Catalog of rank-4 temperaments

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Revision as of 18:25, 6 October 2010 by Wikispaces>genewardsmith (**Imported revision 168437071 - Original comment: **)
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This revision was by author genewardsmith and made on 2010-10-06 18:25:35 UTC.
The original revision id was 168437071.
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Original Wikitext content:

==441/440==

===Commas 441/440, 364/363===

13-limit minimax
[|1 0 0 0 0 0>, |5/3 0 1/3 -1/3 -1/3 1/3>, 
|1/6 0 5/6 2/3 -5/6 1/3>, |0 0 0 1 0 0>, 
|1/6 0 -1/6 2/3 1/6 1/3>, |0 0 0 0 0 1>]
Eigenmonzos: 2, 11/10, 8/7, 16/13

15-limit minimax
[|1 0 0 0 0 0>, |5/4 1/4 1/4 -1/4 -1/4 1/4>, 
|5/4 -3/4 5/4 -1/4 -1/4 1/4>, 
|17/8 -11/8 5/8 -1/8 3/8 1/8>, 
|5/2 -3/2 1/2 -1/2 1/2 1/2>, 
|17/8 -11/8 5/8 -9/8 3/8 9/8>]
Eigenmonzos: 2, 14/13, 6/5, 11/9

Lattice basis: 3/2 1.2263 14/11 1.4629 21/16 1.4657
Map to lattice: [<0 1 1 -1 -1 0|, 
<0 0 1 0 -1 -2|, <0 0 1 1 1 1|]

Map: [<1 0 0 0 -3 -8|, <0 1 0 0 2 5|, 
<0 0 1 0 -1 -2|, <0 0 0 1 2 3|]
Generators: 2, 3, 5
Edos: 15, 23, 26, 29, 41, 43, 46, 58, 113, 130, 159, 217, 289, 393


==9801/9800==

===Commas 2080/2079, 1716/1715===

13 and 15 limit minimax
[|1 0 0 0 0 0>, |7/10 4/5 0 -2/5 0 1/5>, 
|7/10 -1/5 1 -2/5 0 1/5>, |7/5 -2/5 0 1/5 0 2/5>, 
|11/5 -11/5 1 3/5 0 1/5>, |0 0 0 0 0 1>]
Eigenmonzos: 2, 6/5, 16/13, 9/7

Lattice basis: 3/2 length 1.1956 7/4 length 1.4506 14/13 1.8299

Map: [<2 0 0 0 3 -7|, <0 1 0 0 -2 1|, 
<0 0 1 0 1 0|, <0 0 0 1 1 2|]
Generators: 99/70, 3, 5, 7
Edos: 26, 36, 46, 58, 68, 72, 84, 94, 130, 140, 166, 198, 224, 270, 494, 764, 1186, 1892

Original HTML content:

<html><head><title>Rank four temperaments</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-441/440"></a><!-- ws:end:WikiTextHeadingRule:0 -->441/440</h2>
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-441/440-Commas 441/440, 364/363"></a><!-- ws:end:WikiTextHeadingRule:2 -->Commas 441/440, 364/363</h3>
<br />
13-limit minimax<br />
[|1 0 0 0 0 0&gt;, |5/3 0 1/3 -1/3 -1/3 1/3&gt;, <br />
|1/6 0 5/6 2/3 -5/6 1/3&gt;, |0 0 0 1 0 0&gt;, <br />
|1/6 0 -1/6 2/3 1/6 1/3&gt;, |0 0 0 0 0 1&gt;]<br />
Eigenmonzos: 2, 11/10, 8/7, 16/13<br />
<br />
15-limit minimax<br />
[|1 0 0 0 0 0&gt;, |5/4 1/4 1/4 -1/4 -1/4 1/4&gt;, <br />
|5/4 -3/4 5/4 -1/4 -1/4 1/4&gt;, <br />
|17/8 -11/8 5/8 -1/8 3/8 1/8&gt;, <br />
|5/2 -3/2 1/2 -1/2 1/2 1/2&gt;, <br />
|17/8 -11/8 5/8 -9/8 3/8 9/8&gt;]<br />
Eigenmonzos: 2, 14/13, 6/5, 11/9<br />
<br />
Lattice basis: 3/2 1.2263 14/11 1.4629 21/16 1.4657<br />
Map to lattice: [&lt;0 1 1 -1 -1 0|, <br />
&lt;0 0 1 0 -1 -2|, &lt;0 0 1 1 1 1|]<br />
<br />
Map: [&lt;1 0 0 0 -3 -8|, &lt;0 1 0 0 2 5|, <br />
&lt;0 0 1 0 -1 -2|, &lt;0 0 0 1 2 3|]<br />
Generators: 2, 3, 5<br />
Edos: 15, 23, 26, 29, 41, 43, 46, 58, 113, 130, 159, 217, 289, 393<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-9801/9800"></a><!-- ws:end:WikiTextHeadingRule:4 -->9801/9800</h2>
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-9801/9800-Commas 2080/2079, 1716/1715"></a><!-- ws:end:WikiTextHeadingRule:6 -->Commas 2080/2079, 1716/1715</h3>
<br />
13 and 15 limit minimax<br />
[|1 0 0 0 0 0&gt;, |7/10 4/5 0 -2/5 0 1/5&gt;, <br />
|7/10 -1/5 1 -2/5 0 1/5&gt;, |7/5 -2/5 0 1/5 0 2/5&gt;, <br />
|11/5 -11/5 1 3/5 0 1/5&gt;, |0 0 0 0 0 1&gt;]<br />
Eigenmonzos: 2, 6/5, 16/13, 9/7<br />
<br />
Lattice basis: 3/2 length 1.1956 7/4 length 1.4506 14/13 1.8299<br />
<br />
Map: [&lt;2 0 0 0 3 -7|, &lt;0 1 0 0 -2 1|, <br />
&lt;0 0 1 0 1 0|, &lt;0 0 0 1 1 2|]<br />
Generators: 99/70, 3, 5, 7<br />
Edos: 26, 36, 46, 58, 68, 72, 84, 94, 130, 140, 166, 198, 224, 270, 494, 764, 1186, 1892</body></html>