50edo: Difference between revisions

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[[toc]]
//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 [[http://lit.gfax.ch/Harmonics%202nd%20Edition%20%28Robert%20Smith%29.pdf|"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 and its extension meanpop, 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 50edo ||~ Cents value ||~ Ratios* ||~ Generator for ||
|| 0 || 0 || 1/1 ||   ||
|| 1 || 24 || 45/44, 49/48, 56/55, 65/64, 66/65, 78/77, 91/90, 99/98, 100/99, 121/120, 169/168 || [[xenharmonic/Hemimean clan#Sengagen|Sengagen]] ||
|| 2 || 48 || 33/32, 36/35, 50/49, 55/54, 64/63 ||   ||
|| 3 || 72 || 21/20, 25/24, 26/25, 27/26, 28/27 || [[xenharmonic/Vishnu|Vishnu]], [[http://x31eq.com/cgi-bin/rt.cgi?ets=15%2650&limit=11|Coblack]] ||
|| 4 || 96 || 22/21 ||   ||
|| 5 || 120 || 16/15, 15/14, 14/13 ||   ||
|| 6 || 144 || 13/12, 12/11 ||   ||
|| 7 || 168 || 11/10 ||   ||
|| 8 || 192 || 9/8, 10/9 ||   ||
|| 9 || 216 || 25/22 || [[http://x31eq.com/cgi-bin/rt.cgi?ets=50%2661p&limit=2.3.5.11.13|Tremka]] ||
|| 10 || 240 || 8/7, 15/13 ||   ||
|| 11 || 264 || 7/6 ||   ||
|| 12 || 288 || 13/11 ||   ||
|| 13 || 312 || 6/5 ||   ||
|| 14 || 336 || 27/22, 39/32, 40/33, 49/40 ||   ||
|| 15 || 360 || 16/13, 11/9 ||   ||
|| 16 || 384 || 5/4 || [[Marvel temperaments#Wizard-11-limit|Wizard]] ||
|| 17 || 408 || 14/11 || [[Ditonmic family|Ditonic]] ||
|| 18 || 432 || 9/7 ||   ||
|| 19 || 456 || 13/10 || [[xenharmonic/Starling temperaments#Bisemidim|Bisemidim]] ||
|| 20 || 480 || 33/25, 55/42, 64/49 ||   ||
|| 21 || 504 || 4/3 || [[xenharmonic/Meantone|Meantone]]/[[xenharmonic/Meanpop|Meanpop]] ||
|| 22 || 528 || 15/11 ||   ||
|| 23 || 552 || 11/8, 18/13 || [[xenharmonic/Chromatic pairs#Barton|Barton]]/[[xenharmonic/Hemimean clan#Emka|Emka]] ||
|| 24 || 576 || 7/5 ||   ||
|| 25 || 600 || 63/44, 88/63, 78/55, 55/39 ||   ||
|| 26 || 624 || 10/7 ||   ||
|| 27 || 648 || 16/11, 13/9 ||   ||
|| 28 || 672 || 22/15 ||   ||
|| 29 || 696 || 3/2 ||   ||
|| 30 || 720 || 50/33, 84/55, 49/32 ||   ||
|| 31 || 744 || 20/13 ||   ||
|| 32 || 768 || 14/9 ||   ||
|| 33 || 792 || 11/7 ||   ||
|| 34 || 816 || 8/5 ||   ||
|| 35 || 840 || 13/8, 18/11 ||   ||
|| 36 || 864 || 44/27, 64/39, 33/20, 80/49 ||   ||
|| 37 || 888 || 5/3 ||   ||
|| 38 || 912 || 22/13 ||   ||
|| 39 || 936 || 12/7 ||   ||
|| 40 || 960 || 7/4 ||   ||
|| 41 || 984 || 44/25 ||   ||
|| 42 || 1008 || 16/9, 9/5 ||   ||
|| 43 || 1032 || 20/11 ||   ||
|| 44 || 1056 || 24/13, 11/6 ||   ||
|| 45 || 1080 || 15/8, 28/15, 13/7 ||   ||
|| 46 || 1104 || 21/11 ||   ||
|| 47 || 1128 || 40/21, 48/25, 25/13, 52/27, 27/14 ||   ||
|| 48 || 1152 || 64/33, 35/18, 49/25, 108/55, 63/32 ||   ||
|| 49 || 1176 ||   ||   ||
*using the 13-limit patent val
==Intervals by patent val error== 
|| Interval || Error ||
|| 16/13 || 0.528 ||
|| 15/14 || 0.557 ||
|| 11/8 || 0.682 ||
|| 13/11 || -1.210 ||
|| 13/10 || 1.786 ||
|| 5/4 || -2.314 ||
|| 7/6 || -2.871 ||
|| 11/10 || 2.996 ||
|| 9/7 || -3.084 ||
|| 6/5 || -3.641 ||
|| 13/12 || 5.427 ||
|| 4/3 || 5.955 ||
|| 7/5 || -6.512 ||
|| 12/11 || -6.637 ||
|| 15/13 || -7.741 ||
|| 16/15 || 8.269 ||
|| 14/13 || -8.298 ||
|| 8/7 || 8.826 ||
|| 15/11 || -8.951 ||
|| 14/11 || -9.508 ||
|| 10/9 || 9.596 ||
|| 18/13 || -11.382 ||
|| 9/8 || -11.910 ||
|| 11/9 || 12.592 ||

=Commas= 
50 EDO tempers out the following commas. (Note: This assumes the val < 50 79 116 140 173 185 204 212 226 |, comma values rounded to 2 decimal places.) This list is not all-inclusive, and is based on the interval table from Scala version 2.2.
||~ ===In ket format=== ||~ ===In cents=== ||~ ===Ratio=== ||~ ===Name 1=== ||~ ===Name2=== ||
|| | -4 4 -1 > ||> 21.51 ||= 81/80 || Syntonic comma || Didymus comma ||
|| | 23 6 -14 > ||> 3.34 ||= 6115295232/6103515625 || Vishnu comma ||   ||
