Optimal patent val: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 221003002 - Original comment: **
Wikispaces>x31eq
**Imported revision 223821292 - 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>2011-04-17 19:56:59 UTC</tt>.<br>
: This revision was by author [[User:x31eq|x31eq]] and made on <tt>2011-04-28 13:22:28 UTC</tt>.<br>
: The original revision id was <tt>221003002</tt>.<br>
: The original revision id was <tt>223821292</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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Below are tabulated some values. In each case an identifier which uniquely identifies the temperament in question is given. In the codimension one case, where the temperament is defined by a single comma, the comma is given and used as a name. In other cases, for a temperament of rank n, n independent [[Patent val|patent vals]] are given. Normally this is by way of integers conjoined by ampersands, such as 2&amp;10 for 7-limit pajara. This tells us we can use the 7-limit patent vals for 2 and 10 to define the temperament. In case n independent patent vals cannot be found, the [[Normal lists|normal val list]] is given. Note that this differs from the method of [[Graham Breed]]'s [[http://x31eq.com/temper/|regular temperament finder]], which does not assume the numbers refer to patent vals.
Below are tabulated some values. In each case an identifier which uniquely identifies the temperament in question is given. In the codimension one case, where the temperament is defined by a single comma, the comma is given and used as a name. In other cases, for a temperament of rank n, n independent [[Patent val|patent vals]] are given. Normally this is by way of integers conjoined by ampersands, such as 2&amp;10 for 7-limit pajara. This tells us we can use the 7-limit patent vals for 2 and 10 to define the temperament. In case n independent patent vals cannot be found, the [[Normal lists|normal val list]] is given. Note that this differs from the method of [[Graham Breed]]'s [[http://x31eq.com/temper/|regular temperament finder]], which does not assume the numbers refer to patent vals.


=5-limit rank two=
=5-limit rank two=  
Comma: Optimal patent val: 1000 * badness
Comma: Optimal patent val: 1000 * badness
16/15: [[8edo]] 14.884
16/15: [[8edo]] 14.884
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7629394531250/7625597484987: [[3501edo]] 17.191
7629394531250/7625597484987: [[3501edo]] 17.191


=7-limit rank two=
=7-limit rank two=  
Name: Optimal patent val: Val name: 1000*badness
Name: Optimal patent val: Val name: 1000*badness
[[Trienstonic clan|Father]]: [[5edo]] [&lt;1 0 4 -2|, &lt;0 1 -1 3|] 21.312
[[Trienstonic clan|Father]]: [[5edo]] [&lt;1 0 4 -2|, &lt;0 1 -1 3|] 21.312
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[[Minortonic family#Domain|Domain]]: [[22038edo]] 171&amp;1164 13.979
[[Minortonic family#Domain|Domain]]: [[22038edo]] 171&amp;1164 13.979


=7-limit rank three=
=7-limit rank three=  
Comma: Optimal patent val: 10^6 * badness
Comma: Optimal patent val: 10^6 * badness
36/35: [[12edo]] 63.675
36/35: [[12edo]] 63.675
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78125000/78121827: [[101654edo]] 20.457
78125000/78121827: [[101654edo]] 20.457


=11-limit rank two=
=11-limit rank two=  
Name: Optimal patent val: Val name: 1000*badness
Name: Optimal patent val: Val name: 1000*badness
[[Marvel temperaments|Negric]]: [[9edo]] 1&amp;9 30.617
[[Marvel temperaments|Negric]]: [[9edo]] 1&amp;9 30.617
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[[Marvel temperaments|Negri]]: [[19edo]] 9&amp;10 26.190
