Werckismic temperaments: Difference between revisions

Revision as of 16:39, 17 February 2011

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This revision was by author genewardsmith and made on 2011-02-17 16:39:47 UTC.

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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

==Babar==
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-Babar"></a><!-- ws:end:WikiTextHeadingRule:0 -->Babar</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-Babar-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>

@@ 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>2011-02-16 23:22:43 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-17 16:39:47 UTC</tt>.<br>
-: The original revision id was <tt>202610276</tt>.<br>
+: The original revision id was <tt>202891988</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 45: / Line 45: @@
 ==Varuna==
-Commas: 441/440, 8019/8000</pre></div>
+Commas: 441/440, 8019/8000
+Map: [&lt;2 0 0 9 12|, &lt;0 1 0 -4 -6|, &lt;0 0 1 2 3|]
+EDOs: 12, 26, 46, 58, 72, 118, 130, 248, 320
+Generators: 99/70, 3, 5
+Badness: 0.000419</pre></div>
 <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;Werckismic temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;These are rank three temperaments tempering out 441/440, but we can began by looking at the rank four temperament.&lt;br /&gt;
@@ Line 86: / Line 91: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Varuna"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Varuna&lt;/h2&gt;
-Commas: 441/440, 8019/8000&lt;/body&gt;&lt;/html&gt;</pre></div>
+Commas: 441/440, 8019/8000&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;2 0 0 9 12|, &amp;lt;0 1 0 -4 -6|, &amp;lt;0 0 1 2 3|]&lt;br /&gt;
+EDOs: 12, 26, 46, 58, 72, 118, 130, 248, 320&lt;br /&gt;
+Generators: 99/70, 3, 5&lt;br /&gt;
+Badness: 0.000419&lt;/body&gt;&lt;/html&gt;</pre></div>

Werckismic temperaments: Difference between revisions

Revision as of 16:39, 17 February 2011

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