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Keenanismic 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 '''keenanismic family''' of [[Catalog of rank-4 temperaments|rank-4]] temperaments [[Tempering out|tempers out]] the [[keenanisma]], the 11-limit comma 385/384 = {{monzo| -7 -1 1 1 1 }} of 4.503 [[cent]]s.
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-09-09 02:59:33 UTC</tt>.<br>
: The original revision id was <tt>252244616</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 keenanismic family of rank four temperaments tempers out the [[385_384|keenanisma]], the 11-limit comma 385/384 = |-7 -1 1 1 1&gt; of 4.503 cents.


=Keenanismic=  
== Keenanismic ==
Comma: 385/384
[[Subgroup]]: 2.3.5.7.11


Minimax tuning
[[Comma list]]: 385/384
[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;, |7/3 1/3 2/3 -1/3 -1/3&gt;,
|7/3 1/3 -1/3 2/3 -1/3&gt;, |7/3 1/3 -1/3 -1/3 2/3&gt;]
Eigenmonzos: 2, 3, 7/5, 11/5


Map: [&lt;1 0 0 0 7|, &lt;0 1 0 0 1|, &lt;0 0 1 0 -1|, &lt;0 0 0 1 -1|]
{{Mapping|legend=1| 1 0 0 0 7 | 0 1 0 0 1 | 0 0 1 0 -1 | 0 0 0 1 -1 }}
Transpose: [2 3 5 7 385/35]
EDOs: [[19edo|19]], [[22edo|22]], [[31edo|31]], [[41edo|41]], [[53edo|53]], [[68edo|53]], [[72edo|72]], [[118edo|118]], [[159edo|159]], [[190edo|190]], [[212edo|212]] and [[284edo|284]]
10^9*Badness: 15.159


=Martwin=
: mapping generators: ~2, ~3, ~5, ~7
Commas: 385/384, 325/324


Minimax tuning
[[Transpose]]: [2 3 5 7 385/35]
||1 0 0 0 0 0&gt;, |0 1 0 0 0 0&gt;, |2/3 4/3 1/3 0 0 -1/3&gt;,
|17/3 -5/3 1/3 0 -1 2/3&gt;, |2/3 4/3 -2/3 0 1 -1/3&gt;, |2/3 4/3 -2/3 0 0 2/3&gt;]
Eigenmonzos: 2, 3, 11/5, 13/5


Map: [&lt;1 0 0 0 7 2|, &lt;0 1 0 0 1 4|, &lt;0 0 1 0 -1 -2|, &lt;0 0 0 1 -1 0|]
[[Minimax tuning]]:
Transpose: [2 3 5 7 385/35 324/25]
* [[11-odd-limit]]
EDOs: [[7edo|7]], [[15edo|15]], [[19edo|19]], [[26edo|26]], [[34edo|34]], [[41edo|41]], [[46edo|46]], [[53edo|53]], [[72edo|72]], [[87edo|87]], [[140edo|140]], [[159edo|159]], [[212edo|212]] and[[299edo|299]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 7/3 1/3 2/3 -1/3 -1/3 }}, {{monzo| 7/3 1/3 -1/3 2/3 -1/3 }}, {{monzo| 7/3 1/3 -1/3 -1/3 2/3 }}]
10^6*Badness: 2.206
: [[Eigenmonzo basis|Unchanged-interval (eigenmonzo) basis]]: 2.3.7/5.11/5


=Ancient=
{{Optimal ET sequence|legend=1| 9, 10, 12e, 15, 19, 22, 31, 41, 53, 68, 72, 118, 159, 190, 212, 284, 330e, 402de }}
Commas: 385/384, 625/624


Map: [&lt;1 0 0 0 7 -4|, &lt;0 1 0 0 1 -1|, &lt;0 0 1 0 -1 4|, &lt;0 0 0 1 -1 0|]
[[Badness]]: 15.2 × 10<sup>-9</sup>
Transpose: [2 3 5 7 385/35 625/48]
 
EDOs: [[6edo|6]], [[15edo|15]], [[19edo|19]], [[22edo|22]], [31edo|31]], [[50edo|50]], [[53edo|53]], [[72edo|72]], [[87edo|87]], [[103edo|103]], [[140edo|140]], [[159edo|159]], [[190edo|190]]
== Martwin ==
10^6*Badness: 2.573</pre></div>
[[Subgroup]]: 2.3.5.7.11.13
<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;Keenanismic 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="#Keenanismic"&gt;Keenanismic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;!-- ws:start:WikiTextTocRule:8: --&gt; | &lt;a href="#Martwin"&gt;Martwin&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt; | &lt;a href="#Ancient"&gt;Ancient&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;
[[Comma list]]: 325/324, 385/384
&lt;!-- ws:end:WikiTextTocRule:10 --&gt;The keenanismic family of rank four temperaments tempers out the &lt;a class="wiki_link" href="/385_384"&gt;keenanisma&lt;/a&gt;, the 11-limit comma 385/384 = |-7 -1 1 1 1&amp;gt; of 4.503 cents.&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 0 0 0 7 2 | 0 1 0 0 1 4 | 0 0 1 0 -1 -2 | 0 0 0 1 -1 0 }}
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Keenanismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Keenanismic&lt;/h1&gt;
 
Comma: 385/384&lt;br /&gt;
[[Transpose]]: [2 3 5 7 385/35 324/25]
&lt;br /&gt;
 
