wiki_link" href="/Meantone%20family#Septimal meantone-Unidecimal meantone aka Huygens-Grosstone">grosstone</a>, 144/143. Meridetone has generator mapping &lt;0 1 4 10 18 27|, and grosstone &lt;0 1 4 10 18 -16|; 43 supplies the optimal patent val for meridetone.<br />
<br />
The 43 patent val &lt;43 68 100 121 149 169| maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to <a class="wiki_link" href="/Meantone%20family#Jerome">jerome temperament</a>, an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits. It also provides the optimal patent val for 11- and 13-limit <a class="wiki_link" href="/Marvel%20temperaments#Amavil">amavil temperament</a>, which is not a meantone temperament.<br />
<br />
43edo is the 14th <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/41edo">41edo</a> and coming before <a class="wiki_link" href="/47edo">47edo</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x43 tone equal temperament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h2>
 <br />


<table class="wiki_table">
    <tr>
        <td>Degrees of 43-EDO<br />
</td>
        <td>Cents value<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>27.907<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>55.814<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>83.721<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>111.628<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>139.535<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>167.442<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>195.349<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>223.256<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>251.163<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>279.07<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>306.977<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>334.884<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>362.791<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>390.698<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>418.605<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>446.512<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>474.419<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>502.326<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>530.233<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>558.139<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>586.046<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>613.953<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>641.86<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>669.767<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>697.674<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>725.581<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>753.488<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>781.395<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>809.302<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>837.209<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>865.116<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>893.023<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>920.93<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>948.837<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>976.744<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>1004.651<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>1032.558<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>1060.465<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>1088.372<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>1116.279<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>1144.186<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>1172.093<br />
</td>
    </tr>
</table>

<br />
<br />
<a href="http://xenharmonic.wikispaces.com/file/view/43%20edo%20counterpoint.mid">43 edo counterpoint.mid</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Kosmorsky/43%20edo%20counterpoint.mp3" rel="nofollow">mp3</a> Peter Kosmorsky (late 2011)</body></html>