Schismatic family: Difference between revisions

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<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:~~xenwolf~~|~~xenwolf~~]] and made on <tt>2011-08-21 10:56:44 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-21 17:29:37 UTC</tt>.<br>

: The original revision id was <tt>~~247380693~~</tt>.<br>

: The original revision id was <tt>256754056</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>

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[[edo|Edos]]: [[171edo|171]], [[643edo|643]]

Badness: 0.0112

==Sesquart==

Commas: 243/242, 441/440, 16384/16335

POTE generator: ~256/231 = 175.406

Map: [<1 1 7 5 2|, <0 4 -32 -15 10|]

EDOs: 41, 89, 130

Badness: 0.0293

=Sextilififths=

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</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>Schismatic family</title></head><body><a href="#Five limit">Five limit</a> | <a href="#Seven limit children">Seven limit children</a> | <a href="#Garibaldi">Garibaldi</a> | <a href="#Guiron">Guiron</a> | <a href="#Pogo">Pogo</a> | <a href="#Pontiac">Pontiac</a> | <a href="#Grackle">Grackle</a> | <a href="#Bischismic">Bischismic</a> | <a href="#Term">Term</a> | <a href="#Sesquiquartififths">Sesquiquartififths</a> | <a href="#Sextilififths">Sextilififths</a> | <a href="#Tsaharuk">Tsaharuk</a>

<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>Schismatic family</title></head><body><a href="#Five limit">Five limit</a> | <a href="#Seven limit children">Seven limit children</a> | <a href="#Garibaldi">Garibaldi</a> | <a href="#Guiron">Guiron</a> | <a href="#Pogo">Pogo</a> | <a href="#Pontiac">Pontiac</a> | <a href="#Grackle">Grackle</a> | <a href="#Bischismic">Bischismic</a> | <a href="#Term">Term</a> | <a href="#Sesquiquartififths">Sesquiquartififths</a> | <a href="#Sextilififths">Sextilififths</a> | <a href="#Tsaharuk">Tsaharuk</a>

<br />

<br />

<h1 id="toc0"><a name="Five limit"></a>Five limit</h1>

The 5-limit parent comma for the schismatic family is the <a class="wiki_link" href="/schisma">schisma</a> of 32805/32768, which is the amount by which the Pythagorean comma exceeds the <a class="wiki_link" href="/Didymus%20comma">Didymus comma</a> (<a class="wiki_link" href="/81_80">81/80</a>), or alternatively put, the difference between a just major third and a just diminished fourth. Its <a class="wiki_link" href="/monzo">monzo</a> is |-15 8 1&gt;, and flipping that yields &lt;&lt;1 -8 -15|| for the <a class="wiki_link" href="/Wedgies%20and%20Multivals">wedgie</a>. 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. <br />

