50edo: Difference between revisions

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:spt3125|spt3125]] and made on <tt>2014-04-~~21 21~~:45:59 UTC</tt>.<br>

: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-04-22 18:23:25 UTC</tt>.<br>

: The original revision id was <tt>~~503693126~~</tt>.<br>

: The original revision id was <tt>503910738</tt>.<br>

: The revision comment was: <tt></tt><br>

: The revision comment was: <tt>added more temperaments - hope they're correct :)</tt><br>

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

<h4>Original Wikitext content:</h4>

Line 10:

50 tempers out 126/125, 225/224 and 3136/3125 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 ([[http://x31eq.com/cgi-bin/rt.cgi?ets=15%2650&limit=11|Coblack]]). 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 (and similarly as the next step from 31edo in Joseph Yasser's "[[http://books.google.com.au/books/about/A_theory_of_evolving_tonality.html?id=-XUsAAAAMAAJ&redir_esc=y|A Theory of Evolving Tonality]]").

The 50edo system is related to [[7edo]], [[12edo]], [[19edo]], [[31edo]] as the next approximation to the "Golden Tone System" ([[Das Goldene Tonsystem]]) of Thorvald Kornerup (and similarly as the next step from 31edo in Joseph Yasser's "[[http://books.google.com.au/books/about/A_theory_of_evolving_tonality.html?id=-XUsAAAAMAAJ&redir_esc=y|A Theory of Evolving Tonality]]").

=Intervals=

||~ Degrees of 50edo ||~ Cents value ||~ Ratios* ||~ Generator for ||

||~ 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]] ||

|| 3 || 72 || 21/20, 25/24, 26/25, 27/26, 28/27 || [[xenharmonic/Vishnuzmic family#Vishnu|Vishnu]] (2/oct), [[http://x31eq.com/cgi-bin/rt.cgi?ets=15%2650&limit=11|Coblack]] (5/oct) ||

|| 4 || 96 || 22/21 || ||

|| 4 || 96 || 22/21 || [[xenharmonic/Meantone family#Injera|Injera]] (50d val, 2/oct) ||

|| 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]] ||

|| 9 || 216 || 25/22 || [[http://x31eq.com/cgi-bin/rt.cgi?ets=50%2661p&limit=2.3.5.11.13|Tremka]], [[xenharmonic/Subgroup temperaments#x2.9.7.11-Machine|Machine]] (50b val) ||

|| 10 || 240 || 8/7, 15/13 || ||

|| 11 || 264 || 7/6 || [[Marvel temperaments#Septimin|Septimin]] ||

|| 11 || 264 || 7/6 || [[xenharmonic/Marvel temperaments#Septimin-13-limit|Septimin (13-limit)]] ||

|| 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]] ||

|| 16 || 384 || 5/4 || [[xenharmonic/Marvel temperaments#Wizard-11-limit|Wizard]] (2/oct) ||

|| 17 || 408 || 14/11 || [[Ditonmic family|Ditonic]] ||

|| 17 || 408 || 14/11 || [[xenharmonic/Ditonmic family|Ditonic]] ||

|| 18 || 432 || 9/7 || ||

|| 18 || 432 || 9/7 || [[xenharmonic/Porcupine family#Hedgehog|Hedgehog]] (50cc val, 2/oct) ||

|| 19 || 456 || 13/10 || [[xenharmonic/Starling temperaments#Bisemidim|Bisemidim]] ||

|| 19 || 456 || 13/10 || [[xenharmonic/Starling temperaments#Bisemidim|Bisemidim]] (2/oct) ||

|| 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]] ||

|| 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 || ||

Line 69:

Line 66:

|| 48 || 1152 || 64/33, 35/18, 49/25, 108/55, 63/32 || ||

|| 49 || 1176 || || ||

*using the 13-limit patent val

*using the 13-limit patent val except as noted

==Intervals by patent val error==

|| Interval || Error ||

Line 98:

Line 96:

=Commas=

50 EDO tempers out the following commas. (Note: This assumes the val < 50 79 116 140 173 185 204 212 226 |, comma values in cents ~~orunded~~ to 2 decimal places.) This list is not all-inclusive, and is based on the interval table from Scala version 2.2.