[[Marvel temperaments|Negri]]: [[19edo]] 9&amp;10 26.190
[[Marvel temperaments|Meanenneadecal]]: [[19edo]] 12&amp;19 21.182
[[Marvel temperaments|Meanenneadecal]]: [[19edo]] 12&amp;19 21.182
[[Diaschismic family|Pajara]]: [[22edo]] 12&amp;22 20.343  
[[Diaschismic family|Pajara]]: [[22edo]] 12&amp;22 20.343
[[Porcupine family|Nautilus]]: [[29edo]] 15&amp;29 26.023
[[Porcupine family|Nautilus]]: [[29edo]] 15&amp;29 26.023
[[Meantone family|Mohajira]]: [[31edo]] 7&amp;24 26.064
[[Meantone family|Mohajira]]: [[31edo]] 7&amp;24 26.064
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[[Porcupine rank three family|Sonic]]: [[51edo]] 7&amp;15&amp;51 523.158
[[Porcupine rank three family|Sonic]]: [[51edo]] 7&amp;15&amp;51 523.158
[[Nuwell family|Big Brother]]: [[53edo]] 9&amp;22&amp;70 506.556
[[Nuwell family|Big Brother]]: [[53edo]] 9&amp;22&amp;70 506.556
[[Marvel family|Prodigy]]: [[72edo]] 2&amp;10&amp;29 334.745  
[[Marvel family|Prodigy]]: [[72edo]] 2&amp;10&amp;29 334.745
[[Didymus rank three family|Erato]]: [[81edo]] 12&amp;19&amp;31 557.521
[[Didymus rank three family|Erato]]: [[81edo]] 12&amp;19&amp;31 557.521
[[Didymus rank three family|Euterpe]]: [[88edo]] 5&amp;12&amp;26 535.809
[[Didymus rank three family|Euterpe]]: [[88edo]] 5&amp;12&amp;26 535.809
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[[Kalismic temperaments|Odin]]: [[7464edo]] 12&amp;42&amp;72 116.151
[[Kalismic temperaments|Odin]]: [[7464edo]] 12&amp;42&amp;72 116.151


=13-limit rank two=
=13-limit rank two=  
Name: Optimal patent val: Val name: 1000*badness
Name: Optimal patent val: Val name: 1000*badness
[[Quartonic temperaments|Progression]]: [[9edo]] [&lt;1 1 2 2 3 3|, &lt;0 5 3 7 4 6|] 18.158
[[Quartonic temperaments|Progression]]: [[9edo]] [&lt;1 1 2 2 3 3|, &lt;0 5 3 7 4 6|] 18.158
[[Marvel temperaments|Negric]]: [[9edo]] 1&amp;9 20.205
[[Marvel temperaments|Negric]]: [[9edo]] 1&amp;9 20.205
[[Trienstonic clan|Opossum]]: [[15edo]] [&lt;1 2 3 4 4 4|, &lt;0 -3 -5 -9 -4 -2|] 19.389
[[Trienstonic clan|Opossum]]: [[15edo]] [&lt;1 2 3 4 4 4|, &lt;0 -3 -5 -9 -4 -2|] 19.389
[[Marvel temperaments|Negri]]: [[19edo]] 9&amp;10 17.833
[[Marvel temperaments|Negri]]: [[19edo]] 9&amp;10 17.833
[[Starling temperaments|Sensis]]: [[19edo]] [&lt;1 6 8 11 6 10|, &lt;0 -8 -9 -13 -4 -10|] 20.017  
[[Starling temperaments|Sensis]]: [[19edo]] [&lt;1 6 8 11 6 10|, &lt;0 -8 -9 -13 -4 -10|] 20.017
[[Starling temperaments|Keemun]]: [[19edo]] 4&amp;19 29.749
[[Starling temperaments|Keemun]]: [[19edo]] 4&amp;19 29.749
[[Meantone family|Meanenneadecal]]: [[19edo]] [&lt;1 0 -4 -13 -6 -20|, &lt;0 1 4 10 6 15|] 21.182
[[Meantone family|Meanenneadecal]]: [[19edo]] [&lt;1 0 -4 -13 -6 -20|, &lt;0 1 4 10 6 15|] 21.182
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[[Ragismic microtemperaments|Abigail]]: [[1258edo]] 46&amp;178 8.856
[[Ragismic microtemperaments|Abigail]]: [[1258edo]] 46&amp;178 8.856


=13-limit rank three=
=13-limit rank three=  
Name: Optimal patent val: Val name: 10^5 * badness
Name: Optimal patent val: Val name: 10^5 * badness
[[Starling family|Mockingbird]]: [[15edo]] 3&amp;4&amp;15 85.942
[[Starling family|Mockingbird]]: [[15edo]] 3&amp;4&amp;15 85.942
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[[Sengic family|Krypton]]: [[36edo]] 9&amp;10&amp;36 72.673
[[Sengic family|Krypton]]: [[36edo]] 9&amp;10&amp;36 72.673
[[Gamelismic family|Foreboding]]: [[41edo]] 5&amp;10&amp;26 87.267
[[Gamelismic family|Foreboding]]: [[41edo]] 5&amp;10&amp;26 87.267
[[Marvel family|Athene]]: [[53edo]] [&lt;1 0 0 -5 -9 -4|, &lt;0 1 0 2 2 -1|, &lt;0 0 1 2 2 4|] 81.781