|| | 1 2 -3 1 > ||> 13.79 ||= 126/125 || Starling comma || Small septimal comma ||
|| | -5 2 2 -1 > ||> 7.71 ||= 225/224 || Septimal kleisma || Marvel comma ||
|| | 6 0 -5 2 > ||> 6.08 ||= 3136/3125 || Hemimean || Middle second comma ||
|| | -6 -8 2 5 > ||> 1.12 ||= 420175/419904 || Wizma ||   ||
|| |-11 2 7 -3 > ||> 1.63 ||= 703125/702464 || Meter ||   ||
|| | 11 -10 -10 10 > ||> 5.57 ||= 578509309952/576650390625 || Linus ||   ||
|| |-13 10 0 -1 > ||> 50.72 ||= 59049/57344 || Harrison's comma ||   ||
|| | 2 3 1 -2 -1 > ||> 3.21 ||= 540/539 || Swets' comma || Swetisma ||
|| | -3 4 -2 -2 2 > ||> 0.18 ||= 9801/9800 || Kalisma || Gauss' comma ||
|| | 5 -1 3 0 -3 > ||> 3.03 ||= 4000/3993 || Wizardharry || Undecimal schisma ||
|| | -7 -1 1 1 1 > ||> 4.50 ||= 385/384 || Keenanisma || Undecimal kleisma ||
|| | -1 0 1 2 -2 > ||> 21.33 ||= 245/242 || Cassacot ||   ||
|| | 2 -1 0 1 -2 1 > ||> 4.76 ||= 364/363 || Gentle comma ||   ||
|| | 2 -1 -1 2 0 -1 > ||> 8.86 ||= 196/195 || Mynucuma ||   ||
|| | 2 3 0 -1 1 -2 > ||> 7.30 ||= 1188/1183 || Kestrel Comma ||   ||
|| | 3 0 2 0 1 -3 > ||> 2.36 ||= 2200/2197 || Petrma || Parizek comma ||
|| | -3 1 1 1 0 -1 > ||> 16.57 ||= 105/104 || Animist comma || Small tridecimal comma ||   ||
|| | 4 2 0 0 -1 -1 > ||> 12.06 ||= 144/143 || Grossma ||   ||
|| | 3 -2 0 1 -1 -1 0 0 1 > ||> 1.34 ||= 1288/1287 || Triaphonisma ||   ||

[[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]]
[[@http://soonlabel.com/xenharmonic/archives/1118|Fantasia Catalana by Claudi Meneghin]]
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| -4 4 -1 > 21.51 81/80 syntonic comma, Didymus comma</span>
[[http://soonlabel.com/xenharmonic/archives/1929|Fugue on the Dragnet theme by Claudi Meneghin]]
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| -8 8 -2 > 43.01 6561/6400 Mathieu superdiesis</span>
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 23 6 -14 > 3.34 1212717/1210381 Vishnu comma</span>
[[https://www.dropbox.com/sh/4x81rzpkot32qzk/MQ3cJljjkh|50EDO Theory - Intervals, Chords and Scales in 50EDO by Cam Taylor]]
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 1 2 -3 1 > 13.79 126/125 small septimal comma</span>
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| -5 2 2 -1 > 7.71 225/224 septimal kleisma</span>
[[http://iamcamtaylor.wordpress.com/|iamcamtaylor - Blog on 50EDO and extended meantone theory by Cam Taylor]]
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 6 0 -5 2 > 6.08 3136/3125 middle second comma</span>
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| -6 -8 2 5 > 1.12 420175/419904</span>
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">|-11 2 7 -3 > 1.63 703125/702464</span>
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 11 -10 -10 10 > 5.57 6772805/6751042</span>
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">|-13 10 0 -1 > 50.72 59049/57344 Harrison's comma</span>
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 2 3 1 -2 -1 > 3.21 540/539 Swets' comma</span>
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| -3 4 -2 -2 2 > 0.18 9801/9800 kalisma, Gauss' comma</span>
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 5 -1 3 0 -3 > 3.03 4000/3993 undecimal schisma</span>
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| -7 -1 1 1 1 > 4.50 385/384 undecimal kleisma</span>
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 2 -1 0 1 -2 1 > 4.76 364/363</span>
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 2 3 0 -1 1 -2 > 7.30 1188/1183 Kestrel Comma</span>
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 3 0 2 0 1 -3 > 2.36 2200/2197 Parizek comma</span>
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| -3 1 1 1 0 -1 > 16.57 105/104 small tridecimal comma</span>
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 3 -2 0 1 -1 -1 0 0 1 > 1.34 1288/1287 triaphonisma</span>