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Badness: 0.0112<br />

<br />

<h1 id="~~toc19~~"><a name="Sextilififths"></a>Sextilififths</h1>

<h2 id="toc19"><a name="Sesquiquartififths-Sesquart"></a>Sesquart</h2>

Commas: 243/242, 441/440, 16384/16335<br />

<br />

POTE generator: ~256/231 = 175.406<br />

<br />

Map: [&lt;1 1 7 5 2|, &lt;0 4 -32 -15 10|]<br />

EDOs: 41, 89, 130<br />

Badness: 0.0293<br />

<br />

<h1 id="toc20"><a name="Sextilififths"></a>Sextilififths</h1>

Commas: 32768/32805, 235298/234375<br />

<br />

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Badness: 0.1088<br />

<br />

<h2 id="~~toc20~~"><a name="Sextilififths-11-limit"></a>11-limit</h2>

<h2 id="toc21"><a name="Sextilififths-11-limit"></a>11-limit</h2>

Commas: 441/440, 4000/3993, 235298/234375<br />

<br />

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Badness: 0.0455<br />

<br />

<h2 id="~~toc21~~"><a name="Sextilififths-13-limit"></a>13-limit</h2>

<h2 id="toc22"><a name="Sextilififths-13-limit"></a>13-limit</h2>

Commas: 363/363, 441/440, 676/675, 10985/10976<br />

<br />

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Badness: 0.0253<br />

<br />

<h1 id="~~toc22~~"><a name="Tsaharuk"></a>Tsaharuk</h1>

<h1 id="toc23"><a name="Tsaharuk"></a>Tsaharuk</h1>

Commas: 32805/32768, 420175/419904<br />

<br />

@@ 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:xenwolf|xenwolf]] and made on <tt>2011-08-21 10:56:44 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-21 17:29:37 UTC</tt>.<br>
-: The original revision id was <tt>247380693</tt>.<br>
+: The original revision id was <tt>256754056</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 239: / Line 239: @@
 [[edo|Edos]]: [[171edo|171]], [[643edo|643]]
 Badness: 0.0112
+==Sesquart==
+Commas: 243/242, 441/440, 16384/16335
+POTE generator: ~256/231 = 175.406
+Map: [&lt;1 1 7 5 2|, &lt;0 4 -32 -15 10|]
+EDOs: 41, 89, 130
+Badness: 0.0293
 =Sextilififths=
@@ Line 278: / Line 287: @@
 </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;Schismatic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:46:&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:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt;&lt;a href="#Five limit"&gt;Five limit&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt; | &lt;a href="#Seven limit children"&gt;Seven limit children&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt; | &lt;a href="#Garibaldi"&gt;Garibaldi&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt; | &lt;a href="#Guiron"&gt;Guiron&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt; | &lt;a href="#Pogo"&gt;Pogo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt; | &lt;a href="#Pontiac"&gt;Pontiac&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt; | &lt;a href="#Grackle"&gt;Grackle&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt; | &lt;a href="#Bischismic"&gt;Bischismic&lt;/a&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="#Term"&gt;Term&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt; | &lt;a href="#Sesquiquartififths"&gt;Sesquiquartififths&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt; | &lt;a href="#Sextilififths"&gt;Sextilififths&lt;/a&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;a href="#Tsaharuk"&gt;Tsaharuk&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&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:48:&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:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;a href="#Five limit"&gt;Five limit&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt; | &lt;a href="#Seven limit children"&gt;Seven limit children&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt; | &lt;a href="#Garibaldi"&gt;Garibaldi&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt; | &lt;a href="#Guiron"&gt;Guiron&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt; | &lt;a href="#Pogo"&gt;Pogo&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;a href="#Pontiac"&gt;Pontiac&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt; | &lt;a href="#Grackle"&gt;Grackle&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt; | &lt;a href="#Bischismic"&gt;Bischismic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&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;a href="#Term"&gt;Term&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt; | &lt;a href="#Sesquiquartififths"&gt;Sesquiquartififths&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="#Sextilififths"&gt;Sextilififths&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;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt; | &lt;a href="#Tsaharuk"&gt;Tsaharuk&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:73 --&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;
 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;
@@ Line 512: / Line 521: @@
 Badness: 0.0112&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="Sextilififths"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Sextilififths&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Sesquiquartififths-Sesquart"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Sesquart&lt;/h2&gt;
+Commas: 243/242, 441/440, 16384/16335&lt;br /&gt;
+&lt;br /&gt;
+POTE generator: ~256/231 = 175.406&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 1 7 5 2|, &amp;lt;0 4 -32 -15 10|]&lt;br /&gt;
+EDOs: 41, 89, 130&lt;br /&gt;
+Badness: 0.0293&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="Sextilififths"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Sextilififths&lt;/h1&gt;
 Commas: 32768/32805, 235298/234375&lt;br /&gt;
 &lt;br /&gt;
@@ Line 521: / Line 539: @@
 Badness: 0.1088&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="Sextilififths-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Sextilififths-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;11-limit&lt;/h2&gt;
 Commas: 441/440, 4000/3993, 235298/234375&lt;br /&gt;
 &lt;br /&gt;
@@ Line 530: / Line 548: @@
 Badness: 0.0455&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="Sextilififths-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Sextilififths-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;13-limit&lt;/h2&gt;
 Commas: 363/363, 441/440, 676/675, 10985/10976&lt;br /&gt;
 &lt;br /&gt;
@@ Line 539: / Line 557: @@
 Badness: 0.0253&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="Tsaharuk"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Tsaharuk&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc23"&gt;&lt;a name="Tsaharuk"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Tsaharuk&lt;/h1&gt;
 Commas: 32805/32768, 420175/419904&lt;br /&gt;
 &lt;br /&gt;