Ragismic family: Difference between revisions

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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>2012-02-20 16:12:44 UTC</tt>.<br>
: The original revision id was <tt>303438478</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]]
 
=Ragisma=
=Ragisma=
Comma: 4375/4374
Comma: 4375/4374


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


9-limit
9-limit
[|1 0 0 0&gt;, |0 1 0 0&gt;, |1/5 7/5 1/5 -1/5&gt;,  
[|1 0 0 0&gt;, |0 1 0 0&gt;, |1/5 7/5 1/5 -1/5&gt;,  
|1/5 7/5 -4/5 4/5&gt;]
|1/5 7/5 -4/5 4/5&gt;]
Eigenmonzos: 2, 4/3, 7/5
Eigenmonzos: 2, 4/3, 7/5


Lattice basis: 10/9 length=0.789 6/5 length=0.921
Lattice basis: 10/9 length=0.789 6/5 length=0.921
Angle(10/9, 6/5) = 105.299
Angle(10/9, 6/5) = 105.299
Map to lattice: [&lt;0 -1 -1 -3|, &lt;0 -1 -2 1|]
Map to lattice: [&lt;0 -1 -1 -3|, &lt;0 -1 -2 1|]


Map: [&lt;1 0 0 1|, &lt;0 1 0 7|, &lt;0 0 1 -4|]
Map: [&lt;1 0 0 1|, &lt;0 1 0 7|, &lt;0 0 1 -4|]
Generators: 2, 3, 5
Generators: 2, 3, 5
Edos: 9, 19, 26, 27, 45, 46, 53, 72, 80, 91, 99, 171, 270, 441, 494, 612, 665, 935, 1106, 1277, 1376, 1718, 1889, 6279  
Edos: 9, 19, 26, 27, 45, 46, 53, 72, 80, 91, 99, 171, 270, 441, 494, 612, 665, 935, 1106, 1277, 1376, 1718, 1889, 6279  


[[Projection pair]]: 7 4374/625
[[Projection_pair|Projection pair]]: 7 4374/625


Scales: [[ragismic19]]
Scales: [[ragismic19|ragismic19]]


==11 limit children==
==11 limit children==
Line 38: Line 38:


Minimax tuning
Minimax tuning
[|1 0 0 0 0&gt;, |3/4 0 1/2 1/2 -1/2&gt;,  
[|1 0 0 0 0&gt;, |3/4 0 1/2 1/2 -1/2&gt;,  
|25/16 0 7/8 5/8 -7/8&gt;, |0 0 0 1 0&gt;,  
|25/16 0 7/8 5/8 -7/8&gt;, |0 0 0 1 0&gt;,  
|25/16 0 -1/8 5/8 1/8&gt;]
|25/16 0 -1/8 5/8 1/8&gt;]
Eigenmonzos: 2, 11/10, 8/7
Eigenmonzos: 2, 11/10, 8/7


Map: [&lt;2 0 0 2 5|, &lt;0 1 0 7 5|, &lt;0 0 1 -4 -3|]
Map: [&lt;2 0 0 2 5|, &lt;0 1 0 7 5|, &lt;0 0 1 -4 -3|]
Generators: 99/70, 3, 5
Generators: 99/70, 3, 5
Badness: 0.0000888
Badness: 0.0000888


Line 57: Line 61:
|25/16 0 -1/8 5/8 1/8 0&gt;,  
|25/16 0 -1/8 5/8 1/8 0&gt;,  
|99/32 0 -11/16 -1/16 11/16 0&gt;]
|99/32 0 -11/16 -1/16 11/16 0&gt;]
Eigenmonzos: 2, 11/10, 8/7
Eigenmonzos: 2, 11/10, 8/7


15-limit minimax
15-limit minimax
[|1 0 0 0 0 0&gt;, |1/2 1/3 1/3 1/3 -1/3 0&gt;,  
[|1 0 0 0 0 0&gt;, |1/2 1/3 1/3 1/3 -1/3 0&gt;,  
|9/8 7/12 7/12 1/3 -7/12 0&gt;, |0 0 0 1 0 0&gt;,  
|9/8 7/12 7/12 1/3 -7/12 0&gt;, |0 0 0 1 0 0&gt;,  
|13/8 -1/12 -1/12 2/3 1/12 0&gt;,  
|13/8 -1/12 -1/12 2/3 1/12 0&gt;,  
|55/16 -11/24 -11/24 1/6 11/24 0&gt;]
|55/16 -11/24 -11/24 1/6 11/24 0&gt;]
Eigenmonzos: 2, 8/7, 15/11
Eigenmonzos: 2, 8/7, 15/11