Original HTML content:

<html><head><title>50edo</title></head><body><!-- ws:start:WikiTextTocRule:18:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><div style="margin-left: 1em;"><a href="#Relations">Relations</a></div>
<!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><div style="margin-left: 1em;"><a href="#Intervals">Intervals</a></div>
<!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><div style="margin-left: 2em;"><a href="#Intervals-Intervals by patent val error">Intervals by patent val error</a></div>
<!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><div style="margin-left: 1em;"><a href="#Commas">Commas</a></div>
<!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><div style="margin-left: 3em;"><a href="#Commas--In ket format">In ket format</a></div>
<!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><div style="margin-left: 3em;"><a href="#Commas--In cents">In cents</a></div>
<!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><div style="margin-left: 3em;"><a href="#Commas--Ratio">Ratio</a></div>
<!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><div style="margin-left: 3em;"><a href="#Commas--Name 1">Name 1</a></div>
<!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><div style="margin-left: 3em;"><a href="#Commas--Name2">Name2</a></div>
<!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --></div>
<!-- ws:end:WikiTextTocRule:28 --><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 <a class="wiki_link_ext" href="http://lit.gfax.ch/Harmonics%202nd%20Edition%20%28Robert%20Smith%29.pdf" rel="nofollow">&quot;Harmonics or the Philosophy of Musical Sounds&quot;</a> (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 and its extension meanpop, 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;h1&gt; --><h1 id="toc0"><a name="Relations"></a><!-- ws:end:WikiTextHeadingRule:0 -->Relations</h1>
 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;h1&gt; --><h1 id="toc1"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h1>
 

<table class="wiki_table">
    <tr>
        <th>Degrees of 50edo<br />
</th>
        <th>Cents value<br />
</th>
        <th>Ratios*<br />
</th>
        <th>Generator for<br />
</th>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0<br />
</td>
        <td>1/1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>24<br />
</td>
        <td>45/44, 49/48, 56/55, 65/64, 66/65, 78/77, 91/90, 99/98, 100/99, 121/120, 169/168<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Hemimean%20clan#Sengagen">Sengagen</a><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>48<br />
</td>
        <td>33/32, 36/35, 50/49, 55/54, 64/63<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>72<br />
</td>
        <td>21/20, 25/24, 26/25, 27/26, 28/27<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Vishnu">Vishnu</a>, <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=15%2650&amp;limit=11" rel="nofollow">Coblack</a><br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>96<br />
</td>
        <td>22/21<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>120<br />
</td>
        <td>16/15, 15/14, 14/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>144<br />
</td>
        <td>13/12, 12/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>168<br />
</td>
        <td>11/10<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>192<br />
</td>
        <td>9/8, 10/9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>216<br />
</td>
        <td>25/22<br />
</td>
        <td><a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=50%2661p&amp;limit=2.3.5.11.13" rel="nofollow">Tremka</a><br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>240<br />
</td>