50 EDO tempers out the following commas. (Note: This assumes the val < 50 79 116 140 173 185 204 212 226 |, comma values in cents rounded to 2 decimal places.) This list is not all-inclusive, and is based on the interval table from Scala version 2.2.

||~ Monzo ||~ Cents ||~ Ratio ||~ Name 1 ||~ Name 2 ||

|| | -4 4 -1 > ||> 21.51 ||= 81/80 || Syntonic comma || Didymus comma ||

Line 122:

Line 120:

|| | 3 -2 0 1 -1 -1 0 0 1 > ||> 1.34 ||= 1288/1287 || Triaphonisma || ||

=Music=

[[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>~~

=Additional reading=

[[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]]

[[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]]</pre></div>

[[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>~~</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"><html><head><title>50edo</title></head><body><div id="toc"><h1 class="nopad">Table of Contents</h1><div style="margin-left: 1em;"><a href="#Relations">Relations</a></div>

<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"><html><head><title>50edo</title></head><body><div id="toc"><h1 class="nopad">Table of Contents</h1><div style="margin-left: 1em;"><a href="#Relations">Relations</a></div>

<div style="margin-left: 1em;"><a href="#Intervals">Intervals</a></div>

<div style="margin-left: 1em;"><a href="#Intervals">Intervals</a></div>

<div style="margin-left: 2em;"><a href="#Intervals-Intervals by patent val error">Intervals by patent val error</a></div>

<div style="margin-left: 2em;"><a href="#Intervals-Intervals by patent val error">Intervals by patent val error</a></div>

<div style="margin-left: 1em;"><a href="#Commas">Commas</a></div>

<div style="margin-left: 1em;"><a href="#Commas">Commas</a></div>

</div>

<div style="margin-left: 1em;"><a href="#Music">Music</a></div>

<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. 50edo, 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 />

<div style="margin-left: 1em;"><a href="#Additional reading">Additional reading</a></div>

</div>

<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. 50edo, 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, 225/224 and 3136/3125 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 (<a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=15%2650&amp;limit=11" rel="nofollow">Coblack</a>). 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 />

<h1 id="toc0"><a name="Relations"></a>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 (and similarly as the next step from 31edo in Joseph Yasser's &quot;<a class="wiki_link_ext" href="http://books.google.com.au/books/about/A_theory_of_evolving_tonality.html?id=-XUsAAAAMAAJ&amp;redir_esc=y" rel="nofollow">A Theory of Evolving Tonality</a>&quot;).<br />

The 50edo 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 (and similarly as the next step from 31edo in Joseph Yasser's &quot;<a class="wiki_link_ext" href="http://books.google.com.au/books/about/A_theory_of_evolving_tonality.html?id=-XUsAAAAMAAJ&amp;redir_esc=y" rel="nofollow">A Theory of Evolving Tonality</a>&quot;).<br />

<br />

<h1 id="toc1"><a name="Intervals"></a>Intervals</h1>

Line 172:

Line 157:

<th>Ratios*<br />

</th>

<th>Generator for<br />

<th>Generator for*<br />

</th>

</tr>

Line 212:

Line 197:

</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><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Vishnuzmic%20family#Vishnu">Vishnu</a> (2/oct), <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=15%2650&amp;limit=11" rel="nofollow">Coblack</a> (5/oct)<br />

</td>

</tr>

Line 222:

Line 207:

</td>

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meantone%20family#Injera">Injera</a> (50d val, 2/oct)<br />

</td>

</tr>

Line 272:

Line 257:

</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><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>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Subgroup%20temperaments#x2.9.7.11-Machine">Machine</a> (50b val)<br />

</td>

</tr>

Line 292:

Line 277:

</td>

<td><a class="wiki_link" href="/Marvel%20temperaments#Septimin">Septimin</a><br />

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Marvel%20temperaments#Septimin-13-limit">Septimin (13-limit)</a><br />

</td>

</tr>

Line 342:

Line 327:

</td>

<td><a class="wiki_link" href="/Marvel%20temperaments#Wizard-11-limit">Wizard</a><br />

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Marvel%20temperaments#Wizard-11-limit">Wizard</a> (2/oct)<br />

</td>

</tr>

Line 352:

Line 337:

</td>

<td><a class="wiki_link" href="/Ditonmic%20family">Ditonic</a><br />

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ditonmic%20family">Ditonic</a><br />

