36edo: Difference between revisions

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[[toc|flat]]
36edo, by definition, divides the 2:1 octave into 36 equal steps, each of which is exactly 33.333... cents.

36 is a highly composite number, factoring into 2x2x3x3. Since 36 is divisible by 12, it contains the overly-familiar [[12edo]] as a subset. It divides 12edo's 100-cent half step into three microtonal step of approximately 33 cents, which could be called "sixth tones." 36edo also contains [[18edo]] ("third tones") and [[9edo]] ("two-thirds tones") as subsets, not to mention the [[6edo]] whole tone scale, [[4edo]] full-diminished seventh chord, and the [[3edo]] augmented triad, all of which are present in 12edo.

That 36edo contains 12edo as a subset makes in compatible with traditional instruments tuned to 12edo. By tuning one 12-edo instrument up or down about 33 cents, one can arrive at a 24-tone subset of 36 edo (see, for instance, Jacob Barton's piece for two clarinets, [[http://www.jacobbarton.net/2010/02/de-quinin-for-two-clarinets/|De-quinin']]). Three 12edo instruments could play the entire gamut.

=As a harmonic temperament= 

For those interested in approximations to just intonation, 36edo offers no improvement over 12edo in the 5-limit, since its nearest approximation to 5:4 is the overly-familiar 400-cent sharp third. However, it excels at approximations involving 3 and 7. As a 3 and 7 tuning, or in other words as a tuning for the 2.3.7 [[just intonation subgroup]], 36edo's single degree of around 33 cents serves a double function as 49:48, the so-called [[http://en.wikipedia.org/wiki/Septimal_diesis|Slendro diesis]] of around 36 cents, and as 64:63, the so-called [[http://en.wikipedia.org/wiki/Septimal_comma|septimal comma]] of around 27 cents. Meanwhile, its second degree functions as 28:27, the so-called [[http://en.wikipedia.org/wiki/Septimal_third-tone|Septimal third-tone]] (which = 49:48 x 64:63). The 2.3.7 subgroup can be extended to the [[k*N subgroups|2*36 subgroup]] 2.3.25.7.55.13.17, and on this subgroup it tempers out the same commas as [[72edo]] does in the full [[17-limit]].

36 tempers out, like 12, 81/80, 128/125 and 648/625 in the 5-limit. It departs from 12 in the 7-limit, tempering out 686/675, and as a no-fives temperament, 1029/1024 and 118098/117649. In the 11-limit, it tempers out 56/55, 245/242 and 540/539, and is the [[optimal patent val]] for the rank four temperament tempering out 56/55, as well as the rank three temperament [[Didymus rank three family|melpomene]] tempering out 81/80 and 56/55. In the 13-limit, it tempers out 78/77, in the 17-limit 51/50, and in the 19-limit 76/75, 91/90 and 96/95.

As a 5-limit temperament, the patent val for 36edo is [[Wedgies and Multivals|contorted]], meaning there are notes of it which cannot be reached from the unison using only 5-limit intervals. A curious alternative val for the 5-limit is <36 65 116| which is not contorted. It is also a meantone val, in the sense that 81/80 is tempered out. However, the "comma" |29 0 -9> is also tempered out, and the "fifth", 29\36, is actually approximately 7/4, whereas the "major third", 44\36, is actually approximately 7/3. Any 5-limit musical piece or scale which is a [[transversal]] for a meantone piece or scale will be converted to a no-fives piece tempering out 1029/1024 in place of 81/80 by applying this val.

Heinz Bohlen proposed it as a suitable temperament for approximating his 833-cents scale.

=Approximations= 
==3-limit (Pythagorean) approximations (same as 12edo):== 

3/2 = 701.955... cents; 21 degrees of 36edo = 700 cents.
4/3 = 498.045... cents; 15 degrees of 36edo = 500 cents.
9/8 = 203.910... cents; 6 degrees of 36edo = 200 cents.
16/9 = 996.090... cents; 30 degrees of 36edo = 1000 cents.
27/16 = 905.865... cents; 27 degrees of 36edo = 900 cents.
32/27 = 294.135... cents; 9 degrees of 36edo = 300 cents.
81/64 = 407.820... cents; 12 degrees of 36edo = 400 cents.
128/81 = 792.180... cents; 24 degrees of 36edo = 800 cents.


