Horwell 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>2011-12-14 21:28:08 UTC</tt>.<br>
: The original revision id was <tt>286250996</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|flat]]
 
 
The horwell family of rank three temperaments tempers out the horwell comma, 65625/65536.
The horwell family of rank three temperaments tempers out the horwell comma, 65625/65536.


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7-limit minimax
7-limit minimax
[|1 0 0 0&gt;, |16/7 6/7 -5/7 -1/7&gt;,  
[|1 0 0 0&gt;, |16/7 6/7 -5/7 -1/7&gt;,  
|16/7 -1/7 2/7 -1/7&gt;, |16/7 -1/7 -5/7 6/7&gt;]
|16/7 -1/7 2/7 -1/7&gt;, |16/7 -1/7 -5/7 6/7&gt;]
Eigenmonzos: 2, 7/6, 6/5
Eigenmonzos: 2, 7/6, 6/5


9-limit minimax
9-limit minimax
[|1 0 0 0&gt;, |16/13 12/13 -5/13 -1/13&gt;,  
[|1 0 0 0&gt;, |16/13 12/13 -5/13 -1/13&gt;,  
|32/13 -2/13 3/13 -2/13&gt;, |32/13 -2/13 -10/13 11/13&gt;]
|32/13 -2/13 3/13 -2/13&gt;, |32/13 -2/13 -10/13 11/13&gt;]
Eigenmonzos: 2, 9/7, 7/5
Eigenmonzos: 2, 9/7, 7/5


Lattice basis: 5/4 length=0.6213 16/15 length=1.3863
Lattice basis: 5/4 length=0.6213 16/15 length=1.3863
Angle(5/4, 16/15) = 64.6379
Angle(5/4, 16/15) = 64.6379
Map to lattice: [&lt;0 -1 1 -4|, &lt;0 -1 0 -1|]
Map to lattice: [&lt;0 -1 1 -4|, &lt;0 -1 0 -1|]


Map: [&lt;1 0 0 16|, &lt;0 1 0 -1|, &lt;0 0 1 -5|]
Map: [&lt;1 0 0 16|, &lt;0 1 0 -1|, &lt;0 0 1 -5|]
Generators: 2, 3, 5
Generators: 2, 3, 5
Edos: 9, 22, 25, 28, 31, 34, 40, 53, 56, 65, 75, 84, 87, 118, 140, 171, 824, 995
Edos: 9, 22, 25, 28, 31, 34, 40, 53, 56, 65, 75, 84, 87, 118, 140, 171, 824, 995
Badness: 0.000173
Badness: 0.000173


[[Projection pair]]: 7 65536/9375
[[Projection_pair|Projection pair]]: 7 65536/9375


=Horwellic=
=Horwellic=
Line 39: Line 39:


Map: [&lt;1 0 0 16 10|, &lt;0 1 0 -1 1|, &lt;0 0 2 -10 -7|]
Map: [&lt;1 0 0 16 10|, &lt;0 1 0 -1 1|, &lt;0 0 2 -10 -7|]
EDOs: 31, 87, 118, 193, 224, 311, 342
EDOs: 31, 87, 118, 193, 224, 311, 342
Badness: 0.000505
Badness: 0.000505