Lattice basis: 44/39 length = 0.3480 6/5 length = 0.7828
Lattice basis: 44/39 length = 0.3480 6/5 length = 0.7828
Angle(44/39, 6/5) = 85.3977
Angle(44/39, 6/5) = 85.3977
Map to lattice: [&lt;0 2 2 6 4 1|, &lt;0 -1 -2 1 1 2|]
Map to lattice: [&lt;0 2 2 6 4 1|, &lt;0 -1 -2 1 1 2|]


Map: [&lt;2 0 1 -2 2 7|, &lt;0 1 0 7 5 3|, &lt;0 0 2 -8 -6 -5|]
Map: [&lt;2 0 1 -2 2 7|, &lt;0 1 0 7 5 3|, &lt;0 0 2 -8 -6 -5|]
Generators: 99/70, 3, 220/117
Generators: 99/70, 3, 220/117
Edos: 46, 80, 92, 126, 144, 178, 190, 224, 494, 684, 954, 1178, 1942, 3120, 3390
Edos: 46, 80, 92, 126, 144, 178, 190, 224, 494, 684, 954, 1178, 1942, 3120, 3390
Badness: 0.000322
Badness: 0.000322


Scales: [[donar46]]
Scales: [[donar46|donar46]]


==Thunor==
==Thunor==
Line 81: Line 93:


13 and 15 limit minimax
13 and 15 limit minimax
[|1 0 0 0 0 0&gt;, |7/10 4/5 0 -2/5 0 1/5&gt;,  
[|1 0 0 0 0 0&gt;, |7/10 4/5 0 -2/5 0 1/5&gt;,  
|9/8 3/2 0 -3/4 0 1/4&gt;, |7/5 -2/5 0 1/5 0 2/5&gt;, |21/8 -1/2 0 1/4 0 1/4&gt;, |0 0 0 0 0 1&gt;]
|9/8 3/2 0 -3/4 0 1/4&gt;, |7/5 -2/5 0 1/5 0 2/5&gt;, |21/8 -1/2 0 1/4 0 1/4&gt;, |0 0 0 0 0 1&gt;]
Eigenmonzos: 2, 16/13, 9/7
Eigenmonzos: 2, 16/13, 9/7


Lattice basis: 10/9 length 0.4234 6/5 length 0.8426
Lattice basis: 10/9 length 0.4234 6/5 length 0.8426
Angle(10/9, 6/5) = 84.126 degrees
Angle(10/9, 6/5) = 84.126 degrees
Map to lattice: [&lt;0 -1 -2 -3 -2 -7|, &lt;0 -1 -2 1 1 1|]   
Map to lattice: [&lt;0 -1 -2 -3 -2 -7|, &lt;0 -1 -2 1 1 1|]   


Map: [&lt;2 0 0 2 5 -3|, &lt;0 1 0 7 5 15|, &lt;0 0 1 -4 -3 -8|]
Map: [&lt;2 0 0 2 5 -3|, &lt;0 1 0 7 5 15|, &lt;0 0 1 -4 -3 -8|]
Generators: 99/70, 3, 5
Generators: 99/70, 3, 5
Edos: 26, 46, 72, 178, 224, 270, 494
Edos: 26, 46, 72, 178, 224, 270, 494
Badness: 0.000341
Badness: 0.000341


Line 98: Line 117:


Map: [&lt;2 0 0 2 5 22|, &lt;0 1 0 7 5 -9|, &lt;0 0 1 -4 -3 3|]
Map: [&lt;2 0 0 2 5 22|, &lt;0 1 0 7 5 -9|, &lt;0 0 1 -4 -3 3|]
EDOs: 46, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870
EDOs: 46, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870
Badness: 0.000549  
Badness: 0.000549  


Line 111: Line 132:


Map: [&lt;1 0 0 1 6|, &lt;0 1 0 7 -6|, &lt;0 0 1 -4 3|]
Map: [&lt;1 0 0 1 6|, &lt;0 1 0 7 -6|, &lt;0 0 1 -4 3|]
EDOs: 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cde
EDOs: 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cde
Badness: 0.000721
Badness: 0.000721