</td>

</tr>

Line 362:

Line 347:

</td>

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Porcupine%20family#Hedgehog">Hedgehog</a> (50cc val, 2/oct)<br />

</td>

</tr>

Line 372:

Line 357:

</td>

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Starling%20temperaments#Bisemidim">Bisemidim</a><br />

<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Starling%20temperaments#Bisemidim">Bisemidim</a> (2/oct)<br />

</td>

</tr>

Line 412:

Line 397:

</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><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>

Line 677:

Line 662:

</table>

*using the 13-limit patent val<br />

*using the 13-limit patent val except as noted<br />

<br />

<h2 id="toc2"><a name="Intervals-Intervals by patent val error"></a>Intervals by patent val error</h2>

Line 836:

Line 822:

<br />

<h1 id="toc3"><a name="Commas"></a>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 in cents ~~orunded~~ to 2 decimal places.) This list is not all-inclusive, and is based on the interval table from Scala version 2.2.<br />

50 EDO tempers out the following commas. (Note: This assumes the val &lt; 50 79 116 140 173 185 204 212 226 |, comma values in cents rounded to 2 decimal places.) This list is not all-inclusive, and is based on the interval table from Scala version 2.2.<br />

Line 1,109:

Line 1,095:

<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 />

<h1 id="toc4"><a name="Music"></a>Music</h1>

<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 &~~amp~~;gt; ~~43.01 6561~~/~~6400 Mathieu superdiesis~~<~~/span~~><br />

<br />

<~~span style~~="~~display~~: ~~block~~; ~~height: 1px~~; ~~left: -40px~~; ~~overflow: hidden~~; ~~position: absolute~~; ~~top~~: ~~5675~~.~~5px; width: 1px;~~">~~| 23 6 -14~~ &~~amp~~;gt; ~~3.34 1212717/1210381 Vishnu comma~~</~~span~~><br />

<h1 id="toc5"><a name="Additional reading"></a>Additional reading</h1>

<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 />

<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><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></body></html></pre></div>

