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Schismatic family: Difference between revisions

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VisualWikitext
Wikispaces>genewardsmith
**Imported revision 317175900 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 318557610 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-03 04:08:35 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-08 15:18:42 UTC</tt>.<br>
: The original revision id was <tt>317175900</tt>.<br>
: The original revision id was <tt>318557610</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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EDOs: 12, 118, 130, 248, 378
EDOs: 12, 118, 130, 248, 378
Badness: 0.0287
Badness: 0.0287
=Kleischismic=
Commas: 32805/32768, 1500625/1492992
POTE generator: ~36/35 = 50.920
Map: [&lt;2 1 22 -15|, &lt;0 2 -16 19|]
Wedgie: &lt;&lt;4 -32 38 -60 49 178||
EDOs: 24, 94, 118, 212, 330, 542d, 872cd
Badness: 0.1106
==11-limit==
Commas: 385/384, 9801/9800, 14641/14580
POTE generator: ~36/35 = 50.918
Map: [&lt;2 1 22 -15 8|, &lt;0 2 -16 19 -1|]
EDOs: 24, 94, 118, 212, 330e, 542de
Badness: 0.0367
==13-limit==
Commas: 352/351, 385/384, 729/728, 1575/1573
POTE generator: ~36/35 = 50.938
Map: [&lt;2 1 22 -15 8 15|, &lt;0 2 -16 19 -1 -7|]
EDOs: 24, 94, 118, 212f
Badness: 0.0376


=Term=
=Term=
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Badness: 0.0315</pre></div>
Badness: 0.0315</pre></div>
<h4>Original HTML content:</h4>
<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;Schismatic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:56:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;a href="#Five limit"&gt;Five limit&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt; | &lt;a href="#Seven limit children"&gt;Seven limit children&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt; | &lt;a href="#Garibaldi"&gt;Garibaldi&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt; | &lt;a href="#Guiron"&gt;Guiron&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt; | &lt;a href="#Pogo"&gt;Pogo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt;&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt; | &lt;a href="#Schism"&gt;Schism&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt; | &lt;a href="#Pontiac"&gt;Pontiac&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt; | &lt;a href="#Grackle"&gt;Grackle&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt; | &lt;a href="#Bischismic"&gt;Bischismic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt;&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt;&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt; | &lt;a href="#Term"&gt;Term&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt; | &lt;a href="#Sesquiquartififths"&gt;Sesquiquartififths&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt; | &lt;a href="#Sextilififths"&gt;Sextilififths&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&gt;&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt;&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt; | &lt;a href="#Tsaharuk"&gt;Tsaharuk&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt; | &lt;a href="#Quanharuk"&gt;Quanharuk&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt;&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&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;Schismatic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:62:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;a href="#Five limit"&gt;Five limit&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt; | &lt;a href="#Seven limit children"&gt;Seven limit children&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt; | &lt;a href="#Garibaldi"&gt;Garibaldi&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt;&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt; | &lt;a href="#Guiron"&gt;Guiron&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt;&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt;&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt; | &lt;a href="#Pogo"&gt;Pogo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt;&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt; | &lt;a href="#Schism"&gt;Schism&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt; | &lt;a href="#Pontiac"&gt;Pontiac&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt; | &lt;a href="#Grackle"&gt;Grackle&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt; | &lt;a href="#Bischismic"&gt;Bischismic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&gt;&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt;&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt; | &lt;a href="#Kleischismic"&gt;Kleischismic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt;&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt;&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&gt; | &lt;a href="#Term"&gt;Term&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;!-- ws:start:WikiTextTocRule:86: --&gt; | &lt;a href="#Sesquiquartififths"&gt;Sesquiquartififths&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt; | &lt;a href="#Sextilififths"&gt;Sextilififths&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt; | &lt;a href="#Tsaharuk"&gt;Tsaharuk&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;!-- ws:start:WikiTextTocRule:92: --&gt; | &lt;a href="#Quanharuk"&gt;Quanharuk&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&gt;&lt;!-- ws:end:WikiTextTocRule:93 --&gt;&lt;!-- ws:start:WikiTextTocRule:94: --&gt;
&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;br /&gt;
&lt;!-- ws:end:WikiTextTocRule:94 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Five limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Five limit&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Five limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Five limit&lt;/h1&gt;
The 5-limit parent comma for the schismatic family is the &lt;a class="wiki_link" href="/schisma"&gt;schisma&lt;/a&gt; of 32805/32768, which is the amount by which the Pythagorean comma exceeds the &lt;a class="wiki_link" href="/Didymus%20comma"&gt;Didymus comma&lt;/a&gt; (&lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt;), or alternatively put, the difference between a just major third and a just diminished fourth. Its &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is |-15 8 1&amp;gt;, and flipping that yields &amp;lt;&amp;lt;1 -8 -15|| for the &lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;wedgie&lt;/a&gt;. This tells us the generator is a fifth and that we will need eight fourths in succession to reach the pitch class of a major third. In fact, 10 = (4/3)^8 * 32805/32768. &lt;br /&gt;
