Werckismic temperaments: Difference between revisions

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**Imported revision 202891988 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 205392820 - 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>2011-02-17 16:39:47 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-27 11:16:45 UTC</tt>.<br>
: The original revision id was <tt>202891988</tt>.<br>
: The original revision id was <tt>205392820</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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EDOs: 72, 118, 130, 159, 171, 190, 248, 289, 320
EDOs: 72, 118, 130, 159, 171, 190, 248, 289, 320


==Babar==
==History==
Commas: 441/400, 4000/3993
Commas: 441/400, 4000/3993


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EDOs: 72, 118, 130, 159, 171, 190, 248, 289, 320&lt;br /&gt;
EDOs: 72, 118, 130, 159, 171, 190, 248, 289, 320&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Babar"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Babar&lt;/h2&gt;
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Commas: 441/400, 4000/3993&lt;br /&gt;
Commas: 441/400, 4000/3993&lt;br /&gt;
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Badness: 0.000604&lt;br /&gt;
Badness: 0.000604&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Babar-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;13-limit&lt;/h3&gt;
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Commas: 364/363, 441/440, 1001/1000&lt;br /&gt;
Commas: 364/363, 441/440, 1001/1000&lt;br /&gt;
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&lt;br /&gt;

Revision as of 11:16, 27 February 2011

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2011-02-27 11:16:45 UTC.
The original revision id was 205392820.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

These are rank three temperaments tempering out 441/440, but we can began by looking at the rank four temperament.

Minimax tuning
[|1 0 0 0 0>, |1/2 2/3 1/6 -1/3 1/6>, |0 0 1 0 0>, 
|1 -2/3 1/3 1/3 1/3>, |0 0 0 0 1>]
Eigenmonzos: 2, 5, 11, 9/7

Map: [<1 0 0 0 -3|, <0 1 0 0 2|, <0 0 1 0 -1|, <0 0 0 1 2|]
EDOs: 72, 118, 130, 159, 171, 190, 248, 289, 320

==History==
Commas: 441/400, 4000/3993

Minimax tuning
[|1 0 0 0 0>, |4/17 12/17 0 -6/17 6/17>, 
|-27/17 4/17 0 -2/17 19/17>, 
|8/17 -10/17 0 5/17 12/17>, |0 0 0 0 1>]
Eigenmonzos: 2, 11, 9/7

Map: [<1 2 0 0 1|, <0 -6 0 7 2|, <0 0 1 1 1|]
Generators: 2, 21/20, 5
EDOs: 58, 72, 130, 202, 217, 289, 491
Badness: 0.000604

===13-limit===
Commas: 364/363, 441/440, 1001/1000

Minimax tuning
[|1 0 0 0 0 0>, |5/4 0 0 -3/8 0 3/8>, |0 0 1 0 0 0>, 
|7/8 0 1 7/16 0 -7/16>, |5/4 0 1 1/8 0 -1/8>, 
|7/8 0 1 -9/16 0 9/16>]
Eigenmonzos: 2, 5, 13/7

Map: [<1 2 0 0 1 2|, <0 -6 0 7 2 -9|, <0 0 1 1 1 1|]
Generators: 2, 21/20, 5
EDOs: 58, 72, 87, 130, 217, 289
Badness: 0.000540

==Varuna==
Commas: 441/440, 8019/8000

Map: [<2 0 0 9 12|, <0 1 0 -4 -6|, <0 0 1 2 3|]
EDOs: 12, 26, 46, 58, 72, 118, 130, 248, 320
Generators: 99/70, 3, 5
Badness: 0.000419

Original HTML content:

<html><head><title>Werckismic temperaments</title></head><body>These are rank three temperaments tempering out 441/440, but we can began by looking at the rank four temperament.<br />
<br />
Minimax tuning<br />
[|1 0 0 0 0&gt;, |1/2 2/3 1/6 -1/3 1/6&gt;, |0 0 1 0 0&gt;, <br />
|1 -2/3 1/3 1/3 1/3&gt;, |0 0 0 0 1&gt;]<br />
Eigenmonzos: 2, 5, 11, 9/7<br />
<br />
Map: [&lt;1 0 0 0 -3|, &lt;0 1 0 0 2|, &lt;0 0 1 0 -1|, &lt;0 0 0 1 2|]<br />
EDOs: 72, 118, 130, 159, 171, 190, 248, 289, 320<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-History"></a><!-- ws:end:WikiTextHeadingRule:0 -->History</h2>
Commas: 441/400, 4000/3993<br />
<br />
Minimax tuning<br />
[|1 0 0 0 0&gt;, |4/17 12/17 0 -6/17 6/17&gt;, <br />
|-27/17 4/17 0 -2/17 19/17&gt;, <br />
|8/17 -10/17 0 5/17 12/17&gt;, |0 0 0 0 1&gt;]<br />
Eigenmonzos: 2, 11, 9/7<br />
<br />
Map: [&lt;1 2 0 0 1|, &lt;0 -6 0 7 2|, &lt;0 0 1 1 1|]<br />
Generators: 2, 21/20, 5<br />
EDOs: 58, 72, 130, 202, 217, 289, 491<br />
Badness: 0.000604<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-History-13-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->13-limit</h3>
Commas: 364/363, 441/440, 1001/1000<br />
<br />
Minimax tuning<br />
[|1 0 0 0 0 0&gt;, |5/4 0 0 -3/8 0 3/8&gt;, |0 0 1 0 0 0&gt;, <br />
|7/8 0 1 7/16 0 -7/16&gt;, |5/4 0 1 1/8 0 -1/8&gt;, <br />
|7/8 0 1 -9/16 0 9/16&gt;]<br />
Eigenmonzos: 2, 5, 13/7<br />
<br />
Map: [&lt;1 2 0 0 1 2|, &lt;0 -6 0 7 2 -9|, &lt;0 0 1 1 1 1|]<br />
Generators: 2, 21/20, 5<br />
EDOs: 58, 72, 87, 130, 217, 289<br />
Badness: 0.000540<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Varuna"></a><!-- ws:end:WikiTextHeadingRule:4 -->Varuna</h2>
Commas: 441/440, 8019/8000<br />
<br />
Map: [&lt;2 0 0 9 12|, &lt;0 1 0 -4 -6|, &lt;0 0 1 2 3|]<br />
EDOs: 12, 26, 46, 58, 72, 118, 130, 248, 320<br />
Generators: 99/70, 3, 5<br />
Badness: 0.000419</body></html>