Catalog of rank-4 temperaments: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
==441/440==
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>2010-10-08 16:15:34 UTC</tt>.<br>
: The original revision id was <tt>169025383</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>
<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">==441/440==


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


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


15-limit minimax
15-limit minimax
[|1 0 0 0 0 0&gt;, |5/4 1/4 1/4 -1/4 -1/4 1/4&gt;,  
[|1 0 0 0 0 0&gt;, |5/4 1/4 1/4 -1/4 -1/4 1/4&gt;,  
|5/4 -3/4 5/4 -1/4 -1/4 1/4&gt;,  
|5/4 -3/4 5/4 -1/4 -1/4 1/4&gt;,  
Line 22: Line 18:
|5/2 -3/2 1/2 -1/2 1/2 1/2&gt;,  
|5/2 -3/2 1/2 -1/2 1/2 1/2&gt;,  
|17/8 -11/8 5/8 -9/8 3/8 9/8&gt;]
|17/8 -11/8 5/8 -9/8 3/8 9/8&gt;]
Eigenmonzos: 2, 14/13, 6/5, 11/9
Eigenmonzos: 2, 14/13, 6/5, 11/9


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


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


Line 40: Line 42:


13 and 15 limit minimax
13 and 15 limit minimax
[&lt;1 0 0 0 0 0|, &lt;0 1 0 0 0 0|,  
[&lt;1 0 0 0 0 0|, &lt;0 1 0 0 0 0|,  
&lt;2/3 4/3 1/3 0 0 -1/3|,  
&lt;2/3 4/3 1/3 0 0 -1/3|,  
&lt;19/6 -1/6 -1/6 1/2 -1/2 1/6|,  
&lt;19/6 -1/6 -1/6 1/2 -1/2 1/6|,  
&lt;19/6 -1/6 -1/6 -1/2 1/2 1/6|,  
&lt;19/6 -1/6 -1/6 -1/2 1/2 1/6|,  
&lt;2/3 4/3 -2/3 0 0 2/3|]
&lt;2/3 4/3 -2/3 0 0 2/3|]
Eigenmonzos: 2, 14/11, 13/10, 4/3
Eigenmonzos: 2, 14/11, 13/10, 4/3


Line 50: Line 58:


Map: [&lt;1 0 0 0 7 2|, &lt;0 1 0 0 1 4|,  
Map: [&lt;1 0 0 0 7 2|, &lt;0 1 0 0 1 4|,  
&lt;0 0 1 0 -1 -2|, &lt;0 0 0 1 -1 0|]
&lt;0 0 1 0 -1 -2|, &lt;0 0 0 1 -1 0|]
Generators: 2, 3, 5, 7
Generators: 2, 3, 5, 7
Edos: 7, 8, 15, 19, 26, 34, 41, 46, 53, 68, 72, 79, 87, 94, 99, 113, 140, 159, 212, 253
Edos: 7, 8, 15, 19, 26, 34, 41, 46, 53, 68, 72, 79, 87, 94, 99, 113, 140, 159, 212, 253


Line 59: Line 70:


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


Line 67: Line 80:


Map: [&lt;2 0 0 0 3 -7|, &lt;0 1 0 0 -2 1|,  
Map: [&lt;2 0 0 0 3 -7|, &lt;0 1 0 0 -2 1|,  
&lt;0 0 1 0 1 0|, &lt;0 0 0 1 1 2|]
&lt;0 0 1 0 1 0|, &lt;0 0 0 1 1 2|]
Generators: 99/70, 3, 5, 7
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</pre></div>
 