The 5-limit parent comma for the schismatic family is the &lt;a class="wiki_link" href="/schisma"&gt;schisma&lt;/a&gt; of 32805/32768, which is the amount by which the Pythagorean comma exceeds the &lt;a class="wiki_link" href="/Didymus%20comma"&gt;Didymus comma&lt;/a&gt; (&lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt;), or alternatively put, the difference between a just major third and a just diminished fourth. Its &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is |-15 8 1&amp;gt;, and flipping that yields &amp;lt;&amp;lt;1 -8 -15|| for the &lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;wedgie&lt;/a&gt;. This tells us the generator is a fifth and that we will need eight fourths in succession to reach the pitch class of a major third. In fact, 10 = (4/3)^8 * 32805/32768. &lt;br /&gt;
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Badness: 0.0287&lt;br /&gt;
Badness: 0.0287&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Term"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Term&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Kleischismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Kleischismic&lt;/h1&gt;
Commas: 32805/32768, 1500625/1492992&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~36/35 = 50.920&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 22 -15|, &amp;lt;0 2 -16 19|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;4 -32 38 -60 49 178||&lt;br /&gt;
EDOs: 24, 94, 118, 212, 330, 542d, 872cd&lt;br /&gt;
Badness: 0.1106&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Kleischismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;11-limit&lt;/h2&gt;
Commas: 385/384, 9801/9800, 14641/14580&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~36/35 = 50.918&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 22 -15 8|, &amp;lt;0 2 -16 19 -1|]&lt;br /&gt;
EDOs: 24, 94, 118, 212, 330e, 542de&lt;br /&gt;
Badness: 0.0367&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Kleischismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;13-limit&lt;/h2&gt;
Commas: 352/351, 385/384, 729/728, 1575/1573&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~36/35 = 50.938&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 22 -15 8 15|, &amp;lt;0 2 -16 19 -1 -7|]&lt;br /&gt;
EDOs: 24, 94, 118, 212f&lt;br /&gt;
Badness: 0.0376&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc22"&gt;&lt;a name="Term"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Term&lt;/h1&gt;
Commas: 32805/32768, 250047/250000&lt;br /&gt;
Commas: 32805/32768, 250047/250000&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0200&lt;br /&gt;
Badness: 0.0200&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc20"&gt;&lt;a name="Sesquiquartififths"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Sesquiquartififths&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc23"&gt;&lt;a name="Sesquiquartififths"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Sesquiquartififths&lt;/h1&gt;
Commas: 2401/2400, 32805/32768&lt;br /&gt;
Commas: 2401/2400, 32805/32768&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0112&lt;br /&gt;
Badness: 0.0112&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Sesquiquartififths-Sesquart"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Sesquart&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Sesquiquartififths-Sesquart"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Sesquart&lt;/h2&gt;
Commas: 243/242, 441/440, 16384/16335&lt;br /&gt;
Commas: 243/242, 441/440, 16384/16335&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0293&lt;br /&gt;
Badness: 0.0293&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc22"&gt;&lt;a name="Sextilififths"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Sextilififths&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc25"&gt;&lt;a name="Sextilififths"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Sextilififths&lt;/h1&gt;
Commas: 32768/32805, 235298/234375&lt;br /&gt;
Commas: 32768/32805, 235298/234375&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.1088&lt;br /&gt;
Badness: 0.1088&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Sextilififths-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Sextilififths-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;11-limit&lt;/h2&gt;
Commas: 441/440, 4000/3993, 235298/234375&lt;br /&gt;
Commas: 441/440, 4000/3993, 235298/234375&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0455&lt;br /&gt;
Badness: 0.0455&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Sextilififths-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc27"&gt;&lt;a name="Sextilififths-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;13-limit&lt;/h2&gt;
Commas: 363/363, 441/440, 676/675, 10985/10976&lt;br /&gt;
Commas: 363/363, 441/440, 676/675, 10985/10976&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 613: Line 669:
Badness: 0.0253&lt;br /&gt;
Badness: 0.0253&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc25"&gt;&lt;a name="Tsaharuk"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Tsaharuk&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc28"&gt;&lt;a name="Tsaharuk"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;Tsaharuk&lt;/h1&gt;
Commas: 32805/32768, 420175/419904&lt;br /&gt;
Commas: 32805/32768, 420175/419904&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 623: Line 679:
Badness: 0.0307&lt;br /&gt;
Badness: 0.0307&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc26"&gt;&lt;a name="Quanharuk"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;Quanharuk&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc29"&gt;&lt;a name="Quanharuk"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;Quanharuk&lt;/h1&gt;
Commas: 16875/16807, 32805/32768&lt;br /&gt;
Commas: 16875/16807, 32805/32768&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 633: Line 689:
Badness: 0.0720&lt;br /&gt;
Badness: 0.0720&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc27"&gt;&lt;a name="Quanharuk-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc30"&gt;&lt;a name="Quanharuk-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;11-limit&lt;/h2&gt;
Commas: 540/539, 1375/1372, 32805/32768&lt;br /&gt;
Commas: 540/539, 1375/1372, 32805/32768&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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