Line 118: Line 141:


Map: [&lt;1 0 0 1 6 2|, &lt;0 1 0 7 -6 4|, &lt;0 0 1 -4 3 -2|]
Map: [&lt;1 0 0 1 6 2|, &lt;0 1 0 7 -6 4|, &lt;0 0 1 -4 3 -2|]
EDOs: 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190f, 197ef, 243ef
EDOs: 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190f, 197ef, 243ef
Badness: 0.000840
Badness: 0.000840
</pre></div>
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Ragisma family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:20:&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:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Ragisma"&gt;Ragisma&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="#Ragisma-11 limit children"&gt;11 limit children&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="#Thor"&gt;Thor&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="#Thor-Donar"&gt;Donar&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Thor-Thunor"&gt;Thunor&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Thor-Rym"&gt;Rym&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Vidar"&gt;Vidar&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Bragi"&gt;Bragi&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Beyla"&gt;Beyla&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Beyla-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Ragisma"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Ragisma&lt;/h1&gt;
Comma: 4375/4374&lt;br /&gt;
&lt;br /&gt;
7-limit&lt;br /&gt;
[|1 0 0 0&amp;gt;, |-1/7 0 4/7 1/7&amp;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;
9-limit&lt;br /&gt;
[|1 0 0 0&amp;gt;, |0 1 0 0&amp;gt;, |1/5 7/5 1/5 -1/5&amp;gt;, &lt;br /&gt;
|1/5 7/5 -4/5 4/5&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 4/3, 7/5&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 10/9 length=0.789 6/5 length=0.921&lt;br /&gt;
Angle(10/9, 6/5) = 105.299&lt;br /&gt;
Map to lattice: [&amp;lt;0 -1 -1 -3|, &amp;lt;0 -1 -2 1|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 1|, &amp;lt;0 1 0 7|, &amp;lt;0 0 1 -4|]&lt;br /&gt;
Generators: 2, 3, 5&lt;br /&gt;
Edos: 9, 19, 26, 27, 45, 46, 53, 72, 80, 91, 99, 171, 270, 441, 494, 612, 665, 935, 1106, 1277, 1376, 1718, 1889, 6279 &lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;: 7 4374/625&lt;br /&gt;
&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/ragismic19"&gt;ragismic19&lt;/a&gt;&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="Ragisma-11 limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11 limit children&lt;/h2&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Thor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Thor&lt;/h1&gt;
Commas: 4375/4374, 3025/3024&lt;br /&gt;
&lt;br /&gt;
Minimax tuning&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |3/4 0 1/2 1/2 -1/2&amp;gt;, &lt;br /&gt;
|25/16 0 7/8 5/8 -7/8&amp;gt;, |0 0 0 1 0&amp;gt;, &lt;br /&gt;
|25/16 0 -1/8 5/8 1/8&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 11/10, 8/7&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 0 2 5|, &amp;lt;0 1 0 7 5|, &amp;lt;0 0 1 -4 -3|]&lt;br /&gt;
Generators: 99/70, 3, 5&lt;br /&gt;
Badness: 0.0000888&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 2 9801/4900 7 21434787/3062500 11 2310905821257/210087500000 to 3.5.14/11&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="Thor-Donar"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Donar&lt;/h2&gt;
Commas: 4375/4374, 3025/3024, 4225/4224&lt;br /&gt;
&lt;br /&gt;
13-limit&lt;br /&gt;
||1 0 0 0 0 0&amp;gt;, |3/4 0 1/2 1/2 -1/2 0&amp;gt;, &lt;br /&gt;
