Hemifamity family

Revision as of 02:07, 23 September 2010 by Wikispaces>genewardsmith (**Imported revision 164781197 - Original comment: **)

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===Vital statistics===
Comma c = 5120/5103

7-limit minimax: 3 and 7 1/7c sharp, 5 just
[|1 0 0 0>, |10/7 1/7 1/7 -1/7>, 
|0 0 1 0>, |10/7 -6/7 1/7 6/7>]
Eigenmonzos: 2, 5/4, 7/6

9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp
[|1 0 0 0>, |5/4 1/4 1/8 -1/8>, 
|0 0 1 0>, |5/2 -3/2 1/4 3/4>]
Eigenmonzos: 2, 5/4, 9/7

Lattice basis: 3/2 length 0.5670, 10/9 length 1.8063
Angle(3/2, 10/9) = 82.112 degrees
Map to lattice: [<0 1 2 -4|, <0 0 1 1|]
[[edo|EDOs]]: [[99edo|99]], [[140edo|140]], [[239edo|239]], [[292edo|292]], [[490edo|490]], [[531edo|531]]

==11-limit children==

===Pele===
Commas: 441/440, 896/891

Minimax tuning
[|1 0 0 0 0>, |17/10 0 1/10 0 -1/10>, 
|17/5 -2 6/5 0 -1/5>,
|16/5 -2 3/5 0 2/5>, |17/5 -2 1/5 0 4/5>]
Eigenmonzos: 2, 10/9, 11/9

Map: [<1 0 0 10 17|, <0 1 0 -6 -10|, <0 0 1 1 1|]
Generators: 2, 3, 5
Edos: 128, 145, 232

===Laka===
Commas: 5120/5103, 540/539

Minimax tuning
[|1 0 0 0 0>, |4/3 0 2/21 -1/21 1/21>, 
|0 0 1 0 0>, |2 0 3/7 2/7 -2/7>, 
|2 0 3/7 -5/7 5/7>]
Eigenmonzos: 2, 5/4, 14/11

Map: [<1 0 0 10 -18|, <0 1 0 -6 15|, <0 0 1 1 -1|]
Generators: 2, 3, 5
Edos: 94, 111, 152, 345

===Akea===
Commas: 385/384, 2200/2187

Minimax tuning
[|1 0 0 0 0>, |4/3 0 2/21 -1/21 1/21>, 
|0 0 1 0 0>, |2 0 3/7 2/7 -2/7>, 
|2 0 3/7 -5/7 5/7>]
Eigenmonzos: 2, 14/11, 7/5

Map: [<1 0 0 10 -3|, <0 1 0 -6 7|, <0 0 1 1 -2|]
Generators: 2, 3, 5
Edos: 94, 140, 181, 408

===Kapo===
Commas: 5120/5103, 3025/3024

Minimax tuning
[|1 0 0 0 0>, |8/5 2/5 0 -1/15 -2/15>, 
|14/5 6/5 0 7/15 -16/15>, 
|16/5 -6/5 0 13/15 -4/15>, 
|16/5 -6/5 0 -2/15 11/15>]
Eigenmonzos: 2, 11/9, 9/7

Map: [<1 0 0 10 7|, <0 1 1 -5 -2|, <0 0 2 2 -1|]
Generators: 2, 3, 128/99
Edos: 152, 198, 239, 350, 391, 478, 589

Original HTML content:

<html><head><title>Hemifamity family</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--Vital statistics"></a><!-- ws:end:WikiTextHeadingRule:0 -->Vital statistics</h3>
Comma c = 5120/5103<br />
<br />
7-limit minimax: 3 and 7 1/7c sharp, 5 just<br />
[|1 0 0 0&gt;, |10/7 1/7 1/7 -1/7&gt;, <br />
|0 0 1 0&gt;, |10/7 -6/7 1/7 6/7&gt;]<br />
Eigenmonzos: 2, 5/4, 7/6<br />
<br />
9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp<br />
[|1 0 0 0&gt;, |5/4 1/4 1/8 -1/8&gt;, <br />
|0 0 1 0&gt;, |5/2 -3/2 1/4 3/4&gt;]<br />
Eigenmonzos: 2, 5/4, 9/7<br />
<br />
Lattice basis: 3/2 length 0.5670, 10/9 length 1.8063<br />
Angle(3/2, 10/9) = 82.112 degrees<br />
Map to lattice: [&lt;0 1 2 -4|, &lt;0 0 1 1|]<br />
<a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/99edo">99</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/239edo">239</a>, <a class="wiki_link" href="/292edo">292</a>, <a class="wiki_link" href="/490edo">490</a>, <a class="wiki_link" href="/531edo">531</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-11-limit children"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit children</h2>
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-11-limit children-Pele"></a><!-- ws:end:WikiTextHeadingRule:4 -->Pele</h3>
Commas: 441/440, 896/891<br />
<br />
Minimax tuning<br />
[|1 0 0 0 0&gt;, |17/10 0 1/10 0 -1/10&gt;, <br />
|17/5 -2 6/5 0 -1/5&gt;,<br />
|16/5 -2 3/5 0 2/5&gt;, |17/5 -2 1/5 0 4/5&gt;]<br />
Eigenmonzos: 2, 10/9, 11/9<br />
<br />
Map: [&lt;1 0 0 10 17|, &lt;0 1 0 -6 -10|, &lt;0 0 1 1 1|]<br />
Generators: 2, 3, 5<br />
Edos: 128, 145, 232<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-11-limit children-Laka"></a><!-- ws:end:WikiTextHeadingRule:6 -->Laka</h3>
Commas: 5120/5103, 540/539<br />
<br />
Minimax tuning<br />
[|1 0 0 0 0&gt;, |4/3 0 2/21 -1/21 1/21&gt;, <br />
|0 0 1 0 0&gt;, |2 0 3/7 2/7 -2/7&gt;, <br />
|2 0 3/7 -5/7 5/7&gt;]<br />
Eigenmonzos: 2, 5/4, 14/11<br />
<br />
Map: [&lt;1 0 0 10 -18|, &lt;0 1 0 -6 15|, &lt;0 0 1 1 -1|]<br />
Generators: 2, 3, 5<br />
Edos: 94, 111, 152, 345<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-11-limit children-Akea"></a><!-- ws:end:WikiTextHeadingRule:8 -->Akea</h3>
Commas: 385/384, 2200/2187<br />
<br />
Minimax tuning<br />
[|1 0 0 0 0&gt;, |4/3 0 2/21 -1/21 1/21&gt;, <br />
|0 0 1 0 0&gt;, |2 0 3/7 2/7 -2/7&gt;, <br />
|2 0 3/7 -5/7 5/7&gt;]<br />
Eigenmonzos: 2, 14/11, 7/5<br />
<br />
Map: [&lt;1 0 0 10 -3|, &lt;0 1 0 -6 7|, &lt;0 0 1 1 -2|]<br />
Generators: 2, 3, 5<br />
Edos: 94, 140, 181, 408<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="x-11-limit children-Kapo"></a><!-- ws:end:WikiTextHeadingRule:10 -->Kapo</h3>
Commas: 5120/5103, 3025/3024<br />
<br />
Minimax tuning<br />
[|1 0 0 0 0&gt;, |8/5 2/5 0 -1/15 -2/15&gt;, <br />
|14/5 6/5 0 7/15 -16/15&gt;, <br />
|16/5 -6/5 0 13/15 -4/15&gt;, <br />
|16/5 -6/5 0 -2/15 11/15&gt;]<br />
Eigenmonzos: 2, 11/9, 9/7<br />
<br />
Map: [&lt;1 0 0 10 7|, &lt;0 1 1 -5 -2|, &lt;0 0 2 2 -1|]<br />
Generators: 2, 3, 128/99<br />
Edos: 152, 198, 239, 350, 391, 478, 589</body></html>