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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
__FORCETOC__
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>2012-02-18 15:46:04 UTC</tt>.<br>
: The original revision id was <tt>303015160</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">[[toc]]
 
The cataharry family of rank three temperaments tempers out the cataharry comma, 19683/19600.
The cataharry family of rank three temperaments tempers out the cataharry comma, 19683/19600.


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


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


[[Projection pair]]s: 3 19600/6561 7 1033052339200000000/150094635296999121 to 2.5.81/7
[[Projection_pair|Projection pair]]s: 3 19600/6561 7 1033052339200000000/150094635296999121 to 2.5.81/7


=Albus=
=Albus=
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Minimax tuning
Minimax tuning
[|1 0 0 0 0&gt;, |8/3 0 4/3 -2/3 -2/3&gt;,  
[|1 0 0 0 0&gt;, |8/3 0 4/3 -2/3 -2/3&gt;,  
|5 0 7/2 -2 -3/2&gt;, |5 0 5/2 -1 -3/2&gt;,  
|5 0 7/2 -2 -3/2&gt;, |5 0 5/2 -1 -3/2&gt;,  
|5 0 5/2 -2 -1/2&gt;]
|5 0 5/2 -2 -1/2&gt;]
Eigenmonzos: 2, 11/10, 7/5
Eigenmonzos: 2, 11/10, 7/5


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


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


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


Map: [&lt;1 0 0 -2 6 -1|, &lt;0 2 0 9 -12 3|, &lt;0 0 1 -1 3 1|]
Map: [&lt;1 0 0 -2 6 -1|, &lt;0 2 0 9 -12 3|, &lt;0 0 1 -1 3 1|]
Generators: 2, 26/15, 5
Generators: 2, 26/15, 5
Edos: 19, 53, 58, 72, 111, 130, 183, 313
Edos: 19, 53, 58, 72, 111, 130, 183, 313
Badness: 0.000560
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
 
[[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


Projection pairs: 3 676/225 7 1357375919744/192216796875 11 16218292236328125/1491077447838784 13 8788/675 to 2.5.13/3
Projection pairs: 3 676/225 7 1357375919744/192216796875 11 16218292236328125/1491077447838784 13 8788/675 to 2.5.13/3


[[madagascar19]]
[[madagascar19|madagascar19]]


=Snape=
=Snape=
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Map: [&lt;1 0 0 -2 -6|, &lt;0 2 0 9 9|, &lt;0 0 1 -1 1|]
Map: [&lt;1 0 0 -2 -6|, &lt;0 2 0 9 9|, &lt;0 0 1 -1 1|]
EDOs: 24, 34d, 53, 58, 111, 357cd, 468cd
EDOs: 24, 34d, 53, 58, 111, 357cd, 468cd
Badness: 0.001934
Badness: 0.001934