[[Marvel family|Athene]]: [[53edo]] [&lt;1 0 0 -5 -9 -4|, &lt;0 1 0 2 2 -1|, &lt;0 0 1 2 4 4|] 81.781
[[Starling family|Thrush]]: [[58edo]] 31&amp;46&amp;58 67.663
[[Starling family|Thrush]]: [[58edo]] 31&amp;46&amp;58 67.663
[[Starling family|Bluebird]]: [[58edo]] 12&amp;15&amp;31 91.548
[[Starling family|Bluebird]]: [[58edo]] 12&amp;15&amp;31 91.548
[[Starling family|Aplonis]]: [[58edo]] 19&amp;31&amp;58 82.078  
[[Starling family|Aplonis]]: [[58edo]] 19&amp;31&amp;58 82.078
[[Breed family|Jofur]]: [[58edo]] 10&amp;31&amp;58 74.932
[[Breed family|Jofur]]: [[58edo]] 10&amp;31&amp;58 74.932
[[Marvel family|Deecee]]: [[72edo]] 9&amp;22&amp;41 92.048
[[Marvel family|Deecee]]: [[72edo]] 9&amp;22&amp;41 92.048
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&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="x5-limit rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;5-limit rank two&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x5-limit rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;5-limit rank two&lt;/h1&gt;
Comma: Optimal patent val: 1000 * badness&lt;br /&gt;
Comma: Optimal patent val: 1000 * badness&lt;br /&gt;
16/15: &lt;a class="wiki_link" href="/8edo"&gt;8edo&lt;/a&gt; 14.884&lt;br /&gt;
16/15: &lt;a class="wiki_link" href="/8edo"&gt;8edo&lt;/a&gt; 14.884&lt;br /&gt;
648/625: &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; 47.231&lt;br /&gt;
648/625: &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; 47.231&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="x7-limit rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;7-limit rank two&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="x7-limit rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;7-limit rank two&lt;/h1&gt;
Name: Optimal patent val: Val name: 1000*badness&lt;br /&gt;
Name: Optimal patent val: Val name: 1000*badness&lt;br /&gt;
&lt;a class="wiki_link" href="/Trienstonic%20clan"&gt;Father&lt;/a&gt;: &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt; [&amp;lt;1 0 4 -2|, &amp;lt;0 1 -1 3|] 21.312&lt;br /&gt;
&lt;a class="wiki_link" href="/Trienstonic%20clan"&gt;Father&lt;/a&gt;: &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt; [&amp;lt;1 0 4 -2|, &amp;lt;0 1 -1 3|] 21.312&lt;br /&gt;
&lt;a class="wiki_link" href="/Archytas%20clan"&gt;Mother&lt;/a&gt;: &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt; 2&amp;amp;3 24.152&lt;br /&gt;
&lt;a class="wiki_link" href="/Archytas%20clan"&gt;Mother&lt;/a&gt;: &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt; 2&amp;amp;3 24.152&lt;br /&gt;
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&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="x7-limit rank three"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;7-limit rank three&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="x7-limit rank three"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;7-limit rank three&lt;/h1&gt;
Comma: Optimal patent val: 10^6 * badness&lt;br /&gt;
Comma: Optimal patent val: 10^6 * badness&lt;br /&gt;
36/35: &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; 63.675&lt;br /&gt;
36/35: &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; 63.675&lt;br /&gt;
49/48: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; 115.514&lt;br /&gt;
49/48: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; 115.514&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="x11-limit rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;11-limit rank two&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="x11-limit rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;11-limit rank two&lt;/h1&gt;
Name: Optimal patent val: Val name: 1000*badness&lt;br /&gt;