==7-limit approximations:== 

===7 only:=== 
7/4 = 968.826... cents; 29 degrees of 36edo = 966.666... cents.
8/7 = 231.174... cents; 7 degrees of 36edo = 233.333... cents.
49/32 = 737.652... cents; 22 degrees of 36edo = 733.333... cents.
64/49 = 462.348... cents; 14 degrees of 36edo = 466.666... cents.

===3 and 7:=== 
7/6 = 266.871... cents; 8 degrees of 36edo = 266.666... cents.
12/7 = 933.129... cents; 28 degrees of 36 = 933.333... cents.
9/7 = 435.084... cents; 13 degrees of 36edo = 433.333... cents.
14/9 = 764.916... cents; 23 degrees of 36edo = 766.666... cents.
28/27 = 62.961... cents; 2 degrees of 36edo = 66.666... cents.
27/14 = 1137.039... cents; 34 degrees of 36edo = 1133.333... cents.
21/16 = 470.781... cents; 14 degrees of 36edo = 466.666... cents.
32/21 = 729.219... cents; 22 degrees of 36edo = 733.333... cents.
49/48 = 35.697... cents; 1 degree of 36edo = 33.333... cents.
96/49 = 1164.303... cents; 35 degrees of 36edo = 1166.666... cents.
49/36 = 533.742... cents; 16 degrees of 36edo = 533.333... cents.
72/49 = 666.258... cents; 20 degrees of 36edo = 666.666... cents.
64/63 = 27.264... cents; 1 degree of 36edo = 33.333... cents.
63/32 = 1172.736... cents; 35 degrees of 36edo = 1166.666... cents.


And now all that in a table, because tables are good.
||~ Degrees of 36edo ||~ Cents Value ||~ Approx. ratios of 2.3.7 ||
||< 0 ||< 0 ||< 1/1 ||
||< 1 ||< 33.333 ||< 64/63 ~ 49/48 ||
||< 2 ||< 66.667 ||< 28/27 ||
||< 3 ||< 100 ||< 256/243 ||
||< 4 ||< 133.333 ||< 243/224 ||
||< 5 ||< 166.667 ||< 54/49 ||
||< 6 ||< 200 ||< 9/8 ||
||< 7 ||< 233.333 ||< 8/7 ||
||< 8 ||< 266.667 ||< 7/6 ||
||< 9 ||< 300 ||< 32/37 ||
||< 10 ||< 333.333 ||< 98/81 ||
||< 11 ||< 366.667 ||< 243/196 ||
||< 12 ||< 400 ||< 81/64 ||
||< 13 ||< 433.333 ||< 9/7 ||
||< 14 ||< 466.667 ||< 64/49 ~ 21/16 ||
||< 15 ||< 500 ||< 4/3 ||
||< 16 ||< 533.333 ||< 49/36 ||
||< 17 ||< 566.667 ||<   ||
||< 18 ||< 600 ||<   ||
||< 19 ||< 633.333 ||<   ||
||< 20 ||< 666.667 ||< 72/49 ||
||< 21 ||< 700 ||< 3/2 ||
||< 22 ||< 733.333 ||< 49/32 ~ 32/21 ||
||< 23 ||< 766.667 ||< 14/9 ||
||< 24 ||< 800 ||< 128/81 ||
||< 25 ||< 833.333 ||< 392/243 ||
||< 26 ||< 866.667 ||< 81/49 ||
||< 27 ||< 900 ||< 27/16 ||
||< 28 ||< 933.333 ||< 12/7 ||
||< 29 ||< 966.667 ||< 7/4 ||
||< 30 ||< 1000 ||< 16/9 ||
||< 31 ||< 1033.333 ||< 49/27 ||
||< 32 ||< 1066.667 ||< 448/243 ||
||< 33 ||< 1100 ||< 243/128 ||
||< 34 ||< 1133.333 ||< 27/14 ||
||< 35 ||< 1166.667 ||< 63/32 ~ 96/49 ||

=Music= 
* <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/gene_ward_smith/36edo/something.mp3|Something]]</span> by [[Herman Klein]]
* <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/gene_ward_smith/36edo/hay.mp3|Hay]]</span> by [[Joe Hayseed]]
* <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/gene_ward_smith/36edo/boomers.mp3|Boomers]]</span> by [[Ivan Bratt]][[media type="custom" key="9486498"]]
* [[http://micro.soonlabel.com/36edo/20120418-36edo.mp3|Thoughts in Legolas Tuning]] by [[Chris Vaisvil]]

Original HTML content:

<html><head><title>36edo</title></head><body><!-- ws:start:WikiTextTocRule:15:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><a href="#As a harmonic temperament">As a harmonic temperament</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Approximations">Approximations</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: -->
<!-- ws:end:WikiTextTocRule:23 -->36edo, by definition, divides the 2:1 octave into 36 equal steps, each of which is exactly 33.333... cents.<br />
<br />
36 is a highly composite number, factoring into 2x2x3x3. Since 36 is divisible by 12, it contains the overly-familiar <a class="wiki_link" href="/12edo">12edo</a> as a subset. It divides 12edo's 100-cent half step into three microtonal step of approximately 33 cents, which could be called &quot;sixth tones.&quot; 36edo also contains <a class="wiki_link" href="/18edo">18edo</a> (&quot;third tones&quot;) and <a class="wiki_link" href="/9edo">9edo</a> (&quot;two-thirds tones&quot;) as subsets, not to mention the <a class="wiki_link" href="/6edo">6edo</a> whole tone scale, <a class="wiki_link" href="/4edo">4edo</a> full-diminished seventh chord, and the <a class="wiki_link" href="/3edo">3edo</a> augmented triad, all of which are present in 12edo.<br />
<br />
That 36edo contains 12edo as a subset makes in compatible with traditional instruments tuned to 12edo. By tuning one 12-edo instrument up or down about 33 cents, one can arrive at a 24-tone subset of 36 edo (see, for instance, Jacob Barton's piece for two clarinets, <a class="wiki_link_ext" href="http://www.jacobbarton.net/2010/02/de-quinin-for-two-clarinets/" rel="nofollow">De-quinin'</a>). Three 12edo instruments could play the entire gamut.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="As a harmonic temperament"></a><!-- ws:end:WikiTextHeadingRule:1 -->As a harmonic temperament</h1>
 <br />
For those interested in approximations to just intonation, 36edo offers no improvement over 12edo in the 5-limit, since its nearest approximation to 5:4 is the overly-familiar 400-cent sharp third. However, it excels at approximations involving 3 and 7. As a 3 and 7 tuning, or in other words as a tuning for the 2.3.7 <a class="wiki_link" href="/just%20intonation%20subgroup">just intonation subgroup</a>, 36edo's single degree of around 33 cents serves a double function as 49:48, the so-called <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_diesis" rel="nofollow">Slendro diesis</a> of around 36 cents, and as 64:63, the so-called <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_comma" rel="nofollow">septimal comma</a> of around 27 cents. Meanwhile, its second degree functions as 28:27, the so-called <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_third-tone" rel="nofollow">Septimal third-tone</a> (which = 49:48 x 64:63). The 2.3.7 subgroup can be extended to the <a class="wiki_link" href="/k%2AN%20subgroups">2*36 subgroup</a> 2.3.25.7.55.13.17, and on this subgroup it tempers out the same commas as <a class="wiki_link" href="/72edo">72edo</a> does in the full <a class="wiki_link" href="/17-limit">17-limit</a>.<br />
<br />
36 tempers out, like 12, 81/80, 128/125 and 648/625 in the 5-limit. It departs from 12 in the 7-limit, tempering out 686/675, and as a no-fives temperament, 1029/1024 and 118098/117649. In the 11-limit, it tempers out 56/55, 245/242 and 540/539, and is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for the rank four temperament tempering out 56/55, as well as the rank three temperament <a class="wiki_link" href="/Didymus%20rank%20three%20family">melpomene</a> tempering out 81/80 and 56/55. In the 13-limit, it tempers out 78/77, in the 17-limit 51/50, and in the 19-limit 76/75, 91/90 and 96/95.<br />
