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Cataharry family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Technical data page}}
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 04:05:44 UTC</tt>.<br>
: The original revision id was <tt>302948328</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-3 temperament]]s [[tempering out|tempers out]] the [[cataharry comma]] ({{monzo|legend=1| -4 9 -2 -2 }}, [[ratio]]: 19683/19600).


Comma: 19683/19600
== Cataharry ==
Cataharry splits the [[3/1|3rd harmonic]] into two semitwelfths. Bending the semitwelfth up by a [[syntonic comma]] results in ~[[7/4]], and down results in ~[[12/7]].


7 and 9 limit minimax
[[Subgroup]]: 2.3.5.7
[|1 0 0 0&gt;, |4/9 0 2/9 2/9&gt;,
|0 0 1 0&gt;, |0 0 0 1&gt;]
Eigenmonzos: 2, 8/7, 5/4


Map: [&lt;1 0 0 -2|, &lt;0 2 0 9|, &lt;0 0 1 -1|]
[[Comma list]]: 19683/19600
Generators: 2, 140/81, 5
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
{{Mapping|legend=1| 1 0 0 -2 | 0 2 0 9 | 0 0 1 -1 }}
: mapping generators: ~2, ~140/81, ~5


[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.1072{{c}}, ~140/81 = 950.6740{{c}}, ~5/4 = 386.3883{{c}}
: [[error map]]: {{val| +0.107 -0.607 +0.289 +0.423 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~140/81 = 950.6211{{c}}, ~5/4 = 386.4833{{c}}
: error map: {{val| 0.000 -0.713 +0.170 +0.280 }}


==11 limit children==
[[Minimax tuning]]:
* [[7-odd-limit|7-]] and [[9-odd-limit]]:
: {{monzo list| 1 0 0 0 | 4/9 0 2/9 2/9 | 0 0 1 0 | 0 0 0 1 }}
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7


==Albus==
{{Optimal ET sequence|legend=1| 19, 34d, 39d, 53, 72, 130, 183, 202, 385, 587 }}
Commas: 540/539, 8019/8000


Minimax tuning
[[Badness]] (Sintel): 1.33
[|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 5/2 -2 -1/2&gt;]
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|]
[[Projection pair]]s: <code>3 19600/6561 7 1033052339200000000/150094635296999121</code> to 2.5.81/7
Generators: 2, 140/81, 5
Edos: 19, 53, 58, 72, 130, 183, 255, 385, 640
Badness: 0.000621


===Madagascar===  
== Albus ==
Commas: 351/350, 540/539, 676/675
[[Subgroup]]: 2.3.5.7.11


13 and 15 limit minimax
[[Comma list]]: 540/539, 8019/8000
[|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 5/2 -2 -1/2 0&gt;, |8 0 11/2 -3 -5/2 0&gt;]
Eigenmonzos: 2, 11/10, 7/5


Lattice basis: 15/13 0.3019 26/25 0.9477
{{Mapping|legend=1| 1 0 0 -2 6 | 0 2 0 9 -12 | 0 0 1 -1 3 }}
Angle(15/13, 26/25) = 81.6476
: mapping generators: ~2, ~140/81, ~5
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|]
[[Optimal tuning]]s:  
Generators: 2, 26/15, 5
* [[WE]]: ~2 = 1200.0427{{c}}, ~140/81 = 950.6653{{c}}, ~5/4 = 386.3435{{c}}
Edos: 19, 53, 58, 72, 111, 130, 183, 313
: [[error map]]: {{val| +0.043 -0.624 +0.115 +0.647 +0.242 }}
Badness: 0.000560
* [[CWE]]: ~2 = 1200.0000{{c}}, ~140/81 = 950.6425{{c}}, ~5/4 = 386.3889{{c}}
[[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
: error map: {{val| 0.000 -0.670 +0.075 +0.568 +0.139 }}


Projection pairs: 3 676/225 7 1357375919744/192216796875 11 16218292236328125/1491077447838784 13 8788/675 to 2.5.13/3
[[Minimax tuning]]:  
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 8/3 0 4/3 -2/3 -2/3 }}, {{monzo| 5 0 7/2 -2 -3/2 }}, {{monzo| 5 0 5/2 -1 -3/2 }}, {{monzo| 5 0 5/2 -2 -1/2 }}]
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11/5


[[madagascar19]]
{{Optimal ET sequence|legend=1| 19, 33cd, 39d, 53, 58, 72, 130, 183, 255, 385, 640 }}


==Snape==
[[Badness]] (Sintel): 0.746
Commas: 19683/19600, 441/440


13-limit
=== Madagascar ===
Commas: 351/350, 441/440, 729/728
Subgroup: 2.3.5.7.11.13


==Hagrid==
Comma list: 351/350, 540/539, 676/675
Commas: 243/242, 9801/9800


13-limit
Mapping: {{mapping| 1 0 0 -2 6 -1 | 0 2 0 9 -12 3 | 0 0 1 -1 3 1 }}
Commas: 243/242, 351/350, 729/728