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Map: [&lt;1 0 0 16 -9|, &lt;0 1 0 -1 2|, &lt;0 0 1 -5 4|]
Map: [&lt;1 0 0 16 -9|, &lt;0 1 0 -1 2|, &lt;0 0 1 -5 4|]
EDOs: 22, 31, 53, 84, 87, 118, 258e, 376de, 547de, 665dee
EDOs: 22, 31, 53, 84, 87, 118, 258e, 376de, 547de, 665dee
Badness: 0.000642</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.000642
<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;Horwell family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:6:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:6 --&gt;&lt;!-- ws:start:WikiTextTocRule:7: --&gt;&lt;a href="#Horwell"&gt;Horwell&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;!-- ws:start:WikiTextTocRule:8: --&gt; | &lt;a href="#Horwellic"&gt;Horwellic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt; | &lt;a href="#Zelda"&gt;Zelda&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;
&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;br /&gt;
&lt;br /&gt;
The horwell family of rank three temperaments tempers out the horwell comma, 65625/65536.&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="Horwell"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Horwell&lt;/h1&gt;
Comma: 65625/65536&lt;br /&gt;
&lt;br /&gt;
7-limit minimax&lt;br /&gt;
[|1 0 0 0&amp;gt;, |16/7 6/7 -5/7 -1/7&amp;gt;, &lt;br /&gt;
|16/7 -1/7 2/7 -1/7&amp;gt;, |16/7 -1/7 -5/7 6/7&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 7/6, 6/5&lt;br /&gt;
&lt;br /&gt;
9-limit minimax&lt;br /&gt;
[|1 0 0 0&amp;gt;, |16/13 12/13 -5/13 -1/13&amp;gt;, &lt;br /&gt;
|32/13 -2/13 3/13 -2/13&amp;gt;, |32/13 -2/13 -10/13 11/13&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 9/7, 7/5&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 5/4 length=0.6213 16/15 length=1.3863&lt;br /&gt;
Angle(5/4, 16/15) = 64.6379&lt;br /&gt;
Map to lattice: [&amp;lt;0 -1 1 -4|, &amp;lt;0 -1 0 -1|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 16|, &amp;lt;0 1 0 -1|, &amp;lt;0 0 1 -5|]&lt;br /&gt;
Generators: 2, 3, 5&lt;br /&gt;
Edos: 9, 22, 25, 28, 31, 34, 40, 53, 56, 65, 75, 84, 87, 118, 140, 171, 824, 995&lt;br /&gt;
Badness: 0.000173&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;: 7 65536/9375&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="Horwellic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Horwellic&lt;/h1&gt;
Commas: 3025/3024, 65625/65536&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 16 10|, &amp;lt;0 1 0 -1 1|, &amp;lt;0 0 2 -10 -7|]&lt;br /&gt;
EDOs: 31, 87, 118, 193, 224, 311, 342&lt;br /&gt;
Badness: 0.000505&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="Zelda"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Zelda&lt;/h1&gt;
Commas: 385/384, 3388/3375&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 16 -9|, &amp;lt;0 1 0 -1 2|, &amp;lt;0 0 1 -5 4|]&lt;br /&gt;
EDOs: 22, 31, 53, 84, 87, 118, 258e, 376de, 547de, 665dee&lt;br /&gt;
Badness: 0.000642&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

The horwell family of rank three temperaments tempers out the horwell comma, 65625/65536.

Horwell

Comma: 65625/65536

7-limit minimax

[|1 0 0 0>, |16/7 6/7 -5/7 -1/7>, |16/7 -1/7 2/7 -1/7>, |16/7 -1/7 -5/7 6/7>]

Eigenmonzos: 2, 7/6, 6/5

9-limit minimax

[|1 0 0 0>, |16/13 12/13 -5/13 -1/13>, |32/13 -2/13 3/13 -2/13>, |32/13 -2/13 -10/13 11/13>]

Eigenmonzos: 2, 9/7, 7/5

Lattice basis: 5/4 length=0.6213 16/15 length=1.3863

Angle(5/4, 16/15) = 64.6379

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

Map: [<1 0 0 16|, <0 1 0 -1|, <0 0 1 -5|]

Generators: 2, 3, 5

Edos: 9, 22, 25, 28, 31, 34, 40, 53, 56, 65, 75, 84, 87, 118, 140, 171, 824, 995

Badness: 0.000173

Projection pair: 7 65536/9375

Horwellic

Commas: 3025/3024, 65625/65536

Map: [<1 0 0 16 10|, <0 1 0 -1 1|, <0 0 2 -10 -7|]

EDOs: 31, 87, 118, 193, 224, 311, 342

Badness: 0.000505

Zelda

Commas: 385/384, 3388/3375

Map: [<1 0 0 16 -9|, <0 1 0 -1 2|, <0 0 1 -5 4|]

EDOs: 22, 31, 53, 84, 87, 118, 258e, 376de, 547de, 665dee

Badness: 0.000642

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