<br />
As a 5-limit temperament, the patent val for 36edo is <a class="wiki_link" href="/Wedgies%20and%20Multivals">contorted</a>, meaning there are notes of it which cannot be reached from the unison using only 5-limit intervals. A curious alternative val for the 5-limit is &lt;36 65 116| which is not contorted. It is also a meantone val, in the sense that 81/80 is tempered out. However, the &quot;comma&quot; |29 0 -9&gt; is also tempered out, and the &quot;fifth&quot;, 29\36, is actually approximately 7/4, whereas the &quot;major third&quot;, 44\36, is actually approximately 7/3. Any 5-limit musical piece or scale which is a <a class="wiki_link" href="/transversal">transversal</a> for a meantone piece or scale will be converted to a no-fives piece tempering out 1029/1024 in place of 81/80 by applying this val.<br />
<br />
Heinz Bohlen proposed it as a suitable temperament for approximating his 833-cents scale.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc1"><a name="Approximations"></a><!-- ws:end:WikiTextHeadingRule:3 -->Approximations</h1>
 <!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="Approximations-3-limit (Pythagorean) approximations (same as 12edo):"></a><!-- ws:end:WikiTextHeadingRule:5 -->3-limit (Pythagorean) approximations (same as 12edo):</h2>
 <br />
3/2 = 701.955... cents; 21 degrees of 36edo = 700 cents.<br />
4/3 = 498.045... cents; 15 degrees of 36edo = 500 cents.<br />
9/8 = 203.910... cents; 6 degrees of 36edo = 200 cents.<br />
16/9 = 996.090... cents; 30 degrees of 36edo = 1000 cents.<br />
27/16 = 905.865... cents; 27 degrees of 36edo = 900 cents.<br />
32/27 = 294.135... cents; 9 degrees of 36edo = 300 cents.<br />
81/64 = 407.820... cents; 12 degrees of 36edo = 400 cents.<br />
128/81 = 792.180... cents; 24 degrees of 36edo = 800 cents.<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:7:&lt;h2&gt; --><h2 id="toc3"><a name="Approximations-7-limit approximations:"></a><!-- ws:end:WikiTextHeadingRule:7 -->7-limit approximations:</h2>
 <br />
<!-- ws:start:WikiTextHeadingRule:9:&lt;h3&gt; --><h3 id="toc4"><a name="Approximations-7-limit approximations:-7 only:"></a><!-- ws:end:WikiTextHeadingRule:9 -->7 only:</h3>
 7/4 = 968.826... cents; 29 degrees of 36edo = 966.666... cents.<br />
8/7 = 231.174... cents; 7 degrees of 36edo = 233.333... cents.<br />
49/32 = 737.652... cents; 22 degrees of 36edo = 733.333... cents.<br />
64/49 = 462.348... cents; 14 degrees of 36edo = 466.666... cents.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:11:&lt;h3&gt; --><h3 id="toc5"><a name="Approximations-7-limit approximations:-3 and 7:"></a><!-- ws:end:WikiTextHeadingRule:11 -->3 and 7:</h3>
 7/6 = 266.871... cents; 8 degrees of 36edo = 266.666... cents.<br />
12/7 = 933.129... cents; 28 degrees of 36 = 933.333... cents.<br />
9/7 = 435.084... cents; 13 degrees of 36edo = 433.333... cents.<br />
14/9 = 764.916... cents; 23 degrees of 36edo = 766.666... cents.<br />
28/27 = 62.961... cents; 2 degrees of 36edo = 66.666... cents.<br />
27/14 = 1137.039... cents; 34 degrees of 36edo = 1133.333... cents.<br />
21/16 = 470.781... cents; 14 degrees of 36edo = 466.666... cents.<br />
32/21 = 729.219... cents; 22 degrees of 36edo = 733.333... cents.<br />
49/48 = 35.697... cents; 1 degree of 36edo = 33.333... cents.<br />
96/49 = 1164.303... cents; 35 degrees of 36edo = 1166.666... cents.<br />
49/36 = 533.742... cents; 16 degrees of 36edo = 533.333... cents.<br />
72/49 = 666.258... cents; 20 degrees of 36edo = 666.666... cents.<br />
64/63 = 27.264... cents; 1 degree of 36edo = 33.333... cents.<br />
63/32 = 1172.736... cents; 35 degrees of 36edo = 1166.666... cents.<br />
<br />
<br />
And now all that in a table, because tables are good.<br />