==Draco==
[[Mapping to lattice]]: [{{val| 0 -2 -3 -6 3 -6 }}, {{val| 0 0 -1 1 -3 -1 }}]
Commas: 19683/19600, 176/175


Map: [&lt;1 0 0 -2 -6|, &lt;0 2 0 9 9|, &lt;0 0 1 -1 1|]
Lattice basis:  
EDOs: 24, 34d, 53, 58, 111, 357cd, 468cd
: 15/13 length = 0.3019, 26/25 length = 0.9477
Badness: 0.001934
: Angle (15/13, 26/25) = 81.6476


13-limit
Optimal tunings:
Commas: 176/175, 351/350, 676/675
* WE: ~2 = 1199.9446{{c}}, ~26/15 = 950.7332{{c}}, ~5/4 = 387.0575{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 950.7647{{c}}, ~5/4 = 387.0080{{c}}


Map: [&lt;1 0 0 -2 -6 -1|, &lt;0 2 0 9 9 3|, &lt;0 0 1 -1 1 1|]
Minimax tuning:  
EDOs: 24, 34d, 53, 58, 77, 111, 357cdf, 468cdf
* 13- and 15-odd-limit
Badness: 0.000999</pre></div>
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 8/3 0 4/3 -2/3 -2/3 0 }}, {{monzo| 5 0 7/2 -2 -3/2 0 }}, {{monzo| 5 0 5/2 -1 -3/2 0 }}, {{monzo| 5 0 5/2 -2 -1/2 0 }}, {{monzo| 8 0 11/2 -3 -5/2 0 }}]
<h4>Original HTML content:</h4>
: unchanged-interval (eigenmonzo) basis: 2.7/5.11/5
<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:12:&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:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#x-11 limit children"&gt;11 limit children&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#x-Albus"&gt;Albus&lt;/a&gt;&lt;/div&gt;
{{Optimal ET sequence|legend=0| 19, 33cdff, 39df, 53, 58, 72, 111, 130, 183, 313 }}
&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#x-Albus-Madagascar"&gt;Madagascar&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#x-Snape"&gt;Snape&lt;/a&gt;&lt;/div&gt;
Badness (Sintel): 0.524
&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#x-Hagrid"&gt;Hagrid&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#x-Draco"&gt;Draco&lt;/a&gt;&lt;/div&gt;
Complexity 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
&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;br /&gt;
Projection pairs: <code>3 676/225 7 1357375919744/192216796875 11 16218292236328125/1491077447838784 13 8788/675</code> to 2.5.13/3
The cataharry family of rank three temperaments tempers out the cataharry comma, 19683/19600.&lt;br /&gt;
 
&lt;br /&gt;
Scales: [[madagascar19]]
Comma: 19683/19600&lt;br /&gt;
 
&lt;br /&gt;
== Snape ==
7 and 9 limit minimax&lt;br /&gt;
[[Subgroup]]: 2.3.5.7.11
[|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;
[[Comma list]]: 441/440, 19683/19600
Eigenmonzos: 2, 8/7, 5/4&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 0 0 -2 -7 | 0 2 0 9 22 | 0 0 1 -1 -3 }}
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;
[[Optimal tuning]]s:  
Edos: 19, 24, 48, 53, 58, 72, 130, 202, 457, 587, 659, 717&lt;br /&gt;
* [[WE]]: ~2 = 1200.2224{{c}}, ~140/81 = 950.6271{{c}}, ~5/4 = 386.3424{{c}}
&lt;br /&gt;
: [[error map]]: {{val| +0.222 -0.701 +0.474 -0.414 +0.559 }}
&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;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~140/81 = 950.5069{{c}}, ~5/4 = 386.5450{{c}}
&lt;br /&gt;
: error map: {{val| 0.000 -0.941 +0.231 -0.809 +0.198 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-11 limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;11 limit children&lt;/h2&gt;
{{Optimal ET sequence|legend=1| 19e, 33cdee, 39dee, 53e, 58, 72, 130, 202, 351, 423d, 481, 553 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Albus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Albus&lt;/h2&gt;
[[Badness]] (Sintel): 1.19
Commas: 540/539, 8019/8000&lt;br /&gt;
 
&lt;br /&gt;
=== 13-limit ===
Minimax tuning&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
[|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;
Comma list: 351/350, 441/440, 676/675
|5 0 5/2 -2 -1/2&amp;gt;]&lt;br /&gt;
 
Eigenmonzos: 2, 11/10, 7/5&lt;br /&gt;
Mapping: {{mapping| 1 0 0 -2 -7 -1 | 0 2 0 9 22 3 | 0 0 1 -1 -3 1 }}
&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;
Optimal tunings:  
Generators: 2, 140/81, 5&lt;br /&gt;
* WE: ~2 = 1200.1732{{c}}, ~26/15 = 950.6934{{c}}, ~5/4 = 387.0339{{c}}
Edos: 19, 53, 58, 72, 130, 183, 255, 385, 640&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 950.5975{{c}}, ~5/4 = 387.1756{{c}}
Badness: 0.000621&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 19e, 33cdeeff, 39deef, 53e, 58, 72, 130, 279, 409 }}
&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, 676/675&lt;br /&gt;
Badness (Sintel): 0.735
&lt;br /&gt;
 
