Cataharry family: Difference between revisions

Revision as of 18:26, 28 February 2011

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This revision was by author genewardsmith and made on 2011-02-28 18:26:36 UTC.

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The cataharry family of rank three temperaments tempers out the cataharry comma, 19683/19600.

Comma: 19683/19600

7 and 9 limit minimax
[|1 0 0 0>, |4/9 0 2/9 2/9>, 
|0 0 1 0>, |0 0 0 1>]
Eigenmonzos: 2, 8/7, 5/4

Map: [<1 0 0 -2|, <0 2 0 9|, <0 0 1 -1|]
Generators: 2, 140/81, 5
Edos: 19, 24, 48, 53, 58, 72, 130, 202, 457, 587, 659, 717

==11 limit children==

==Albus==
Commas: 540/539, 8019/8000

Minimax tuning
[|1 0 0 0 0>, |8/3 0 4/3 -2/3 -2/3>, 
|5 0 7/2 -2 -3/2>, |5 0 5/2 -1 -3/2>, 
|5 0 5/2 -2 -1/2>]
Eigenmonzos: 2, 11/10, 7/5

Map: [<1 0 0 -2 6|, <0 2 0 9 -12|, <0 0 1 -1 3|]
Generators: 2, 140/81, 5
Edos: 19, 53, 58, 72, 130, 183, 255, 385, 640
Badness: 0.000621

===Madagascar=== 
Commas: 351/350, 540/539, 676/675

13 and 15 limit minimax
[|1 0 0 0 0 0>, |8/3 0 4/3 -2/3 -2/3 0>, 
|5 0 7/2 -2 -3/2 0>, |5 0 5/2 -1 -3/2 0>, 
|5 0 5/2 -2 -1/2 0>, |8 0 11/2 -3 -5/2 0>]
Eigenmonzos: 2, 11/10, 7/5

Lattice basis: 15/13 0.3019 26/25 0.9477
Angle(15/13, 26/25) = 81.6476
Map to lattice: [<0 -2 -3 -6 3 -6|, <0 0 -1 1 -3 -1|]

Map: [<1 0 0 -2 6 -1|, <0 2 0 9 -12 3|, <0 0 1 -1 3 1|]
Generators: 2, 26/15, 5
Edos: 19, 53, 58, 72, 111, 130, 183, 313
Badness: 0.000560
[[Spectrum of a temperament|Spectrum]]: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11

==Snape==
Commas: 19683/19600, 441/440

13-limit
Commas: 351/350, 441/440, 729/728

==Hagrid==
Commas: 243/242, 9801/9800

13-limit
Commas: 243/242, 351/350, 729/728

==Draco==
Commas: 19683/19600, 176/175

13-limit
Commas: 176/175, 351/350, 676/675

Original HTML content:

<html><head><title>Cataharry family</title></head><body>The cataharry family of rank three temperaments tempers out the cataharry comma, 19683/19600.<br />
<br />
Comma: 19683/19600<br />
<br />
7 and 9 limit minimax<br />
[|1 0 0 0&gt;, |4/9 0 2/9 2/9&gt;, <br />
|0 0 1 0&gt;, |0 0 0 1&gt;]<br />
Eigenmonzos: 2, 8/7, 5/4<br />
<br />
Map: [&lt;1 0 0 -2|, &lt;0 2 0 9|, &lt;0 0 1 -1|]<br />
Generators: 2, 140/81, 5<br />
Edos: 19, 24, 48, 53, 58, 72, 130, 202, 457, 587, 659, 717<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-11 limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->11 limit children</h2>
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Albus"></a><!-- ws:end:WikiTextHeadingRule:2 -->Albus</h2>
Commas: 540/539, 8019/8000<br />
<br />
Minimax tuning<br />
[|1 0 0 0 0&gt;, |8/3 0 4/3 -2/3 -2/3&gt;, <br />
|5 0 7/2 -2 -3/2&gt;, |5 0 5/2 -1 -3/2&gt;, <br />
|5 0 5/2 -2 -1/2&gt;]<br />
Eigenmonzos: 2, 11/10, 7/5<br />
<br />
Map: [&lt;1 0 0 -2 6|, &lt;0 2 0 9 -12|, &lt;0 0 1 -1 3|]<br />
Generators: 2, 140/81, 5<br />
Edos: 19, 53, 58, 72, 130, 183, 255, 385, 640<br />
Badness: 0.000621<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Albus-Madagascar"></a><!-- ws:end:WikiTextHeadingRule:4 -->Madagascar</h3>
 Commas: 351/350, 540/539, 676/675<br />
<br />
13 and 15 limit minimax<br />
[|1 0 0 0 0 0&gt;, |8/3 0 4/3 -2/3 -2/3 0&gt;, <br />
|5 0 7/2 -2 -3/2 0&gt;, |5 0 5/2 -1 -3/2 0&gt;, <br />
|5 0 5/2 -2 -1/2 0&gt;, |8 0 11/2 -3 -5/2 0&gt;]<br />
Eigenmonzos: 2, 11/10, 7/5<br />
<br />
Lattice basis: 15/13 0.3019 26/25 0.9477<br />
Angle(15/13, 26/25) = 81.6476<br />
Map to lattice: [&lt;0 -2 -3 -6 3 -6|, &lt;0 0 -1 1 -3 -1|]<br />
<br />
Map: [&lt;1 0 0 -2 6 -1|, &lt;0 2 0 9 -12 3|, &lt;0 0 1 -1 3 1|]<br />
Generators: 2, 26/15, 5<br />
Edos: 19, 53, 58, 72, 111, 130, 183, 313<br />
Badness: 0.000560<br />
<a class="wiki_link" href="/Spectrum%20of%20a%20temperament">Spectrum</a>: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Snape"></a><!-- ws:end:WikiTextHeadingRule:6 -->Snape</h2>
Commas: 19683/19600, 441/440<br />
<br />
13-limit<br />
Commas: 351/350, 441/440, 729/728<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x-Hagrid"></a><!-- ws:end:WikiTextHeadingRule:8 -->Hagrid</h2>
Commas: 243/242, 9801/9800<br />
<br />
13-limit<br />
Commas: 243/242, 351/350, 729/728<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x-Draco"></a><!-- ws:end:WikiTextHeadingRule:10 -->Draco</h2>
Commas: 19683/19600, 176/175<br />
<br />
13-limit<br />
Commas: 176/175, 351/350, 676/675</body></html>

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 <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>2011-02-17 17:25:20 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-28 18:26:36 UTC</tt>.<br>
-: The original revision id was <tt>202905072</tt>.<br>
+: The original revision id was <tt>205868494</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 35: / Line 35: @@
 Badness: 0.000621
-===13-limit===
+===Madagascar===
-Commas: 351/350, 540/539, 729/728
+Commas: 351/350, 540/539, 676/675
 and 15 limit minimax
@@ Line 52: / Line 52: @@
 Edos: 19, 53, 58, 72, 111, 130, 183, 313
 Badness: 0.000560
+[[Spectrum of a temperament|Spectrum]]: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11
 ==Snape==
@@ Line 100: / Line 101: @@
 Badness: 0.000621&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-Albus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Albus-Madagascar"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Madagascar&lt;/h3&gt;
-  Commas: 351/350, 540/539, 729/728&lt;br /&gt;
+  Commas: 351/350, 540/539, 676/675&lt;br /&gt;
 &lt;br /&gt;
 and 15 limit minimax&lt;br /&gt;
@@ Line 117: / Line 118: @@
 Edos: 19, 53, 58, 72, 111, 130, 183, 313&lt;br /&gt;
 Badness: 0.000560&lt;br /&gt;
+&lt;a class="wiki_link" href="/Spectrum%20of%20a%20temperament"&gt;Spectrum&lt;/a&gt;: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-Snape"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Snape&lt;/h2&gt;

Cataharry family: Difference between revisions

Revision as of 18:26, 28 February 2011

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