        <td>8/7, 15/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>264<br />
</td>
        <td>7/6<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>288<br />
</td>
        <td>13/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>312<br />
</td>
        <td>6/5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>336<br />
</td>
        <td>27/22, 39/32, 40/33, 49/40<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>360<br />
</td>
        <td>16/13, 11/9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>384<br />
</td>
        <td>5/4<br />
</td>
        <td><a class="wiki_link" href="/Marvel%20temperaments#Wizard-11-limit">Wizard</a><br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>408<br />
</td>
        <td>14/11<br />
</td>
        <td><a class="wiki_link" href="/Ditonmic%20family">Ditonic</a><br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>432<br />
</td>
        <td>9/7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>456<br />
</td>
        <td>13/10<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Starling%20temperaments#Bisemidim">Bisemidim</a><br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>480<br />
</td>
        <td>33/25, 55/42, 64/49<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>504<br />
</td>
        <td>4/3<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meantone">Meantone</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meanpop">Meanpop</a><br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>528<br />
</td>
        <td>15/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>552<br />
</td>
        <td>11/8, 18/13<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Chromatic%20pairs#Barton">Barton</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Hemimean%20clan#Emka">Emka</a><br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>576<br />
</td>
        <td>7/5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>600<br />
</td>
        <td>63/44, 88/63, 78/55, 55/39<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>624<br />
</td>
        <td>10/7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>648<br />
</td>
        <td>16/11, 13/9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>672<br />
</td>
        <td>22/15<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>696<br />
</td>
        <td>3/2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>720<br />
</td>
        <td>50/33, 84/55, 49/32<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>744<br />
</td>
        <td>20/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>768<br />
</td>
        <td>14/9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>792<br />
</td>
        <td>11/7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>816<br />
</td>
        <td>8/5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>840<br />
</td>
        <td>13/8, 18/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>864<br />
</td>
        <td>44/27, 64/39, 33/20, 80/49<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>888<br />
</td>
        <td>5/3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>912<br />
</td>
        <td>22/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>936<br />
</td>
        <td>12/7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>960<br />
</td>
        <td>7/4<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>984<br />
</td>
        <td>44/25<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>1008<br />
</td>
        <td>16/9, 9/5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>1032<br />
</td>
        <td>20/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>1056<br />
</td>
        <td>24/13, 11/6<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>1080<br />
</td>
        <td>15/8, 28/15, 13/7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>1104<br />
