50edo: Difference between revisions

Revision as of 19:43, 16 April 2012

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//50edo// divides the [[octave]] into 50 equal parts of precisely 24 [[cent]]s each. In the [[5-limit]], it tempers out 81/80, making it a [[meantone]] system, and in that capacity has historically has drawn some notice. In "Harmonics or the Philosophy of Musical Sounds" (1759) by Robert Smith, a musical temperament is described where the octave is divided into 50 equal parts - 50edo, in one word. Later W. S. B. Woolhouse noted it was fairly close to the [[Target tunings|least squares]] tuning for 5-limit meantone. 50, however, is especially interesting from a higher limit point of view. While [[31edo]] extends meantone with a [[7_4|7/4]] which is nearly pure, 50 has a flat 7/4 but both [[11_8|11/8]] and [[13_8|13/8]] are nearly pure. 

50 tempers out 126/125 in the [[7-limit]], indicating it supports septimal meantone; 245/242, 385/384 and 540/539 in the [[11-limit]] and  105/104, 144/143 and 196/195 in the [[13-limit]], and can be used for even higher limits. Aside from meantone, it can be used to advantage for the 15&50 temperament. It is also the unique equal temperament tempering out both 81/80 and the [[vishnuzma]], 6115295232/6103515625 = |23 6 -14>, so that in 50et seven chromatic semitones are a perfect fourth. In 12et by comparison this gives a fifth, in 31et a doubly diminished fifth, and in 19et a diminished fourth.

[[http://www.archive.org/details/harmonicsorphilo00smit|Robert Smith's book online]]
[[http://www.music.ed.ac.uk/russell/conference/robertsmithkirckman.html|More information about Robert Smith's temperament]]

==Relations== 
The 50-edo system is related to [[7edo]], [[12edo]], [[19edo]], [[31edo]] as the next approximation to the "Golden Tone System" ([[Das Goldene Tonsystem]]) of Thorvald Kornerup.

==Intervals== 

|| Degrees of 50-EDO || Cents value ||
|| 0 || 0 ||
|| 1 || 24 ||
|| 2 || 48 ||
|| 3 || 72 ||
|| 4 || 96 ||
|| 5 || 120 ||
|| 6 || 144 ||
|| 7 || 168 ||
|| 8 || 192 ||
|| 9 || 216 ||
|| 10 || 240 ||
|| 11 || 264 ||
|| 12 || 288 ||
|| 13 || 312 ||
|| 14 || 336 ||
|| 15 || 360 ||
|| 16 || 384 ||
|| 17 || 408 ||
|| 18 || 432 ||
|| 19 || 456 ||
|| 20 || 480 ||
|| 21 || 504 ||
|| 22 || 528 ||
|| 23 || 552 ||
|| 24 || 576 ||
|| 25 || 600 ||
|| 26 || 624 ||
|| 27 || 648 ||
|| 28 || 672 ||
|| 29 || 696 ||
|| 30 || 720 ||
|| 31 || 744 ||
|| 32 || 768 ||
|| 33 || 792 ||
|| 34 || 816 ||
|| 35 || 840 ||
|| 36 || 864 ||
|| 37 || 888 ||
|| 38 || 912 ||
|| 39 || 936 ||
|| 40 || 960 ||
|| 41 || 984 ||
|| 42 || 1008 ||
|| 43 || 1032 ||
|| 44 || 1056 ||
|| 45 || 1080 ||
|| 46 || 1104 ||
|| 47 || 1128 ||
|| 48 || 1152 ||
|| 49 || 1176 ||

[[http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3|Twinkle canon – 50 edo]] by [[http://soonlabel.com/xenharmonic/archives/573|Claudi Meneghin]]

Original HTML content:

