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Horwell 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>
The '''horwell family''' of rank-3 temperaments tempers out the [[horwell comma]], 65625/65536 = {{monzo| -16 1 5 1 }}.
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-22 13:39:55 UTC</tt>.<br>
: The original revision id was <tt>247713017</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]]


== Horwell ==
[[Subgroup]]: 2.3.5.7


The horwell family of rank three temperaments tempers out the horwell comma, 65625/65536.
[[Comma list]]: 65625/65536


=Horwell=
{{Mapping|legend=1| 1 0 0 16 | 0 1 0 -1 | 0 0 1 -5 }}
Comma: 65625/65536


7-limit minimax
: mapping generators: ~2, ~3, ~5
[|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;]
Eigenmonzos: 2, 7/6, 6/5


9-limit minimax
[[Mapping to lattice]]: [{{val| 0 -1 1 -4 }}, {{val| 0 -1 0 -1 }}]
[|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;]
Eigenmonzos: 2, 9/7, 7/5


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


Map: [&lt;1 0 0 16|, &lt;0 1 0 -1|, &lt;0 0 1 -5|]
[[Minimax tuning]]:  
Generators: 2, 3, 5
* [[7-odd-limit]]
Edos: 9, 22, 25, 28, 31, 34, 40, 53, 56, 65, 75, 84, 87, 118, 140, 171, 824, 995
: {{monzo list| 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 }}
Badness: 0.000173
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5/3.7/3
* [[9-odd-limit]]
: {{monzo list| 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 }}
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.9/7
 
{{Optimal ET sequence|legend=1| 22, 31, 53, 84, 87, 118, 140, 171, 1592c, 1763c, 1934c, 2074c, 2105c, 2245cd, 2416cd, 2587cd, 2758cd, 2929cd, 3100cd, 3271ccd, 3442ccd, 3613ccd, 5034bcccdd, 5205bcccdd }}
 
[[Badness]]: 0.173 × 10<sup>-3</sup>


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


=Horwellic=
== Zelda ==
Commas: 3025/3024, 65625/65536
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 385/384, 3388/3375
 
{{Mapping|legend=1| 1 0 0 16 -9 | 0 1 0 -1 2 | 0 0 1 -5 4 }}
 
{{Optimal ET sequence|legend=1| 22, 31, 53, 84, 87, 118, 258e, 376de, 547de }}
 
[[Badness]]: 0.642 × 10<sup>-3</sup>
 
== Horwellic ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 3025/3024, 65625/65536
 
{{Mapping|legend=1| 1 0 0 16 10 | 0 1 0 -1 1 | 0 0 2 -10 -7 }}
 
{{Optimal ET sequence|legend=1| 31, 75e, 87, 118, 193, 224, 311, 342, 1592c, 1934ce, 2276cde, 2587cde, 2929cde, 3271ccde, 3613ccde, 5205bcccddee }}
 
[[Badness]]: 0.505 × 10<sup>-3</sup>


Map: [&lt;1 0 0 16 10|, &lt;0 1 0 -1 1|, &lt;0 0 2 -10 -7|]
[[Category:Temperament families]]
EDOs: 31, 87, 118, 193, 224, 311, 342
[[Category:Pages with mostly numerical content]]
Badness: 0.000505</pre></div>
[[Category:Horwell family| ]] <!-- main article -->
<h4>Original HTML content:</h4>
[[Category:Horwell| ]] <!-- key article -->
<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:4:&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:4 --&gt;&lt;!-- ws:start:WikiTextTocRule:5: --&gt;&lt;a href="#Horwell"&gt;Horwell&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:5 --&gt;&lt;!-- ws:start:WikiTextTocRule:6: --&gt; | &lt;a href="#Horwellic"&gt;Horwellic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:6 --&gt;&lt;!-- ws:start:WikiTextTocRule:7: --&gt;
[[Category:Rank 3]]
&lt;!-- ws:end:WikiTextTocRule:7 --&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;/body&gt;&lt;/html&gt;</pre></div>
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