</td>
        <td>21/11<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>1128<br />
</td>
        <td>40/21, 48/25, 25/13, 52/27, 27/14<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>1152<br />
</td>
        <td>64/33, 35/18, 49/25, 108/55, 63/32<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>1176<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

*using the 13-limit patent val<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Intervals-Intervals by patent val error"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals by patent val error</h2>
 

<table class="wiki_table">
    <tr>
        <td>Interval<br />
</td>
        <td>Error<br />
</td>
    </tr>
    <tr>
        <td>16/13<br />
</td>
        <td>0.528<br />
</td>
    </tr>
    <tr>
        <td>15/14<br />
</td>
        <td>0.557<br />
</td>
    </tr>
    <tr>
        <td>11/8<br />
</td>
        <td>0.682<br />
</td>
    </tr>
    <tr>
        <td>13/11<br />
</td>
        <td>-1.210<br />
</td>
    </tr>
    <tr>
        <td>13/10<br />
</td>
        <td>1.786<br />
</td>
    </tr>
    <tr>
        <td>5/4<br />
</td>
        <td>-2.314<br />
</td>
    </tr>
    <tr>
        <td>7/6<br />
</td>
        <td>-2.871<br />
</td>
    </tr>
    <tr>
        <td>11/10<br />
</td>
        <td>2.996<br />
</td>
    </tr>
    <tr>
        <td>9/7<br />
</td>
        <td>-3.084<br />
</td>
    </tr>
    <tr>
        <td>6/5<br />
</td>
        <td>-3.641<br />
</td>
    </tr>
    <tr>
        <td>13/12<br />
</td>
        <td>5.427<br />
</td>
    </tr>
    <tr>
        <td>4/3<br />
</td>
        <td>5.955<br />
</td>
    </tr>
    <tr>
        <td>7/5<br />
</td>
        <td>-6.512<br />
</td>
    </tr>
    <tr>
        <td>12/11<br />
</td>
        <td>-6.637<br />
</td>
    </tr>
    <tr>
        <td>15/13<br />
</td>
        <td>-7.741<br />
</td>
    </tr>
    <tr>
        <td>16/15<br />
</td>
        <td>8.269<br />
</td>
    </tr>
    <tr>
        <td>14/13<br />
</td>
        <td>-8.298<br />
</td>
    </tr>
    <tr>
        <td>8/7<br />
</td>
        <td>8.826<br />
</td>
    </tr>
    <tr>
        <td>15/11<br />
</td>
        <td>-8.951<br />
</td>
    </tr>
    <tr>
        <td>14/11<br />
</td>
        <td>-9.508<br />
</td>
    </tr>
    <tr>
        <td>10/9<br />
</td>
        <td>9.596<br />
</td>
    </tr>
    <tr>
        <td>18/13<br />
</td>
        <td>-11.382<br />
</td>
    </tr>
    <tr>
        <td>9/8<br />
</td>
        <td>-11.910<br />
</td>
    </tr>
    <tr>
        <td>11/9<br />
</td>
        <td>12.592<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:6 -->Commas</h1>
 50 EDO tempers out the following commas. (Note: This assumes the val &lt; 50 79 116 140 173 185 204 212 226 |, comma values rounded to 2 decimal places.) This list is not all-inclusive, and is based on the interval table from Scala version 2.2.<br />


<table class="wiki_table">
    <tr>
        <th><!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="Commas--In ket format"></a><!-- ws:end:WikiTextHeadingRule:8 -->In ket format</h3>
</th>
        <th><!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Commas--In cents"></a><!-- ws:end:WikiTextHeadingRule:10 -->In cents</h3>
</th>
        <th><!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="Commas--Ratio"></a><!-- ws:end:WikiTextHeadingRule:12 -->Ratio</h3>
</th>
        <th><!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Commas--Name 1"></a><!-- ws:end:WikiTextHeadingRule:14 -->Name 1</h3>
</th>
        <th><!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Commas--Name2"></a><!-- ws:end:WikiTextHeadingRule:16 -->Name2</h3>
</th>
    </tr>
    <tr>
        <td>| -4 4 -1 &gt;<br />
</td>
        <td style="text-align: right;">21.51<br />
</td>