|25/16 0 7/8 5/8 -7/8 0&amp;gt;, |0 0 0 1 0 0&amp;gt;, &lt;br /&gt;
|25/16 0 -1/8 5/8 1/8 0&amp;gt;, &lt;br /&gt;
|99/32 0 -11/16 -1/16 11/16 0&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 11/10, 8/7&lt;br /&gt;
&lt;br /&gt;
15-limit minimax&lt;br /&gt;
[|1 0 0 0 0 0&amp;gt;, |1/2 1/3 1/3 1/3 -1/3 0&amp;gt;, &lt;br /&gt;
|9/8 7/12 7/12 1/3 -7/12 0&amp;gt;, |0 0 0 1 0 0&amp;gt;, &lt;br /&gt;
|13/8 -1/12 -1/12 2/3 1/12 0&amp;gt;, &lt;br /&gt;
|55/16 -11/24 -11/24 1/6 11/24 0&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 8/7, 15/11&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 44/39 length = 0.3480 6/5 length = 0.7828&lt;br /&gt;
Angle(44/39, 6/5) = 85.3977&lt;br /&gt;
Map to lattice: [&amp;lt;0 2 2 6 4 1|, &amp;lt;0 -1 -2 1 1 2|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 1 -2 2 7|, &amp;lt;0 1 0 7 5 3|, &amp;lt;0 0 2 -8 -6 -5|]&lt;br /&gt;
Generators: 99/70, 3, 220/117&lt;br /&gt;
Edos: 46, 80, 92, 126, 144, 178, 190, 224, 494, 684, 954, 1178, 1942, 3120, 3390&lt;br /&gt;
Badness: 0.000322&lt;br /&gt;
&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/donar46"&gt;donar46&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Thor-Thunor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Thunor&lt;/h2&gt;
Commas: 4375/4374, 3025/3024, 1716/1715&lt;br /&gt;
&lt;br /&gt;
13 and 15 limit minimax&lt;br /&gt;
[|1 0 0 0 0 0&amp;gt;, |7/10 4/5 0 -2/5 0 1/5&amp;gt;, &lt;br /&gt;
|9/8 3/2 0 -3/4 0 1/4&amp;gt;, |7/5 -2/5 0 1/5 0 2/5&amp;gt;, |21/8 -1/2 0 1/4 0 1/4&amp;gt;, |0 0 0 0 0 1&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 16/13, 9/7&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 10/9 length 0.4234 6/5 length 0.8426&lt;br /&gt;
Angle(10/9, 6/5) = 84.126 degrees&lt;br /&gt;
Map to lattice: [&amp;lt;0 -1 -2 -3 -2 -7|, &amp;lt;0 -1 -2 1 1 1|]  &lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 0 2 5 -3|, &amp;lt;0 1 0 7 5 15|, &amp;lt;0 0 1 -4 -3 -8|]&lt;br /&gt;
Generators: 99/70, 3, 5&lt;br /&gt;
Edos: 26, 46, 72, 178, 224, 270, 494&lt;br /&gt;
Badness: 0.000341&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="Thor-Rym"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Rym&lt;/h2&gt;
Commas: 4375/4374, 3025/3024, 4096/4095&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 0 2 5 22|, &amp;lt;0 1 0 7 5 -9|, &amp;lt;0 0 1 -4 -3 3|]&lt;br /&gt;
EDOs: 46, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870&lt;br /&gt;
Badness: 0.000549 &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="Vidar"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Vidar&lt;/h1&gt;
Commas: 4375/4374, 100663296/100656875&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Bragi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Bragi&lt;/h1&gt;
Commas: 4375/4374, 2097152/2096325&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Beyla"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Beyla&lt;/h1&gt;
Commas: 4374/4375, 385/384&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 1 6|, &amp;lt;0 1 0 7 -6|, &amp;lt;0 0 1 -4 3|]&lt;br /&gt;
EDOs: 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cde&lt;br /&gt;
Badness: 0.000721&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Beyla-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;13-limit&lt;/h2&gt;
Commas: 169/168, 325/324, 385/384&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 1 6 2|, &amp;lt;0 1 0 7 -6 4|, &amp;lt;0 0 1 -4 3 -2|]&lt;br /&gt;
EDOs: 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190f, 197ef, 243ef&lt;br /&gt;
Badness: 0.000840&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