<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></pre></div>

@@ 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:spt3125|spt3125]] and made on <tt>2014-04-21 21:45:59 UTC</tt>.<br>
+: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-04-22 18:23:25 UTC</tt>.<br>
-: The original revision id was <tt>503693126</tt>.<br>
+: The original revision id was <tt>503910738</tt>.<br>
-: The revision comment was: <tt></tt><br>
+: The revision comment was: <tt>added more temperaments - hope they're correct :)</tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
@@ Line 10: / Line 10: @@
 tempers out 126/125, 225/224 and 3136/3125 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&amp;50 temperament ([[http://x31eq.com/cgi-bin/rt.cgi?ets=15%2650&amp;limit=11|Coblack]]). It is also the unique equal temperament tempering out both 81/80 and the [[vishnuzma]], 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.
-[[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 (and similarly as the next step from 31edo in Joseph Yasser's "[[http://books.google.com.au/books/about/A_theory_of_evolving_tonality.html?id=-XUsAAAAMAAJ&amp;redir_esc=y|A Theory of Evolving Tonality]]").
+The 50edo system is related to [[7edo]], [[12edo]], [[19edo]], [[31edo]] as the next approximation to the "Golden Tone System" ([[Das Goldene Tonsystem]]) of Thorvald Kornerup (and similarly as the next step from 31edo in Joseph Yasser's "[[http://books.google.com.au/books/about/A_theory_of_evolving_tonality.html?id=-XUsAAAAMAAJ&amp;redir_esc=y|A Theory of Evolving Tonality]]").
 =Intervals=
-||~ Degrees of 50edo ||~ Cents value ||~ Ratios* ||~ Generator for ||
+||~ 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&amp;limit=11|Coblack]] ||
+|| 3 || 72 || 21/20, 25/24, 26/25, 27/26, 28/27 || [[xenharmonic/Vishnuzmic family#Vishnu|Vishnu]] (2/oct), [[http://x31eq.com/cgi-bin/rt.cgi?ets=15%2650&amp;limit=11|Coblack]] (5/oct) ||
-|| 4 || 96 || 22/21 ||   ||
+|| 4 || 96 || 22/21 || [[xenharmonic/Meantone family#Injera|Injera]] (50d val, 2/oct) ||
 || 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&amp;limit=2.3.5.11.13|Tremka]] ||
+|| 9 || 216 || 25/22 || [[http://x31eq.com/cgi-bin/rt.cgi?ets=50%2661p&amp;limit=2.3.5.11.13|Tremka]], [[xenharmonic/Subgroup temperaments#x2.9.7.11-Machine|Machine]] (50b val) ||
 || 10 || 240 || 8/7, 15/13 ||   ||
-|| 11 || 264 || 7/6 || [[Marvel temperaments#Septimin|Septimin]] ||
+|| 11 || 264 || 7/6 || [[xenharmonic/Marvel temperaments#Septimin-13-limit|Septimin (13-limit)]] ||
 || 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]] ||
+|| 16 || 384 || 5/4 || [[xenharmonic/Marvel temperaments#Wizard-11-limit|Wizard]] (2/oct) ||
-|| 17 || 408 || 14/11 || [[Ditonmic family|Ditonic]] ||
+|| 17 || 408 || 14/11 || [[xenharmonic/Ditonmic family|Ditonic]] ||
-|| 18 || 432 || 9/7 ||   ||
+|| 18 || 432 || 9/7 || [[xenharmonic/Porcupine family#Hedgehog|Hedgehog]] (50cc val, 2/oct) ||
-|| 19 || 456 || 13/10 || [[xenharmonic/Starling temperaments#Bisemidim|Bisemidim]] ||
+|| 19 || 456 || 13/10 || [[xenharmonic/Starling temperaments#Bisemidim|Bisemidim]] (2/oct) ||
 || 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]] ||
+|| 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 ||   ||
@@ Line 69: / Line 66: @@
 || 48 || 1152 || 64/33, 35/18, 49/25, 108/55, 63/32 ||   ||
 || 49 || 1176 ||   ||   ||
-*using the 13-limit patent val
+*using the 13-limit patent val except as noted
 ==Intervals by patent val error==
 || Interval || Error ||
@@ Line 98: / Line 96: @@
 =Commas=
-EDO tempers out the following commas. (Note: This assumes the val &lt; 50 79 116 140 173 185 204 212 226 |, comma values in cents orunded to 2 decimal places.) This list is not all-inclusive, and is based on the interval table from Scala version 2.2.
+EDO tempers out the following commas. (Note: This assumes the val &lt; 50 79 116 140 173 185 204 212 226 |, comma values in cents rounded to 2 decimal places.) This list is not all-inclusive, and is based on the interval table from Scala version 2.2.
 ||~ Monzo ||~ Cents ||~ Ratio ||~ Name 1 ||~ Name 2 ||
 || | -4 4 -1 &gt; ||&gt; 21.51 ||= 81/80 || Syntonic comma || Didymus comma ||
@@ Line 122: / Line 120: @@
 || | 3 -2 0 1 -1 -1 0 0 1 &gt; ||&gt; 1.34 ||= 1288/1287 || Triaphonisma ||   ||
+=Music=
 [[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]]
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -4 4 -1 &gt; 21.51 81/80 syntonic comma, Didymus comma&lt;/span&gt;
 [[http://soonlabel.com/xenharmonic/archives/1929|Fugue on the Dragnet theme by Claudi Meneghin]]
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -8 8 -2 &gt; 43.01 6561/6400 Mathieu superdiesis&lt;/span&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 23 6 -14 &gt; 3.34 1212717/1210381 Vishnu comma&lt;/span&gt;
+=Additional reading=
+[[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]]