        <td style="text-align: center;">81/80<br />
</td>
        <td>Syntonic comma<br />
</td>
        <td>Didymus comma<br />
</td>
    </tr>
    <tr>
        <td>| 23 6 -14 &gt;<br />
</td>
        <td style="text-align: right;">3.34<br />
</td>
        <td style="text-align: center;">6115295232/6103515625<br />
</td>
        <td>Vishnu comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>| 1 2 -3 1 &gt;<br />
</td>
        <td style="text-align: right;">13.79<br />
</td>
        <td style="text-align: center;">126/125<br />
</td>
        <td>Starling comma<br />
</td>
        <td>Small septimal comma<br />
</td>
    </tr>
    <tr>
        <td>| -5 2 2 -1 &gt;<br />
</td>
        <td style="text-align: right;">7.71<br />
</td>
        <td style="text-align: center;">225/224<br />
</td>
        <td>Septimal kleisma<br />
</td>
        <td>Marvel comma<br />
</td>
    </tr>
    <tr>
        <td>| 6 0 -5 2 &gt;<br />
</td>
        <td style="text-align: right;">6.08<br />
</td>
        <td style="text-align: center;">3136/3125<br />
</td>
        <td>Hemimean<br />
</td>
        <td>Middle second comma<br />
</td>
    </tr>
    <tr>
        <td>| -6 -8 2 5 &gt;<br />
</td>
        <td style="text-align: right;">1.12<br />
</td>
        <td style="text-align: center;">420175/419904<br />
</td>
        <td>Wizma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>|-11 2 7 -3 &gt;<br />
</td>
        <td style="text-align: right;">1.63<br />
</td>
        <td style="text-align: center;">703125/702464<br />
</td>
        <td>Meter<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>| 11 -10 -10 10 &gt;<br />
</td>
        <td style="text-align: right;">5.57<br />
</td>
        <td style="text-align: center;">578509309952/576650390625<br />
</td>
        <td>Linus<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>|-13 10 0 -1 &gt;<br />
</td>
        <td style="text-align: right;">50.72<br />
</td>
        <td style="text-align: center;">59049/57344<br />
</td>
        <td>Harrison's comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>| 2 3 1 -2 -1 &gt;<br />
</td>
        <td style="text-align: right;">3.21<br />
</td>
        <td style="text-align: center;">540/539<br />
</td>
        <td>Swets' comma<br />
</td>
        <td>Swetisma<br />
</td>
    </tr>
    <tr>
        <td>| -3 4 -2 -2 2 &gt;<br />
</td>
        <td style="text-align: right;">0.18<br />
</td>
        <td style="text-align: center;">9801/9800<br />
</td>
        <td>Kalisma<br />
</td>
        <td>Gauss' comma<br />
</td>
    </tr>
    <tr>
        <td>| 5 -1 3 0 -3 &gt;<br />
</td>
        <td style="text-align: right;">3.03<br />
</td>
        <td style="text-align: center;">4000/3993<br />
</td>
        <td>Wizardharry<br />
</td>
        <td>Undecimal schisma<br />
</td>
    </tr>
    <tr>
        <td>| -7 -1 1 1 1 &gt;<br />
</td>
        <td style="text-align: right;">4.50<br />
</td>
        <td style="text-align: center;">385/384<br />
</td>
        <td>Keenanisma<br />
</td>
        <td>Undecimal kleisma<br />
</td>
    </tr>
    <tr>
        <td>| -1 0 1 2 -2 &gt;<br />
</td>
        <td style="text-align: right;">21.33<br />
</td>
        <td style="text-align: center;">245/242<br />
</td>
        <td>Cassacot<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>| 2 -1 0 1 -2 1 &gt;<br />
</td>
        <td style="text-align: right;">4.76<br />
</td>
        <td style="text-align: center;">364/363<br />
</td>
        <td>Gentle comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>| 2 -1 -1 2 0 -1 &gt;<br />
</td>
        <td style="text-align: right;">8.86<br />
</td>
        <td style="text-align: center;">196/195<br />
</td>
        <td>Mynucuma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>| 2 3 0 -1 1 -2 &gt;<br />
</td>
        <td style="text-align: right;">7.30<br />