Ragisma

Comma: 4375/4374

7-limit

[|1 0 0 0>, |-1/7 0 4/7 1/7>, |0 0 1 0>, |0 0 0 1>]

Eigenmonzos: 2, 8/7, 5/4

9-limit

[|1 0 0 0>, |0 1 0 0>, |1/5 7/5 1/5 -1/5>, |1/5 7/5 -4/5 4/5>]

Eigenmonzos: 2, 4/3, 7/5

Lattice basis: 10/9 length=0.789 6/5 length=0.921

Angle(10/9, 6/5) = 105.299

Map to lattice: [<0 -1 -1 -3|, <0 -1 -2 1|]

Map: [<1 0 0 1|, <0 1 0 7|, <0 0 1 -4|]

Generators: 2, 3, 5

Edos: 9, 19, 26, 27, 45, 46, 53, 72, 80, 91, 99, 171, 270, 441, 494, 612, 665, 935, 1106, 1277, 1376, 1718, 1889, 6279

Projection pair: 7 4374/625

Scales: ragismic19

11 limit children

Thor

Commas: 4375/4374, 3025/3024

Minimax tuning

[|1 0 0 0 0>, |3/4 0 1/2 1/2 -1/2>, |25/16 0 7/8 5/8 -7/8>, |0 0 0 1 0>, |25/16 0 -1/8 5/8 1/8>]

Eigenmonzos: 2, 11/10, 8/7

Map: [<2 0 0 2 5|, <0 1 0 7 5|, <0 0 1 -4 -3|]

Generators: 99/70, 3, 5

Badness: 0.0000888

Projection pairs: 2 9801/4900 7 21434787/3062500 11 2310905821257/210087500000 to 3.5.14/11

Donar

Commas: 4375/4374, 3025/3024, 4225/4224

13-limit ||1 0 0 0 0 0>, |3/4 0 1/2 1/2 -1/2 0>, |25/16 0 7/8 5/8 -7/8 0>, |0 0 0 1 0 0>, |25/16 0 -1/8 5/8 1/8 0>, |99/32 0 -11/16 -1/16 11/16 0>]

Eigenmonzos: 2, 11/10, 8/7

15-limit minimax

[|1 0 0 0 0 0>, |1/2 1/3 1/3 1/3 -1/3 0>, |9/8 7/12 7/12 1/3 -7/12 0>, |0 0 0 1 0 0>, |13/8 -1/12 -1/12 2/3 1/12 0>, |55/16 -11/24 -11/24 1/6 11/24 0>]

Eigenmonzos: 2, 8/7, 15/11

Lattice basis: 44/39 length = 0.3480 6/5 length = 0.7828

Angle(44/39, 6/5) = 85.3977

Map to lattice: [<0 2 2 6 4 1|, <0 -1 -2 1 1 2|]

Map: [<2 0 1 -2 2 7|, <0 1 0 7 5 3|, <0 0 2 -8 -6 -5|]

Generators: 99/70, 3, 220/117

Edos: 46, 80, 92, 126, 144, 178, 190, 224, 494, 684, 954, 1178, 1942, 3120, 3390

Badness: 0.000322

Scales: donar46

Thunor

Commas: 4375/4374, 3025/3024, 1716/1715

13 and 15 limit minimax

[|1 0 0 0 0 0>, |7/10 4/5 0 -2/5 0 1/5>, |9/8 3/2 0 -3/4 0 1/4>, |7/5 -2/5 0 1/5 0 2/5>, |21/8 -1/2 0 1/4 0 1/4>, |0 0 0 0 0 1>]

Eigenmonzos: 2, 16/13, 9/7

Lattice basis: 10/9 length 0.4234 6/5 length 0.8426

Angle(10/9, 6/5) = 84.126 degrees

Map to lattice: [<0 -1 -2 -3 -2 -7|, <0 -1 -2 1 1 1|]

Map: [<2 0 0 2 5 -3|, <0 1 0 7 5 15|, <0 0 1 -4 -3 -8|]

Generators: 99/70, 3, 5

Edos: 26, 46, 72, 178, 224, 270, 494

Badness: 0.000341

Rym

Commas: 4375/4374, 3025/3024, 4096/4095

Map: [<2 0 0 2 5 22|, <0 1 0 7 5 -9|, <0 0 1 -4 -3 3|]

EDOs: 46, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870

Badness: 0.000549

Vidar

Commas: 4375/4374, 100663296/100656875

Bragi

Commas: 4375/4374, 2097152/2096325

Beyla

Commas: 4374/4375, 385/384

Map: [<1 0 0 1 6|, <0 1 0 7 -6|, <0 0 1 -4 3|]

EDOs: 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cde

Badness: 0.000721

13-limit

Commas: 169/168, 325/324, 385/384

Map: [<1 0 0 1 6 2|, <0 1 0 7 -6 4|, <0 0 1 -4 3 -2|]

EDOs: 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190f, 197ef, 243ef

Badness: 0.000840

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