<h4>Original HTML content:</h4>
Edos: 26, 36, 46, 58, 68, 72, 84, 94, 130, 140, 166, 198, 224, 270, 494, 764, 1186, 1892
<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;Rank four temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-441/440"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;441/440&lt;/h2&gt;
[[Category:rank]]
&lt;br /&gt;
[[Category:rank_4]]
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-441/440-Commas 441/440, 364/363"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Commas 441/440, 364/363&lt;/h3&gt;
[[Category:temperament]]
&lt;br /&gt;
[[Category:theory]]
13-limit minimax&lt;br /&gt;
[|1 0 0 0 0 0&amp;gt;, |5/3 0 1/3 -1/3 -1/3 1/3&amp;gt;, &lt;br /&gt;
|1/6 0 5/6 2/3 -5/6 1/3&amp;gt;, |0 0 0 1 0 0&amp;gt;, &lt;br /&gt;
|1/6 0 -1/6 2/3 1/6 1/3&amp;gt;, |0 0 0 0 0 1&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 11/10, 8/7, 16/13&lt;br /&gt;
&lt;br /&gt;
15-limit minimax&lt;br /&gt;
[|1 0 0 0 0 0&amp;gt;, |5/4 1/4 1/4 -1/4 -1/4 1/4&amp;gt;, &lt;br /&gt;
|5/4 -3/4 5/4 -1/4 -1/4 1/4&amp;gt;, &lt;br /&gt;
|17/8 -11/8 5/8 -1/8 3/8 1/8&amp;gt;, &lt;br /&gt;
|5/2 -3/2 1/2 -1/2 1/2 1/2&amp;gt;, &lt;br /&gt;
|17/8 -11/8 5/8 -9/8 3/8 9/8&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 14/13, 6/5, 11/9&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 3/2 1.2263 14/11 1.4629 21/16 1.4657&lt;br /&gt;
Map to lattice: [&amp;lt;0 1 1 -1 -1 0|, &lt;br /&gt;
&amp;lt;0 0 1 0 -1 -2|, &amp;lt;0 0 1 1 1 1|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 0 -3 -8|, &amp;lt;0 1 0 0 2 5|, &lt;br /&gt;
&amp;lt;0 0 1 0 -1 -2|, &amp;lt;0 0 0 1 2 3|]&lt;br /&gt;
Generators: 2, 3, 5&lt;br /&gt;
Edos: 15, 23, 26, 29, 41, 43, 46, 58, 113, 130, 159, 217, 289, 393&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-441/440-Commas 441/440, 351/350"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Commas 441/440, 351/350&lt;/h3&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-385/384"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;385/384&lt;/h2&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x-385/384-Commas 385/384, 325/324"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Commas 385/384, 325/324&lt;/h3&gt;
&lt;br /&gt;
13 and 15 limit minimax&lt;br /&gt;
[&amp;lt;1 0 0 0 0 0|, &amp;lt;0 1 0 0 0 0|, &lt;br /&gt;
&amp;lt;2/3 4/3 1/3 0 0 -1/3|, &lt;br /&gt;
&amp;lt;19/6 -1/6 -1/6 1/2 -1/2 1/6|, &lt;br /&gt;
&amp;lt;19/6 -1/6 -1/6 -1/2 1/2 1/6|, &lt;br /&gt;
&amp;lt;2/3 4/3 -2/3 0 0 2/3|]&lt;br /&gt;
Eigenmonzos: 2, 14/11, 13/10, 4/3&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 4/3 1.0820 6/5 1.3935 10/9 1.6247&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 0 7 2|, &amp;lt;0 1 0 0 1 4|, &lt;br /&gt;
&amp;lt;0 0 1 0 -1 -2|, &amp;lt;0 0 0 1 -1 0|]&lt;br /&gt;
Generators: 2, 3, 5, 7&lt;br /&gt;
Edos: 7, 8, 15, 19, 26, 34, 41, 46, 53, 68, 72, 79, 87, 94, 99, 113, 140, 159, 212, 253&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-9801/9800"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;9801/9800&lt;/h2&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="x-9801/9800-Commas 2080/2079, 1716/1715"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Commas 2080/2079, 1716/1715&lt;/h3&gt;
&lt;br /&gt;
13 and 15 limit minimax&lt;br /&gt;
[|1 0 0 0 0 0&amp;gt;, |7/10 4/5 0 -2/5 0 1/5&amp;gt;, &lt;br /&gt;
|7/10 -1/5 1 -2/5 0 1/5&amp;gt;, |7/5 -2/5 0 1/5 0 2/5&amp;gt;, &lt;br /&gt;
|11/5 -11/5 1 3/5 0 1/5&amp;gt;, |0 0 0 0 0 1&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 6/5, 16/13, 9/7&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 3/2 length 1.1956 7/4 length 1.4506 14/13 1.8299&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 0 0 3 -7|, &amp;lt;0 1 0 0 -2 1|, &lt;br /&gt;
&amp;lt;0 0 1 0 1 0|, &amp;lt;0 0 0 1 1 2|]&lt;br /&gt;
Generators: 99/70, 3, 5, 7&lt;br /&gt;
Edos: 26, 36, 46, 58, 68, 72, 84, 94, 130, 140, 166, 198, 224, 270, 494, 764, 1186, 1892&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

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

Commas 441/440, 351/350

385/384

Commas 385/384, 325/324

13 and 15 limit minimax

[<1 0 0 0 0 0|, <0 1 0 0 0 0|,

<2/3 4/3 1/3 0 0 -1/3|,

<19/6 -1/6 -1/6 1/2 -1/2 1/6|,

<19/6 -1/6 -1/6 -1/2 1/2 1/6|,

<2/3 4/3 -2/3 0 0 2/3|]

Eigenmonzos: 2, 14/11, 13/10, 4/3

Lattice basis: 4/3 1.0820 6/5 1.3935 10/9 1.6247

Map: [<1 0 0 0 7 2|, <0 1 0 0 1 4|,

<0 0 1 0 -1 -2|, <0 0 0 1 -1 0|]

Generators: 2, 3, 5, 7

Edos: 7, 8, 15, 19, 26, 34, 41, 46, 53, 68, 72, 79, 87, 94, 99, 113, 140, 159, 212, 253

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

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