 [[https://www.dropbox.com/sh/4x81rzpkot32qzk/MQ3cJljjkh|50EDO Theory - Intervals, Chords and Scales in 50EDO by Cam Taylor]]
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 1 2 -3 1 &gt; 13.79 126/125 small septimal comma&lt;/span&gt;&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -5 2 2 -1 &gt; 7.71 225/224 septimal kleisma&lt;/span&gt;
+[[http://iamcamtaylor.wordpress.com/|iamcamtaylor - Blog on 50EDO and extended meantone theory by Cam Taylor]]</pre></div>
-[[http://iamcamtaylor.wordpress.com/|iamcamtaylor - Blog on 50EDO and extended meantone theory by Cam Taylor]]
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 6 0 -5 2 &gt; 6.08 3136/3125 middle second comma&lt;/span&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -6 -8 2 5 &gt; 1.12 420175/419904&lt;/span&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;|-11 2 7 -3 &gt; 1.63 703125/702464&lt;/span&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 11 -10 -10 10 &gt; 5.57 6772805/6751042&lt;/span&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;|-13 10 0 -1 &gt; 50.72 59049/57344 Harrison's comma&lt;/span&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 2 3 1 -2 -1 &gt; 3.21 540/539 Swets' comma&lt;/span&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -3 4 -2 -2 2 &gt; 0.18 9801/9800 kalisma, Gauss' comma&lt;/span&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 5 -1 3 0 -3 &gt; 3.03 4000/3993 undecimal schisma&lt;/span&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -7 -1 1 1 1 &gt; 4.50 385/384 undecimal kleisma&lt;/span&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 2 -1 0 1 -2 1 &gt; 4.76 364/363&lt;/span&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 2 3 0 -1 1 -2 &gt; 7.30 1188/1183 Kestrel Comma&lt;/span&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 3 0 2 0 1 -3 &gt; 2.36 2200/2197 Parizek comma&lt;/span&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -3 1 1 1 0 -1 &gt; 16.57 105/104 small tridecimal comma&lt;/span&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 3 -2 0 1 -1 -1 0 0 1 &gt; 1.34 1288/1287 triaphonisma&lt;/span&gt;</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;!-- ws:start:WikiTextTocRule:8:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Relations"&gt;Relations&lt;/a&gt;&lt;/div&gt;
+<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;!-- ws:start:WikiTextTocRule:12:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Relations"&gt;Relations&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;!-- ws:start:WikiTextTocRule:11: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Intervals-Intervals by patent val error"&gt;Intervals by patent val error&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Intervals-Intervals by patent val error"&gt;Intervals by patent val error&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Commas"&gt;Commas&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Commas"&gt;Commas&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Music"&gt;Music&lt;/a&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:13 --&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 &lt;a class="wiki_link_ext" href="http://lit.gfax.ch/Harmonics%202nd%20Edition%20%28Robert%20Smith%29.pdf" rel="nofollow"&gt;&amp;quot;Harmonics or the Philosophy of Musical Sounds&amp;quot;&lt;/a&gt; (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. 50edo, 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;
+&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Additional reading"&gt;Additional reading&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:19 --&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 &lt;a class="wiki_link_ext" href="http://lit.gfax.ch/Harmonics%202nd%20Edition%20%28Robert%20Smith%29.pdf" rel="nofollow"&gt;&amp;quot;Harmonics or the Philosophy of Musical Sounds&amp;quot;&lt;/a&gt; (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. 50edo, 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;
 &lt;br /&gt;
 tempers out 126/125, 225/224 and 3136/3125 in the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, indicating it supports septimal meantone; 245/242, 385/384 and 540/539 in the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; and 105/104, 144/143 and 196/195 in the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;, 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;amp;50 temperament (&lt;a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=15%2650&amp;amp;limit=11" rel="nofollow"&gt;Coblack&lt;/a&gt;). It is also the unique equal temperament tempering out both 81/80 and the &lt;a class="wiki_link" href="/vishnuzma"&gt;vishnuzma&lt;/a&gt;, 6115295232/6103515625 = |23 6 -14&amp;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.&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://www.archive.org/details/harmonicsorphilo00smit" rel="nofollow"&gt;Robert Smith's book online&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://www.music.ed.ac.uk/russell/conference/robertsmithkirckman.html" rel="nofollow"&gt;More information about Robert Smith's temperament&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Relations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Relations&lt;/h1&gt;