Name: Optimal patent val: Val name: 1000*badness&lt;br /&gt;
&lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;Negric&lt;/a&gt;: &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt; 1&amp;amp;9 30.617&lt;br /&gt;
&lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;Negric&lt;/a&gt;: &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt; 1&amp;amp;9 30.617&lt;br /&gt;
&lt;a class="wiki_link" href="/Jubilismic%20clan"&gt;Diminished&lt;/a&gt;: &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; 4&amp;amp;12 22.132&lt;br /&gt;
&lt;a class="wiki_link" href="/Jubilismic%20clan"&gt;Diminished&lt;/a&gt;: &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; 4&amp;amp;12 22.132&lt;br /&gt;
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&lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;Negri&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; 9&amp;amp;10 26.190&lt;br /&gt;
&lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;Negri&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; 9&amp;amp;10 26.190&lt;br /&gt;
&lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;Meanenneadecal&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; 12&amp;amp;19 21.182&lt;br /&gt;
&lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;Meanenneadecal&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; 12&amp;amp;19 21.182&lt;br /&gt;
&lt;a class="wiki_link" href="/Diaschismic%20family"&gt;Pajara&lt;/a&gt;: &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; 12&amp;amp;22 20.343 &lt;br /&gt;
&lt;a class="wiki_link" href="/Diaschismic%20family"&gt;Pajara&lt;/a&gt;: &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; 12&amp;amp;22 20.343&lt;br /&gt;
&lt;a class="wiki_link" href="/Porcupine%20family"&gt;Nautilus&lt;/a&gt;: &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt; 15&amp;amp;29 26.023&lt;br /&gt;
&lt;a class="wiki_link" href="/Porcupine%20family"&gt;Nautilus&lt;/a&gt;: &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt; 15&amp;amp;29 26.023&lt;br /&gt;
&lt;a class="wiki_link" href="/Meantone%20family"&gt;Mohajira&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 7&amp;amp;24 26.064&lt;br /&gt;
&lt;a class="wiki_link" href="/Meantone%20family"&gt;Mohajira&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 7&amp;amp;24 26.064&lt;br /&gt;
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&lt;a class="wiki_link" href="/Porcupine%20rank%20three%20family"&gt;Sonic&lt;/a&gt;: &lt;a class="wiki_link" href="/51edo"&gt;51edo&lt;/a&gt; 7&amp;amp;15&amp;amp;51 523.158&lt;br /&gt;
&lt;a class="wiki_link" href="/Porcupine%20rank%20three%20family"&gt;Sonic&lt;/a&gt;: &lt;a class="wiki_link" href="/51edo"&gt;51edo&lt;/a&gt; 7&amp;amp;15&amp;amp;51 523.158&lt;br /&gt;
&lt;a class="wiki_link" href="/Nuwell%20family"&gt;Big Brother&lt;/a&gt;: &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; 9&amp;amp;22&amp;amp;70 506.556&lt;br /&gt;
&lt;a class="wiki_link" href="/Nuwell%20family"&gt;Big Brother&lt;/a&gt;: &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; 9&amp;amp;22&amp;amp;70 506.556&lt;br /&gt;
&lt;a class="wiki_link" href="/Marvel%20family"&gt;Prodigy&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; 2&amp;amp;10&amp;amp;29 334.745 &lt;br /&gt;
&lt;a class="wiki_link" href="/Marvel%20family"&gt;Prodigy&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; 2&amp;amp;10&amp;amp;29 334.745&lt;br /&gt;
&lt;a class="wiki_link" href="/Didymus%20rank%20three%20family"&gt;Erato&lt;/a&gt;: &lt;a class="wiki_link" href="/81edo"&gt;81edo&lt;/a&gt; 12&amp;amp;19&amp;amp;31 557.521&lt;br /&gt;