13 and 15 limit minimax&lt;br /&gt;
== Hagrid ==
[|1 0 0 0 0 0&amp;gt;, |8/3 0 4/3 -2/3 -2/3 0&amp;gt;, &lt;br /&gt;
[[Subgroup]]: 2.3.5.7.11
|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;
[[Comma list]]: 243/242, 9801/9800
Eigenmonzos: 2, 11/10, 7/5&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 2 0 0 -4 -1 | 0 2 0 9 5 | 0 0 1 -1 0 }}
Lattice basis: 15/13 0.3019 26/25 0.9477&lt;br /&gt;
: mapping generators: ~99/70, ~140/81, ~5
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;
[[Optimal tuning]]s:  
&lt;br /&gt;
* [[WE]]: ~99/70 = 600.0301{{c}}, ~140/81 = 950.5810{{c}}, ~5/4 = 386.1803{{c}}
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;
: [[error map]]: {{val| +0.060 -0.793 -0.013 -0.019 +1.557 }}
Generators: 2, 26/15, 5&lt;br /&gt;
* [[CWE]]: ~99/70 = 600.0000{{c}}, ~140/81 = 950.5516{{c}}, ~5/4 = 386.2351{{c}}
Edos: 19, 53, 58, 72, 111, 130, 183, 313&lt;br /&gt;
: error map: {{val| 0.000 -0.852 -0.079 -0.096 +1.440 }}
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;
{{Optimal ET sequence|legend=1| 24, 34d, 48, 58, 72, 130, 202 }}
&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;
[[Badness]] (Sintel): 1.34
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/madagascar19"&gt;madagascar19&lt;/a&gt;&lt;br /&gt;
=== 13-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&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;
 
Commas: 19683/19600, 441/440&lt;br /&gt;
Comma list: 243/242, 351/350, 364/363
&lt;br /&gt;
 
13-limit&lt;br /&gt;
Mapping: {{mapping| 2 0 0 -4 -1 -2 | 0 2 0 9 5 3 | 0 0 1 -1 0 1 }}
Commas: 351/350, 441/440, 729/728&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:  
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x-Hagrid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Hagrid&lt;/h2&gt;
* WE: ~55/39 = 599.9896{{c}}, ~26/15 = 950.6467{{c}}, ~5/4 = 387.0194{{c}}
Commas: 243/242, 9801/9800&lt;br /&gt;
* CWE: ~55/39 = 600.0000{{c}}, ~26/15 = 950.6571{{c}}, ~5/4 = 387.0028{{c}}
&lt;br /&gt;
 
13-limit&lt;br /&gt;
{{Optimal ET sequence|legend=0| 24, 34d, 58, 72, 130 }}
Commas: 243/242, 351/350, 729/728&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 0.819
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-Draco"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Draco&lt;/h2&gt;
 
Commas: 19683/19600, 176/175&lt;br /&gt;
== Draco ==
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7.11
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;
[[Comma list]]: 176/175, 19683/19600
Badness: 0.001934&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 0 0 -2 -6 | 0 2 0 9 9 | 0 0 1 -1 1 }}
13-limit&lt;br /&gt;
 
Commas: 176/175, 351/350, 676/675&lt;br /&gt;
[[Optimal tuning]]s:
&lt;br /&gt;
* [[WE]]: ~2 = 1199.3870{{c}}, ~140/81 = 950.8204{{c}}, ~5/4 = 389.4825{{c}}
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;
: [[error map]]: {{val| -0.613 -0.314 +1.943 +1.527 -2.000 }}
EDOs: 24, 34d, 53, 58, 77, 111, 357cdf, 468cdf&lt;br /&gt;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~140/81 = 951.2120{{c}}, ~5/4 = 389.3756{{c}}
Badness: 0.000999&lt;/body&gt;&lt;/html&gt;</pre></div>
: error map: {{val| 0.000 +0.469 +3.062 +2.706 -1.035 }}
 
{{Optimal ET sequence|legend=1| 19e, 24, 34d, 53, 58, 111, 280cd }}
 
[[Badness]] (Sintel): 2.32
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 176/175, 351/350, 676/675
 
Mapping: {{mapping| 1 0 0 -2 -6 -1 | 0 2 0 9 9 3 | 0 0 1 -1 1 1 }}
 
Optimal tunings:
* WE: ~2 = 1199.3551{{c}}, ~26/15 = 950.7982{{c}}, ~5/4 = 389.3905{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.2095{{c}}, ~5/4 = 389.2432{{c}}
 
{{Optimal ET sequence|legend=0| 19e, 24, 34d, 53, 58, 111, 280cdf }}
 
Badness (Sintel): 0.934
 
[[Category:Temperament families]]
[[Category:Cataharry family| ]] <!-- main article -->
[[Category:Rank 3]]
Retrieved from "https://en.xen.wiki/w/Cataharry_family"