-  The 50-edo system is related to &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; as the next approximation to the &amp;quot;Golden Tone System&amp;quot; (&lt;a class="wiki_link" href="/Das%20Goldene%20Tonsystem"&gt;Das Goldene Tonsystem&lt;/a&gt;) of Thorvald Kornerup (and similarly as the next step from 31edo in Joseph Yasser's &amp;quot;&lt;a class="wiki_link_ext" href="http://books.google.com.au/books/about/A_theory_of_evolving_tonality.html?id=-XUsAAAAMAAJ&amp;amp;redir_esc=y" rel="nofollow"&gt;A Theory of Evolving Tonality&lt;/a&gt;&amp;quot;).&lt;br /&gt;
+  The 50edo system is related to &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; as the next approximation to the &amp;quot;Golden Tone System&amp;quot; (&lt;a class="wiki_link" href="/Das%20Goldene%20Tonsystem"&gt;Das Goldene Tonsystem&lt;/a&gt;) of Thorvald Kornerup (and similarly as the next step from 31edo in Joseph Yasser's &amp;quot;&lt;a class="wiki_link_ext" href="http://books.google.com.au/books/about/A_theory_of_evolving_tonality.html?id=-XUsAAAAMAAJ&amp;amp;redir_esc=y" rel="nofollow"&gt;A Theory of Evolving Tonality&lt;/a&gt;&amp;quot;).&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Intervals&lt;/h1&gt;
@@ Line 172: / Line 157: @@
          &lt;th&gt;Ratios*&lt;br /&gt;
 &lt;/th&gt;
-         &lt;th&gt;Generator for&lt;br /&gt;
+         &lt;th&gt;Generator for*&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;
@@ Line 212: / Line 197: @@
          &lt;td&gt;21/20, 25/24, 26/25, 27/26, 28/27&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Vishnu"&gt;Vishnu&lt;/a&gt;, &lt;a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=15%2650&amp;amp;limit=11" rel="nofollow"&gt;Coblack&lt;/a&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Vishnuzmic%20family#Vishnu"&gt;Vishnu&lt;/a&gt; (2/oct), &lt;a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=15%2650&amp;amp;limit=11" rel="nofollow"&gt;Coblack&lt;/a&gt; (5/oct)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 222: / Line 207: @@
          &lt;td&gt;22/21&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meantone%20family#Injera"&gt;Injera&lt;/a&gt; (50d val, 2/oct)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 272: / Line 257: @@
          &lt;td&gt;25/22&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=50%2661p&amp;amp;limit=2.3.5.11.13" rel="nofollow"&gt;Tremka&lt;/a&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=50%2661p&amp;amp;limit=2.3.5.11.13" rel="nofollow"&gt;Tremka&lt;/a&gt;, &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Subgroup%20temperaments#x2.9.7.11-Machine"&gt;Machine&lt;/a&gt; (50b val)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 292: / Line 277: @@
          &lt;td&gt;7/6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="/Marvel%20temperaments#Septimin"&gt;Septimin&lt;/a&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Marvel%20temperaments#Septimin-13-limit"&gt;Septimin (13-limit)&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 342: / Line 327: @@
          &lt;td&gt;5/4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="/Marvel%20temperaments#Wizard-11-limit"&gt;Wizard&lt;/a&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Marvel%20temperaments#Wizard-11-limit"&gt;Wizard&lt;/a&gt; (2/oct)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 352: / Line 337: @@
          &lt;td&gt;14/11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="/Ditonmic%20family"&gt;Ditonic&lt;/a&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ditonmic%20family"&gt;Ditonic&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 362: / Line 347: @@
          &lt;td&gt;9/7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Porcupine%20family#Hedgehog"&gt;Hedgehog&lt;/a&gt; (50cc val, 2/oct)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 372: / Line 357: @@
          &lt;td&gt;13/10&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Starling%20temperaments#Bisemidim"&gt;Bisemidim&lt;/a&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Starling%20temperaments#Bisemidim"&gt;Bisemidim&lt;/a&gt; (2/oct)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 412: / Line 397: @@
          &lt;td&gt;11/8, 18/13&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Chromatic%20pairs#Barton"&gt;Barton&lt;/a&gt;/&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Hemimean%20clan#Emka"&gt;Emka&lt;/a&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Chromatic%20pairs#Barton"&gt;Barton&lt;/a&gt;, &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Hemimean%20clan#Emka"&gt;Emka&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 677: / Line 662: @@
 &lt;/table&gt;