&lt;a class="wiki_link" href="/Didymus%20rank%20three%20family"&gt;Erato&lt;/a&gt;: &lt;a class="wiki_link" href="/81edo"&gt;81edo&lt;/a&gt; 12&amp;amp;19&amp;amp;31 557.521&lt;br /&gt;
&lt;a class="wiki_link" href="/Didymus%20rank%20three%20family"&gt;Euterpe&lt;/a&gt;: &lt;a class="wiki_link" href="/88edo"&gt;88edo&lt;/a&gt; 5&amp;amp;12&amp;amp;26 535.809&lt;br /&gt;
&lt;a class="wiki_link" href="/Didymus%20rank%20three%20family"&gt;Euterpe&lt;/a&gt;: &lt;a class="wiki_link" href="/88edo"&gt;88edo&lt;/a&gt; 5&amp;amp;12&amp;amp;26 535.809&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="x13-limit rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit rank two&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="x13-limit rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit rank two&lt;/h1&gt;
Name: Optimal patent val: Val name: 1000*badness&lt;br /&gt;
Name: Optimal patent val: Val name: 1000*badness&lt;br /&gt;
&lt;a class="wiki_link" href="/Quartonic%20temperaments"&gt;Progression&lt;/a&gt;: &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt; [&amp;lt;1 1 2 2 3 3|, &amp;lt;0 5 3 7 4 6|] 18.158&lt;br /&gt;
&lt;a class="wiki_link" href="/Quartonic%20temperaments"&gt;Progression&lt;/a&gt;: &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt; [&amp;lt;1 1 2 2 3 3|, &amp;lt;0 5 3 7 4 6|] 18.158&lt;br /&gt;
&lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;Negric&lt;/a&gt;: &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt; 1&amp;amp;9 20.205&lt;br /&gt;
&lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;Negric&lt;/a&gt;: &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt; 1&amp;amp;9 20.205&lt;br /&gt;
&lt;a class="wiki_link" href="/Trienstonic%20clan"&gt;Opossum&lt;/a&gt;: &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt; [&amp;lt;1 2 3 4 4 4|, &amp;lt;0 -3 -5 -9 -4 -2|] 19.389&lt;br /&gt;
&lt;a class="wiki_link" href="/Trienstonic%20clan"&gt;Opossum&lt;/a&gt;: &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt; [&amp;lt;1 2 3 4 4 4|, &amp;lt;0 -3 -5 -9 -4 -2|] 19.389&lt;br /&gt;
&lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;Negri&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; 9&amp;amp;10 17.833&lt;br /&gt;
&lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;Negri&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; 9&amp;amp;10 17.833&lt;br /&gt;
&lt;a class="wiki_link" href="/Starling%20temperaments"&gt;Sensis&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; [&amp;lt;1 6 8 11 6 10|, &amp;lt;0 -8 -9 -13 -4 -10|] 20.017 &lt;br /&gt;
&lt;a class="wiki_link" href="/Starling%20temperaments"&gt;Sensis&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; [&amp;lt;1 6 8 11 6 10|, &amp;lt;0 -8 -9 -13 -4 -10|] 20.017&lt;br /&gt;
&lt;a class="wiki_link" href="/Starling%20temperaments"&gt;Keemun&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; 4&amp;amp;19 29.749&lt;br /&gt;
&lt;a class="wiki_link" href="/Starling%20temperaments"&gt;Keemun&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; 4&amp;amp;19 29.749&lt;br /&gt;
&lt;a class="wiki_link" href="/Meantone%20family"&gt;Meanenneadecal&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; [&amp;lt;1 0 -4 -13 -6 -20|, &amp;lt;0 1 4 10 6 15|] 21.182&lt;br /&gt;
&lt;a class="wiki_link" href="/Meantone%20family"&gt;Meanenneadecal&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; [&amp;lt;1 0 -4 -13 -6 -20|, &amp;lt;0 1 4 10 6 15|] 21.182&lt;br /&gt;
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Name: Optimal patent val: Val name: 10^5 * badness&lt;br /&gt;
Name: Optimal patent val: Val name: 10^5 * badness&lt;br /&gt;