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Map: [&lt;1 0 0 -2 -6 -1|, &lt;0 2 0 9 9 3|, &lt;0 0 1 -1 1 1|]
Map: [&lt;1 0 0 -2 -6 -1|, &lt;0 2 0 9 9 3|, &lt;0 0 1 -1 1 1|]
EDOs: 24, 34d, 53, 58, 77, 111, 357cdf, 468cdf
EDOs: 24, 34d, 53, 58, 77, 111, 357cdf, 468cdf
Badness: 0.000999</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.000999
<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;Cataharry family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:16:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Albus"&gt;Albus&lt;/a&gt;&lt;/div&gt;
[[Category:cataharry]]
&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Albus-Madagascar"&gt;Madagascar&lt;/a&gt;&lt;/div&gt;
[[Category:family]]
&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Snape"&gt;Snape&lt;/a&gt;&lt;/div&gt;
[[Category:theory]]
&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Snape-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hagrid"&gt;Hagrid&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hagrid-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Draco"&gt;Draco&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Draco-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;br /&gt;
The cataharry family of rank three temperaments tempers out the cataharry comma, 19683/19600.&lt;br /&gt;
&lt;br /&gt;
Comma: 19683/19600&lt;br /&gt;
&lt;br /&gt;
7 and 9 limit minimax&lt;br /&gt;
[|1 0 0 0&amp;gt;, |4/9 0 2/9 2/9&amp;gt;, &lt;br /&gt;
|0 0 1 0&amp;gt;, |0 0 0 1&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 8/7, 5/4&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -2|, &amp;lt;0 2 0 9|, &amp;lt;0 0 1 -1|]&lt;br /&gt;
Generators: 2, 140/81, 5&lt;br /&gt;
Edos: 19, 24, 48, 53, 58, 72, 130, 202, 457, 587, 659, 717&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 3 19600/6561 7 1033052339200000000/150094635296999121 to 2.5.81/7&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Albus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Albus&lt;/h1&gt;
Commas: 540/539, 8019/8000&lt;br /&gt;
&lt;br /&gt;
Minimax tuning&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |8/3 0 4/3 -2/3 -2/3&amp;gt;, &lt;br /&gt;
|5 0 7/2 -2 -3/2&amp;gt;, |5 0 5/2 -1 -3/2&amp;gt;, &lt;br /&gt;
|5 0 5/2 -2 -1/2&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 11/10, 7/5&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -2 6|, &amp;lt;0 2 0 9 -12|, &amp;lt;0 0 1 -1 3|]&lt;br /&gt;
Generators: 2, 140/81, 5&lt;br /&gt;
Edos: 19, 53, 58, 72, 130, 183, 255, 385, 640&lt;br /&gt;
Badness: 0.000621&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Albus-Madagascar"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Madagascar&lt;/h2&gt;
Commas: 351/350, 540/539, 676/675&lt;br /&gt;
&lt;br /&gt;
13 and 15 limit minimax&lt;br /&gt;
[|1 0 0 0 0 0&amp;gt;, |8/3 0 4/3 -2/3 -2/3 0&amp;gt;, &lt;br /&gt;
|5 0 7/2 -2 -3/2 0&amp;gt;, |5 0 5/2 -1 -3/2 0&amp;gt;, &lt;br /&gt;
|5 0 5/2 -2 -1/2 0&amp;gt;, |8 0 11/2 -3 -5/2 0&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 11/10, 7/5&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 15/13 0.3019 26/25 0.9477&lt;br /&gt;
Angle(15/13, 26/25) = 81.6476&lt;br /&gt;
Map to lattice: [&amp;lt;0 -2 -3 -6 3 -6|, &amp;lt;0 0 -1 1 -3 -1|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -2 6 -1|, &amp;lt;0 2 0 9 -12 3|, &amp;lt;0 0 1 -1 3 1|]&lt;br /&gt;
Generators: 2, 26/15, 5&lt;br /&gt;
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;
Projection pairs: 3 676/225 7 1357375919744/192216796875 11 16218292236328125/1491077447838784 13 8788/675 to 2.5.13/3&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/madagascar19"&gt;madagascar19&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Snape"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Snape&lt;/h1&gt;
Commas: 19683/19600, 441/440&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="Snape-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
Commas: 351/350, 441/440, 729/728&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Hagrid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Hagrid&lt;/h1&gt;
Commas: 243/242, 9801/9800&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="Hagrid-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit&lt;/h2&gt;
Commas: 243/242, 351/350, 729/728&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Draco"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Draco&lt;/h1&gt;
Commas: 19683/19600, 176/175&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -2 -6|, &amp;lt;0 2 0 9 9|, &amp;lt;0 0 1 -1 1|]&lt;br /&gt;
EDOs: 24, 34d, 53, 58, 111, 357cd, 468cd&lt;br /&gt;
Badness: 0.001934&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Draco-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;13-limit&lt;/h2&gt;
Commas: 176/175, 351/350, 676/675&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -2 -6 -1|, &amp;lt;0 2 0 9 9 3|, &amp;lt;0 0 1 -1 1 1|]&lt;br /&gt;
EDOs: 24, 34d, 53, 58, 77, 111, 357cdf, 468cdf&lt;br /&gt;
Badness: 0.000999&lt;/body&gt;&lt;/html&gt;</pre></div>
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