-*using the 13-limit patent val&lt;br /&gt;
+*using the 13-limit patent val except as noted&lt;br /&gt;
+&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Intervals-Intervals by patent val error"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Intervals by patent val error&lt;/h2&gt;
@@ Line 836: / Line 822: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Commas&lt;/h1&gt;
-EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 50 79 116 140 173 185 204 212 226 |, comma values in cents orunded to 2 decimal places.) This list is not all-inclusive, and is based on the interval table from Scala version 2.2.&lt;br /&gt;
+EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 50 79 116 140 173 185 204 212 226 |, comma values in cents rounded to 2 decimal places.) This list is not all-inclusive, and is based on the interval table from Scala version 2.2.&lt;br /&gt;
@@ Line 1,109: / Line 1,095: @@
 &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;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Music&lt;/h1&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;br /&gt;
 &lt;a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/1118" rel="nofollow" target="_blank"&gt;Fantasia Catalana by Claudi Meneghin&lt;/a&gt;&lt;br /&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -4 4 -1 &amp;gt; 21.51 81/80 syntonic comma, Didymus comma&lt;/span&gt;&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/1929" rel="nofollow"&gt;Fugue on the Dragnet theme by Claudi Meneghin&lt;/a&gt;&lt;br /&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -8 8 -2 &amp;gt; 43.01 6561/6400 Mathieu superdiesis&lt;/span&gt;&lt;br /&gt;
+&lt;br /&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 23 6 -14 &amp;gt; 3.34 1212717/1210381 Vishnu comma&lt;/span&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Additional reading"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Additional reading&lt;/h1&gt;
+ &lt;a class="wiki_link_ext" href="http://www.archive.org/details/harmonicsorphilo00smit" rel="nofollow"&gt;Robert Smith's book online&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://www.music.ed.ac.uk/russell/conference/robertsmithkirckman.html" rel="nofollow"&gt;More information about Robert Smith's temperament&lt;/a&gt;&lt;br /&gt;
+&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="https://www.dropbox.com/sh/4x81rzpkot32qzk/MQ3cJljjkh" rel="nofollow"&gt;50EDO Theory - Intervals, Chords and Scales in 50EDO by Cam Taylor&lt;/a&gt;&lt;br /&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 1 2 -3 1 &amp;gt; 13.79 126/125 small septimal comma&lt;/span&gt;&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -5 2 2 -1 &amp;gt; 7.71 225/224 septimal kleisma&lt;/span&gt;&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://iamcamtaylor.wordpress.com/" rel="nofollow"&gt;iamcamtaylor - Blog on 50EDO and extended meantone theory by Cam Taylor&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
-&lt;a class="wiki_link_ext" href="http://iamcamtaylor.wordpress.com/" rel="nofollow"&gt;iamcamtaylor - Blog on 50EDO and extended meantone theory by Cam Taylor&lt;/a&gt;&lt;br /&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 6 0 -5 2 &amp;gt; 6.08 3136/3125 middle second comma&lt;/span&gt;&lt;br /&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -6 -8 2 5 &amp;gt; 1.12 420175/419904&lt;/span&gt;&lt;br /&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;|-11 2 7 -3 &amp;gt; 1.63 703125/702464&lt;/span&gt;&lt;br /&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 11 -10 -10 10 &amp;gt; 5.57 6772805/6751042&lt;/span&gt;&lt;br /&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;|-13 10 0 -1 &amp;gt; 50.72 59049/57344 Harrison's comma&lt;/span&gt;&lt;br /&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 2 3 1 -2 -1 &amp;gt; 3.21 540/539 Swets' comma&lt;/span&gt;&lt;br /&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -3 4 -2 -2 2 &amp;gt; 0.18 9801/9800 kalisma, Gauss' comma&lt;/span&gt;&lt;br /&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 5 -1 3 0 -3 &amp;gt; 3.03 4000/3993 undecimal schisma&lt;/span&gt;&lt;br /&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -7 -1 1 1 1 &amp;gt; 4.50 385/384 undecimal kleisma&lt;/span&gt;&lt;br /&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 2 -1 0 1 -2 1 &amp;gt; 4.76 364/363&lt;/span&gt;&lt;br /&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 2 3 0 -1 1 -2 &amp;gt; 7.30 1188/1183 Kestrel Comma&lt;/span&gt;&lt;br /&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 3 0 2 0 1 -3 &amp;gt; 2.36 2200/2197 Parizek comma&lt;/span&gt;&lt;br /&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -3 1 1 1 0 -1 &amp;gt; 16.57 105/104 small tridecimal comma&lt;/span&gt;&lt;br /&gt;
-&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 3 -2 0 1 -1 -1 0 0 1 &amp;gt; 1.34 1288/1287 triaphonisma&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>