&lt;a class="wiki_link" href="/Starling%20family"&gt;Mockingbird&lt;/a&gt;: &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt; 3&amp;amp;4&amp;amp;15 85.942&lt;br /&gt;
&lt;a class="wiki_link" href="/Starling%20family"&gt;Mockingbird&lt;/a&gt;: &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt; 3&amp;amp;4&amp;amp;15 85.942&lt;br /&gt;
&lt;a class="wiki_link" href="/Starling%20family"&gt;Catbird&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; [&amp;lt;1 0 0 -1 2 0|, &amp;lt;0 1 0 -2 -2 -5|, &amp;lt;0 0 1 3 2 5|] 90.475&lt;br /&gt;
&lt;a class="wiki_link" href="/Starling%20family"&gt;Catbird&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; [&amp;lt;1 0 0 -1 2 0|, &amp;lt;0 1 0 -2 -2 -5|, &amp;lt;0 0 1 3 2 5|] 90.475&lt;br /&gt;
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&lt;a class="wiki_link" href="/Sengic%20family"&gt;Krypton&lt;/a&gt;: &lt;a class="wiki_link" href="/36edo"&gt;36edo&lt;/a&gt; 9&amp;amp;10&amp;amp;36 72.673&lt;br /&gt;
&lt;a class="wiki_link" href="/Sengic%20family"&gt;Krypton&lt;/a&gt;: &lt;a class="wiki_link" href="/36edo"&gt;36edo&lt;/a&gt; 9&amp;amp;10&amp;amp;36 72.673&lt;br /&gt;
&lt;a class="wiki_link" href="/Gamelismic%20family"&gt;Foreboding&lt;/a&gt;: &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt; 5&amp;amp;10&amp;amp;26 87.267&lt;br /&gt;
&lt;a class="wiki_link" href="/Gamelismic%20family"&gt;Foreboding&lt;/a&gt;: &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt; 5&amp;amp;10&amp;amp;26 87.267&lt;br /&gt;
&lt;a class="wiki_link" href="/Marvel%20family"&gt;Athene&lt;/a&gt;: &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; [&amp;lt;1 0 0 -5 -9 -4|, &amp;lt;0 1 0 2 2 -1|, &amp;lt;0 0 1 2 2 4|] 81.781&lt;br /&gt;
&lt;a class="wiki_link" href="/Marvel%20family"&gt;Athene&lt;/a&gt;: &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; [&amp;lt;1 0 0 -5 -9 -4|, &amp;lt;0 1 0 2 2 -1|, &amp;lt;0 0 1 2 4 4|] 81.781&lt;br /&gt;
&lt;a class="wiki_link" href="/Starling%20family"&gt;Thrush&lt;/a&gt;: &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt; 31&amp;amp;46&amp;amp;58 67.663&lt;br /&gt;
&lt;a class="wiki_link" href="/Starling%20family"&gt;Thrush&lt;/a&gt;: &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt; 31&amp;amp;46&amp;amp;58 67.663&lt;br /&gt;
&lt;a class="wiki_link" href="/Starling%20family"&gt;Bluebird&lt;/a&gt;: &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt; 12&amp;amp;15&amp;amp;31 91.548&lt;br /&gt;
&lt;a class="wiki_link" href="/Starling%20family"&gt;Bluebird&lt;/a&gt;: &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt; 12&amp;amp;15&amp;amp;31 91.548&lt;br /&gt;
&lt;a class="wiki_link" href="/Starling%20family"&gt;Aplonis&lt;/a&gt;: &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt; 19&amp;amp;31&amp;amp;58 82.078 &lt;br /&gt;
&lt;a class="wiki_link" href="/Starling%20family"&gt;Aplonis&lt;/a&gt;: &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt; 19&amp;amp;31&amp;amp;58 82.078&lt;br /&gt;
&lt;a class="wiki_link" href="/Breed%20family"&gt;Jofur&lt;/a&gt;: &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt; 10&amp;amp;31&amp;amp;58 74.932&lt;br /&gt;
&lt;a class="wiki_link" href="/Breed%20family"&gt;Jofur&lt;/a&gt;: &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt; 10&amp;amp;31&amp;amp;58 74.932&lt;br /&gt;
&lt;a class="wiki_link" href="/Marvel%20family"&gt;Deecee&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; 9&amp;amp;22&amp;amp;41 92.048&lt;br /&gt;
&lt;a class="wiki_link" href="/Marvel%20family"&gt;Deecee&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; 9&amp;amp;22&amp;amp;41 92.048&lt;br /&gt;