Minimax tuning&lt;br /&gt;
[[Minimax tuning]]: {{confirm}} <!-- contradiction with the data in Rank-4 temperament -->
[|1 0 0 0 0&amp;gt;, |0 1 0 0 0&amp;gt;, |7/3 1/3 2/3 -1/3 -1/3&amp;gt;,&lt;br /&gt;
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 0 1 0 0 0 0 }}, {{monzo| 2/3 4/3 1/3 0 0 -1/3 }}, {{monzo| 17/3 -5/3 1/3 0 -1 2/3 }}, {{monzo| 2/3 4/3 -2/3 0 1 -1/3 }}, {{monzo| 2/3 4/3 -2/3 0 0 2/3 }}]
|7/3 1/3 -1/3 2/3 -1/3&amp;gt;, |7/3 1/3 -1/3 -1/3 2/3&amp;gt;]&lt;br /&gt;
: [[Eigenmonzo basis|Unchanged-interval (eigenmonzo) basis]]: 2.3.11/5.13/5
Eigenmonzos: 2, 3, 7/5, 11/5&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 12e, 15, 19, 22f, 26, 31f, 41, 46, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 465cef, 677cdeeff, 764cdeeff }}
Map: [&amp;lt;1 0 0 0 7|, &amp;lt;0 1 0 0 1|, &amp;lt;0 0 1 0 -1|, &amp;lt;0 0 0 1 -1|]&lt;br /&gt;
 
Transpose: [2 3 5 7 385/35]&lt;br /&gt;
[[Badness]]: 2.21 × 10<sup>-6</sup>
EDOs: &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/68edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/118edo"&gt;118&lt;/a&gt;, &lt;a class="wiki_link" href="/159edo"&gt;159&lt;/a&gt;, &lt;a class="wiki_link" href="/190edo"&gt;190&lt;/a&gt;, &lt;a class="wiki_link" href="/212edo"&gt;212&lt;/a&gt; and &lt;a class="wiki_link" href="/284edo"&gt;284&lt;/a&gt;&lt;br /&gt;
 
10^9*Badness: 15.159&lt;br /&gt;
== Ancient ==
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7.11.13
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Martwin"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Martwin&lt;/h1&gt;
 
Commas: 385/384, 325/324&lt;br /&gt;
[[Comma list]]: 385/384, 625/624
&lt;br /&gt;
 
Minimax tuning&lt;br /&gt;
{{Mapping|legend=1| 1 0 0 0 7 -4 | 0 1 0 0 1 -1 | 0 0 1 0 -1 4 | 0 0 0 1 -1 0 }}
||1 0 0 0 0 0&amp;gt;, |0 1 0 0 0 0&amp;gt;, |2/3 4/3 1/3 0 0 -1/3&amp;gt;,&lt;br /&gt;
 
|17/3 -5/3 1/3 0 -1 2/3&amp;gt;, |2/3 4/3 -2/3 0 1 -1/3&amp;gt;, |2/3 4/3 -2/3 0 0 2/3&amp;gt;]&lt;br /&gt;
[[Transpose]]: [2 3 5 7 385/35 625/48]
Eigenmonzos: 2, 3, 11/5, 13/5&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 15, 19, 22, 31, 50, 53, 72, 87, 103, 140, 159, 190, 243e, 315ef, 330e, 402def }}
Map: [&amp;lt;1 0 0 0 7 2|, &amp;lt;0 1 0 0 1 4|, &amp;lt;0 0 1 0 -1 -2|, &amp;lt;0 0 0 1 -1 0|]&lt;br /&gt;
 
Transpose: [2 3 5 7 385/35 324/25]&lt;br /&gt;
[[Badness]]: 2.57 × 10<sup>-6</sup>
EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/26edo"&gt;26&lt;/a&gt;, &lt;a class="wiki_link" href="/34edo"&gt;34&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;, &lt;a class="wiki_link" href="/46edo"&gt;46&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140&lt;/a&gt;, &lt;a class="wiki_link" href="/159edo"&gt;159&lt;/a&gt;, &lt;a class="wiki_link" href="/212edo"&gt;212&lt;/a&gt; and&lt;a class="wiki_link" href="/299edo"&gt;299&lt;/a&gt;&lt;br /&gt;
 
10^6*Badness: 2.206&lt;br /&gt;
== Zaxa ==
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7.11.13
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Ancient"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Ancient&lt;/h1&gt;
 
Commas: 385/384, 625/624&lt;br /&gt;
[[Comma list]]: 352/351, 385/384
&lt;br /&gt;
 
Map: [&amp;lt;1 0 0 0 7 -4|, &amp;lt;0 1 0 0 1 -1|, &amp;lt;0 0 1 0 -1 4|, &amp;lt;0 0 0 1 -1 0|]&lt;br /&gt;
{{Mapping|legend=1| 1 0 0 0 7 12 |0 1 0 0 1 -2 | 0 0 1 0 -1 -1 | 0 0 0 1 -1 -1 }}
Transpose: [2 3 5 7 385/35 625/48]&lt;br /&gt;
 
EDOs: &lt;a class="wiki_link" href="/6edo"&gt;6&lt;/a&gt;, &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, [31edo|31]], &lt;a class="wiki_link" href="/50edo"&gt;50&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/103edo"&gt;103&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140&lt;/a&gt;, &lt;a class="wiki_link" href="/159edo"&gt;159&lt;/a&gt;, &lt;a class="wiki_link" href="/190edo"&gt;190&lt;/a&gt;&lt;br /&gt;
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.657, ~5/4 = 385.632, ~7/4 = 967.829
10^6*Badness: 2.573&lt;/body&gt;&lt;/html&gt;</pre></div>
 
{{Optimal ET sequence|legend=1| 7, 10, 15f, 17, 19f, 22, 31, 41, 46, 53, 77, 87, 118, 140, 258e, 461e }}
 
[[Badness]]: 3.35 × 10<sup>-6</sup>
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Keenanismic family| ]] <!-- main article -->
[[Category:Keenanismic| ]] <!-- key article -->
[[Category:Rank 4]]
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