<html><head><title>50edo</title></head><body><em>50edo</em> divides the <a class="wiki_link" href="/octave">octave</a> into 50 equal parts of precisely 24 <a class="wiki_link" href="/cent">cent</a>s each. In the <a class="wiki_link" href="/5-limit">5-limit</a>, it tempers out 81/80, making it a <a class="wiki_link" href="/meantone">meantone</a> system, and in that capacity has historically has drawn some notice. In &quot;Harmonics or the Philosophy of Musical Sounds&quot; (1759) by Robert Smith, a musical temperament is described where the octave is divided into 50 equal parts - 50edo, in one word. Later W. S. B. Woolhouse noted it was fairly close to the <a class="wiki_link" href="/Target%20tunings">least squares</a> tuning for 5-limit meantone. 50, however, is especially interesting from a higher limit point of view. While <a class="wiki_link" href="/31edo">31edo</a> extends meantone with a <a class="wiki_link" href="/7_4">7/4</a> which is nearly pure, 50 has a flat 7/4 but both <a class="wiki_link" href="/11_8">11/8</a> and <a class="wiki_link" href="/13_8">13/8</a> are nearly pure. <br />
<br />
50 tempers out 126/125 in the <a class="wiki_link" href="/7-limit">7-limit</a>, indicating it supports septimal meantone; 245/242, 385/384 and 540/539 in the <a class="wiki_link" href="/11-limit">11-limit</a> and  105/104, 144/143 and 196/195 in the <a class="wiki_link" href="/13-limit">13-limit</a>, and can be used for even higher limits. Aside from meantone, it can be used to advantage for the 15&amp;50 temperament. It is also the unique equal temperament tempering out both 81/80 and the <a class="wiki_link" href="/vishnuzma">vishnuzma</a>, 6115295232/6103515625 = |23 6 -14&gt;, so that in 50et seven chromatic semitones are a perfect fourth. In 12et by comparison this gives a fifth, in 31et a doubly diminished fifth, and in 19et a diminished fourth.<br />
<br />
<a class="wiki_link_ext" href="http://www.archive.org/details/harmonicsorphilo00smit" rel="nofollow">Robert Smith's book online</a><br />
<a class="wiki_link_ext" href="http://www.music.ed.ac.uk/russell/conference/robertsmithkirckman.html" rel="nofollow">More information about Robert Smith's temperament</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Relations"></a><!-- ws:end:WikiTextHeadingRule:0 -->Relations</h2>
 The 50-edo system is related to <a class="wiki_link" href="/7edo">7edo</a>, <a class="wiki_link" href="/12edo">12edo</a>, <a class="wiki_link" href="/19edo">19edo</a>, <a class="wiki_link" href="/31edo">31edo</a> as the next approximation to the &quot;Golden Tone System&quot; (<a class="wiki_link" href="/Das%20Goldene%20Tonsystem">Das Goldene Tonsystem</a>) of Thorvald Kornerup.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2>
 <br />


<table class="wiki_table">
    <tr>
        <td>Degrees of 50-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>24<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>48<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>72<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>96<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>120<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>144<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>168<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>192<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>216<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>240<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>264<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>288<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>312<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>336<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>360<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>384<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>408<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>432<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>456<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>480<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>504<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>528<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>552<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>576<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>600<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>624<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>648<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>672<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>696<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>720<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>744<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>768<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>792<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>816<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>840<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>864<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>888<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>912<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>936<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>960<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>984<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>1008<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>1032<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>1056<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>1080<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>1104<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>1128<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>1152<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>1176<br />
</td>
    </tr>
</table>

<br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3" rel="nofollow">Twinkle canon – 50 edo</a> by <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/573" rel="nofollow">Claudi Meneghin</a></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>2011-11-03 14:05:16 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-16 19:43:10 UTC</tt>.<br>
-: The original revision id was <tt>271600980</tt>.<br>
+: The original revision id was <tt>321254968</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 68: / Line 68: @@
 || 47 || 1128 ||
 || 48 || 1152 ||
-|| 49 || 1176 ||</pre></div>
+|| 49 || 1176 ||
+[[http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3|Twinkle canon – 50 edo]] by [[http://soonlabel.com/xenharmonic/archives/573|Claudi Meneghin]]
+</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;50edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;50edo&lt;/em&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 50 equal parts of precisely 24 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. In the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;, it tempers out 81/80, making it a &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; system, and in that capacity has historically has drawn some notice. In &amp;quot;Harmonics or the Philosophy of Musical Sounds&amp;quot; (1759) by Robert Smith, a musical temperament is described where the octave is divided into 50 equal parts - 50edo, in one word. Later W. S. B. Woolhouse noted it was fairly close to the &lt;a class="wiki_link" href="/Target%20tunings"&gt;least squares&lt;/a&gt; tuning for 5-limit meantone. 50, however, is especially interesting from a higher limit point of view. While &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; extends meantone with a &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt; which is nearly pure, 50 has a flat 7/4 but both &lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt; and &lt;a class="wiki_link" href="/13_8"&gt;13/8&lt;/a&gt; are nearly pure. &lt;br /&gt;
@@ Line 393: / Line 396: @@
 &lt;/table&gt;
-&lt;/body&gt;&lt;/html&gt;</pre></div>
+&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3" rel="nofollow"&gt;Twinkle canon – 50 edo&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/573" rel="nofollow"&gt;Claudi Meneghin&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

50edo: Difference between revisions

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IMPORTED REVISION FROM WIKISPACES

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