Didymus rank-3 family: Difference between revisions

Revision as of 21:46, 11 December 2010

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This revision was by author genewardsmith and made on 2010-12-11 21:46:42 UTC.

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These are the rank three temperaments tempering out the didymus comma, 81/80. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.

==Euterpe==
Commas: 81/80, 99/98

Minimax tuning
[|1 0 0 0 0>, |1 0 1/4 0 0>, |0 0 1 0 0>, 
|0 0 0 1 0>, |-1 0 -1/2 2 0>]
Eigenmonzos: 2, 5, 7

Map: [<1 0 -4 0 1|, <0 1 4 0 -2|, <0 0 0 1 2|]
EDOs: 31, 74, 88, 105

==Calliope==
Commas: 81/80, 45/44

Minimax tuning
[|1 0 0 0 0>, |1 0 0 0 1/6>, |0 0 0 0 2/3>, 
|1 -1 0 1 1/6>, |0 0 0 0 1>]
Eigenmonzos: 2, 7/3, 11

Map: [<1 0 -4 0 -6|, <0 1 4 0 6|, <0 0 0 1 0|]
EDOs: 19, 26, 45

==Erato==
Commas: 81/80, 441/440

==Clio==
Commas: 81/80, 176/175

==Polyhymnia==
Commas: 81/80, 385/384

==Thalia==
Commas: 81/80, 55/54

==Melpomene==
Commas: 81/80, 56/55

==Urania==
Commas: 81/80, 121/120

==Terpsichore==
Commas: 81/80, 540/539

Original HTML content:

<html><head><title>Didymus rank three family</title></head><body>These are the rank three temperaments tempering out the didymus comma, 81/80. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Euterpe"></a><!-- ws:end:WikiTextHeadingRule:0 -->Euterpe</h2>
Commas: 81/80, 99/98<br />
<br />
Minimax tuning<br />
[|1 0 0 0 0&gt;, |1 0 1/4 0 0&gt;, |0 0 1 0 0&gt;, <br />
|0 0 0 1 0&gt;, |-1 0 -1/2 2 0&gt;]<br />
Eigenmonzos: 2, 5, 7<br />
<br />
Map: [&lt;1 0 -4 0 1|, &lt;0 1 4 0 -2|, &lt;0 0 0 1 2|]<br />
EDOs: 31, 74, 88, 105<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Calliope"></a><!-- ws:end:WikiTextHeadingRule:2 -->Calliope</h2>
Commas: 81/80, 45/44<br />
<br />
Minimax tuning<br />
[|1 0 0 0 0&gt;, |1 0 0 0 1/6&gt;, |0 0 0 0 2/3&gt;, <br />
|1 -1 0 1 1/6&gt;, |0 0 0 0 1&gt;]<br />
Eigenmonzos: 2, 7/3, 11<br />
<br />
Map: [&lt;1 0 -4 0 -6|, &lt;0 1 4 0 6|, &lt;0 0 0 1 0|]<br />
EDOs: 19, 26, 45<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Erato"></a><!-- ws:end:WikiTextHeadingRule:4 -->Erato</h2>
Commas: 81/80, 441/440<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Clio"></a><!-- ws:end:WikiTextHeadingRule:6 -->Clio</h2>
Commas: 81/80, 176/175<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x-Polyhymnia"></a><!-- ws:end:WikiTextHeadingRule:8 -->Polyhymnia</h2>
Commas: 81/80, 385/384<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x-Thalia"></a><!-- ws:end:WikiTextHeadingRule:10 -->Thalia</h2>
Commas: 81/80, 55/54<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x-Melpomene"></a><!-- ws:end:WikiTextHeadingRule:12 -->Melpomene</h2>
Commas: 81/80, 56/55<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-Urania"></a><!-- ws:end:WikiTextHeadingRule:14 -->Urania</h2>
Commas: 81/80, 121/120<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x-Terpsichore"></a><!-- ws:end:WikiTextHeadingRule:16 -->Terpsichore</h2>
Commas: 81/80, 540/539</body></html>

@@ 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:genewardsmith|genewardsmith]] and made on <tt>2010-12-11 21:13:26 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-11 21:46:42 UTC</tt>.<br>
-: The original revision id was <tt>187409809</tt>.<br>
+: The original revision id was <tt>187412557</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 17: / Line 17: @@
 Map: [&lt;1 0 -4 0 1|, &lt;0 1 4 0 -2|, &lt;0 0 0 1 2|]
-EDOs: 34, 74, 88, 105
+EDOs: 31, 74, 88, 105
 ==Calliope==
 Commas: 81/80, 45/44
+Minimax tuning
+[|1 0 0 0 0&gt;, |1 0 0 0 1/6&gt;, |0 0 0 0 2/3&gt;,
+|1 -1 0 1 1/6&gt;, |0 0 0 0 1&gt;]
+Eigenmonzos: 2, 7/3, 11
+Map: [&lt;1 0 -4 0 -6|, &lt;0 1 4 0 6|, &lt;0 0 0 1 0|]
+EDOs: 19, 26, 45
 ==Erato==
@@ Line 54: / Line 62: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 0 -4 0 1|, &amp;lt;0 1 4 0 -2|, &amp;lt;0 0 0 1 2|]&lt;br /&gt;
-EDOs: 34, 74, 88, 105&lt;br /&gt;
+EDOs: 31, 74, 88, 105&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Calliope"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Calliope&lt;/h2&gt;
 Commas: 81/80, 45/44&lt;br /&gt;
+&lt;br /&gt;
+Minimax tuning&lt;br /&gt;
+[|1 0 0 0 0&amp;gt;, |1 0 0 0 1/6&amp;gt;, |0 0 0 0 2/3&amp;gt;, &lt;br /&gt;
+|1 -1 0 1 1/6&amp;gt;, |0 0 0 0 1&amp;gt;]&lt;br /&gt;
+Eigenmonzos: 2, 7/3, 11&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 0 -4 0 -6|, &amp;lt;0 1 4 0 6|, &amp;lt;0 0 0 1 0|]&lt;br /&gt;
+EDOs: 19, 26, 45&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="x-Erato"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Erato&lt;/h2&gt;

Didymus rank-3 family: Difference between revisions

Revision as of 21:46, 11 December 2010

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