<table class="wiki_table">
    <tr>
        <th>Degrees of 36edo<br />
</th>
        <th>Cents Value<br />
</th>
        <th>Approx. ratios of 2.3.7<br />
</th>
    </tr>
    <tr>
        <td style="text-align: left;">0<br />
</td>
        <td style="text-align: left;">0<br />
</td>
        <td style="text-align: left;">1/1<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">1<br />
</td>
        <td style="text-align: left;">33.333<br />
</td>
        <td style="text-align: left;">64/63 ~ 49/48<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">2<br />
</td>
        <td style="text-align: left;">66.667<br />
</td>
        <td style="text-align: left;">28/27<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">3<br />
</td>
        <td style="text-align: left;">100<br />
</td>
        <td style="text-align: left;">256/243<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">4<br />
</td>
        <td style="text-align: left;">133.333<br />
</td>
        <td style="text-align: left;">243/224<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">5<br />
</td>
        <td style="text-align: left;">166.667<br />
</td>
        <td style="text-align: left;">54/49<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">6<br />
</td>
        <td style="text-align: left;">200<br />
</td>
        <td style="text-align: left;">9/8<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">7<br />
</td>
        <td style="text-align: left;">233.333<br />
</td>
        <td style="text-align: left;">8/7<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">8<br />
</td>
        <td style="text-align: left;">266.667<br />
</td>
        <td style="text-align: left;">7/6<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">9<br />
</td>
        <td style="text-align: left;">300<br />
</td>
        <td style="text-align: left;">32/37<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">10<br />
</td>
        <td style="text-align: left;">333.333<br />
</td>
        <td style="text-align: left;">98/81<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">11<br />
</td>
        <td style="text-align: left;">366.667<br />
</td>
        <td style="text-align: left;">243/196<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">12<br />
</td>
        <td style="text-align: left;">400<br />
</td>
        <td style="text-align: left;">81/64<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">13<br />
</td>
        <td style="text-align: left;">433.333<br />
</td>
        <td style="text-align: left;">9/7<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">14<br />
</td>
        <td style="text-align: left;">466.667<br />
</td>
        <td style="text-align: left;">64/49 ~ 21/16<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">15<br />
</td>
        <td style="text-align: left;">500<br />
</td>
        <td style="text-align: left;">4/3<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">16<br />
</td>
        <td style="text-align: left;">533.333<br />
</td>
        <td style="text-align: left;">49/36<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">17<br />
</td>
        <td style="text-align: left;">566.667<br />
</td>
        <td style="text-align: left;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">18<br />
</td>
        <td style="text-align: left;">600<br />
</td>
        <td style="text-align: left;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">19<br />
</td>
        <td style="text-align: left;">633.333<br />
</td>
        <td style="text-align: left;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">20<br />
</td>
        <td style="text-align: left;">666.667<br />
</td>
        <td style="text-align: left;">72/49<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">21<br />
</td>
        <td style="text-align: left;">700<br />
</td>
        <td style="text-align: left;">3/2<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">22<br />
</td>
        <td style="text-align: left;">733.333<br />
</td>
        <td style="text-align: left;">49/32 ~ 32/21<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">23<br />
</td>
        <td style="text-align: left;">766.667<br />
</td>
        <td style="text-align: left;">14/9<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">24<br />
</td>
        <td style="text-align: left;">800<br />
</td>
        <td style="text-align: left;">128/81<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">25<br />
</td>
        <td style="text-align: left;">833.333<br />
</td>
        <td style="text-align: left;">392/243<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">26<br />
</td>
        <td style="text-align: left;">866.667<br />
</td>
        <td style="text-align: left;">81/49<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">27<br />
</td>
        <td style="text-align: left;">900<br />
</td>
        <td style="text-align: left;">27/16<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">28<br />
</td>
        <td style="text-align: left;">933.333<br />
</td>
        <td style="text-align: left;">12/7<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">29<br />
</td>
        <td style="text-align: left;">966.667<br />
</td>
        <td style="text-align: left;">7/4<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">30<br />
</td>
        <td style="text-align: left;">1000<br />