</td>
        <td style="text-align: center;">1188/1183<br />
</td>
        <td>Kestrel Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>| 3 0 2 0 1 -3 &gt;<br />
</td>
        <td style="text-align: right;">2.36<br />
</td>
        <td style="text-align: center;">2200/2197<br />
</td>
        <td>Petrma<br />
</td>
        <td>Parizek comma<br />
</td>
    </tr>
    <tr>
        <td>| -3 1 1 1 0 -1 &gt;<br />
</td>
        <td style="text-align: right;">16.57<br />
</td>
        <td style="text-align: center;">105/104<br />
</td>
        <td>Animist comma<br />
</td>
        <td>Small tridecimal comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>| 4 2 0 0 -1 -1 &gt;<br />
</td>
        <td style="text-align: right;">12.06<br />
</td>
        <td style="text-align: center;">144/143<br />
</td>
        <td>Grossma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>| 3 -2 0 1 -1 -1 0 0 1 &gt;<br />
</td>
        <td style="text-align: right;">1.34<br />
</td>
        <td style="text-align: center;">1288/1287<br />
</td>
        <td>Triaphonisma<br />
</td>
        <td><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><br />
<a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/1118" rel="nofollow" target="_blank">Fantasia Catalana by Claudi Meneghin</a><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| -4 4 -1 &gt; 21.51 81/80 syntonic comma, Didymus comma</span><br />
<a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/1929" rel="nofollow">Fugue on the Dragnet theme by Claudi Meneghin</a><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| -8 8 -2 &gt; 43.01 6561/6400 Mathieu superdiesis</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 23 6 -14 &gt; 3.34 1212717/1210381 Vishnu comma</span><br />
<a class="wiki_link_ext" href="https://www.dropbox.com/sh/4x81rzpkot32qzk/MQ3cJljjkh" rel="nofollow">50EDO Theory - Intervals, Chords and Scales in 50EDO by Cam Taylor</a><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 1 2 -3 1 &gt; 13.79 126/125 small septimal comma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| -5 2 2 -1 &gt; 7.71 225/224 septimal kleisma</span><br />
<a class="wiki_link_ext" href="http://iamcamtaylor.wordpress.com/" rel="nofollow">iamcamtaylor - Blog on 50EDO and extended meantone theory by Cam Taylor</a><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 6 0 -5 2 &gt; 6.08 3136/3125 middle second comma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| -6 -8 2 5 &gt; 1.12 420175/419904</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">|-11 2 7 -3 &gt; 1.63 703125/702464</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 11 -10 -10 10 &gt; 5.57 6772805/6751042</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">|-13 10 0 -1 &gt; 50.72 59049/57344 Harrison's comma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 2 3 1 -2 -1 &gt; 3.21 540/539 Swets' comma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| -3 4 -2 -2 2 &gt; 0.18 9801/9800 kalisma, Gauss' comma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 5 -1 3 0 -3 &gt; 3.03 4000/3993 undecimal schisma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| -7 -1 1 1 1 &gt; 4.50 385/384 undecimal kleisma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 2 -1 0 1 -2 1 &gt; 4.76 364/363</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 2 3 0 -1 1 -2 &gt; 7.30 1188/1183 Kestrel Comma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 3 0 2 0 1 -3 &gt; 2.36 2200/2197 Parizek comma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| -3 1 1 1 0 -1 &gt; 16.57 105/104 small tridecimal comma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| 3 -2 0 1 -1 -1 0 0 1 &gt; 1.34 1288/1287 triaphonisma</span></body></html>

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