Schismatic family: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 164140823 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 164147795 - 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>2010-09-20 22:46:54 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-09-20 23:27:27 UTC</tt>.<br>
: The original revision id was <tt>164140823</tt>.<br>
: The original revision id was <tt>164147795</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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Map: [&lt;3 0 45 94|, &lt;0 1 -8 -18|]
Map: [&lt;3 0 45 94|, &lt;0 1 -8 -18|]
Edos: 171, 1038, 1209</pre></div>
Edos: 171, 1038, 1209
 
===Sesquiquartififths===
Commas: 2401/2400, 32805/32768
 
7-limit minimax
Eigenmonzos: 2, 7/6
 
9-limit minimax
Eigenmonzos: 2, 9/7
 
Map: [&lt;1 1 7 5|, &lt;0 4 -32 -15|]
Edos: 171, 643</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;The 5-limit parent comma for the schismatic family is the schisma of 32805/32768, which is the amount by which the Pythagorean comma exceeds the Didymus comma (81/80), 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;
<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;The 5-limit parent comma for the schismatic family is the schisma of 32805/32768, which is the amount by which the Pythagorean comma exceeds the Didymus comma (81/80), 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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&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;3 0 45 94|, &amp;lt;0 1 -8 -18|]&lt;br /&gt;
Map: [&amp;lt;3 0 45 94|, &amp;lt;0 1 -8 -18|]&lt;br /&gt;
Edos: 171, 1038, 1209&lt;/body&gt;&lt;/html&gt;</pre></div>
Edos: 171, 1038, 1209&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="x-Seven limit children-Sesquiquartififths"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Sesquiquartififths&lt;/h3&gt;
Commas: 2401/2400, 32805/32768&lt;br /&gt;
&lt;br /&gt;
7-limit minimax&lt;br /&gt;
Eigenmonzos: 2, 7/6&lt;br /&gt;
&lt;br /&gt;
9-limit minimax&lt;br /&gt;
Eigenmonzos: 2, 9/7&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 7 5|, &amp;lt;0 4 -32 -15|]&lt;br /&gt;
Edos: 171, 643&lt;/body&gt;&lt;/html&gt;</pre></div>