</td>
        <td style="text-align: left;">16/9<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">31<br />
</td>
        <td style="text-align: left;">1033.333<br />
</td>
        <td style="text-align: left;">49/27<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">32<br />
</td>
        <td style="text-align: left;">1066.667<br />
</td>
        <td style="text-align: left;">448/243<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">33<br />
</td>
        <td style="text-align: left;">1100<br />
</td>
        <td style="text-align: left;">243/128<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">34<br />
</td>
        <td style="text-align: left;">1133.333<br />
</td>
        <td style="text-align: left;">27/14<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">35<br />
</td>
        <td style="text-align: left;">1166.667<br />
</td>
        <td style="text-align: left;">63/32 ~ 96/49<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc6"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:13 -->Music</h1>
 <ul><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/36edo/something.mp3" rel="nofollow">Something</a></span> by <a class="wiki_link" href="/Herman%20Klein">Herman Klein</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/36edo/hay.mp3" rel="nofollow">Hay</a></span> by <a class="wiki_link" href="/Joe%20Hayseed">Joe Hayseed</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/36edo/boomers.mp3" rel="nofollow">Boomers</a></span> by <a class="wiki_link" href="/Ivan%20Bratt">Ivan Bratt</a><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/9486498?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;9486498&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js">
</script><!-- ws:end:WikiTextMediaRule:0 --></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/36edo/20120418-36edo.mp3" rel="nofollow">Thoughts in Legolas Tuning</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li></ul></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:hearneg|hearneg]] and made on <tt>2014-01-21 01:33:15 UTC</tt>.<br>
+: This revision was by author [[User:hearneg|hearneg]] and made on <tt>2014-01-21 01:40:29 UTC</tt>.<br>
-: The original revision id was <tt>484175766</tt>.<br>
+: The original revision id was <tt>484176514</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 67: / Line 67: @@
 ||&lt; 2 ||&lt; 66.667 ||&lt; 28/27 ||
 ||&lt; 3 ||&lt; 100 ||&lt; 256/243 ||
-||&lt; 4 ||&lt; 133.333 ||&lt;   ||
+||&lt; 4 ||&lt; 133.333 ||&lt; 243/224 ||
-||&lt; 5 ||&lt; 166.667 ||&lt;   ||
+||&lt; 5 ||&lt; 166.667 ||&lt; 54/49 ||
 ||&lt; 6 ||&lt; 200 ||&lt; 9/8 ||
 ||&lt; 7 ||&lt; 233.333 ||&lt; 8/7 ||
 ||&lt; 8 ||&lt; 266.667 ||&lt; 7/6 ||
 ||&lt; 9 ||&lt; 300 ||&lt; 32/37 ||
-||&lt; 10 ||&lt; 333.333 ||&lt;   ||
+||&lt; 10 ||&lt; 333.333 ||&lt; 98/81 ||
-||&lt; 11 ||&lt; 366.667 ||&lt;   ||
+||&lt; 11 ||&lt; 366.667 ||&lt; 243/196 ||
 ||&lt; 12 ||&lt; 400 ||&lt; 81/64 ||
 ||&lt; 13 ||&lt; 433.333 ||&lt; 9/7 ||
@@ Line 88: / Line 88: @@
 ||&lt; 23 ||&lt; 766.667 ||&lt; 14/9 ||
 ||&lt; 24 ||&lt; 800 ||&lt; 128/81 ||
-||&lt; 25 ||&lt; 833.333 ||&lt;   ||
+||&lt; 25 ||&lt; 833.333 ||&lt; 392/243 ||
-||&lt; 26 ||&lt; 866.667 ||&lt;   ||
+||&lt; 26 ||&lt; 866.667 ||&lt; 81/49 ||
 ||&lt; 27 ||&lt; 900 ||&lt; 27/16 ||
 ||&lt; 28 ||&lt; 933.333 ||&lt; 12/7 ||
 ||&lt; 29 ||&lt; 966.667 ||&lt; 7/4 ||
 ||&lt; 30 ||&lt; 1000 ||&lt; 16/9 ||
-||&lt; 31 ||&lt; 1033.333 ||&lt;   ||
+||&lt; 31 ||&lt; 1033.333 ||&lt; 49/27 ||
-||&lt; 32 ||&lt; 1066.667 ||&lt;   ||
+||&lt; 32 ||&lt; 1066.667 ||&lt; 448/243 ||
 ||&lt; 33 ||&lt; 1100 ||&lt; 243/128 ||
 ||&lt; 34 ||&lt; 1133.333 ||&lt; 27/14 ||
@@ Line 210: / Line 210: @@
          &lt;td style="text-align: left;"&gt;133.333&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;243/224&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 218: / Line 218: @@
          &lt;td style="text-align: left;"&gt;166.667&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;54/49&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 258: / Line 258: @@
          &lt;td style="text-align: left;"&gt;333.333&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;98/81&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 266: / Line 266: @@
          &lt;td style="text-align: left;"&gt;366.667&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;243/196&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 378: / Line 378: @@
          &lt;td style="text-align: left;"&gt;833.333&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;392/243&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 386: / Line 386: @@
          &lt;td style="text-align: left;"&gt;866.667&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;81/49&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 426: / Line 426: @@
          &lt;td style="text-align: left;"&gt;1033.333&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;49/27&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 434: / Line 434: @@
          &lt;td style="text-align: left;"&gt;1066.667&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;448/243&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;

36edo: Difference between revisions

Revision as of 01:40, 21 January 2014

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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