Keenanismic family: Difference between revisions

Line 1:

~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

__FORCETOC__

~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~

The keenanismic family of rank four temperaments tempers out the [[385/384|keenanisma]], the 11-limit comma 385/384 = |-7 -1 1 1 1> of 4.503 cents.

~~: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-01-21 13:23:17 UTC</tt>.<br>~~

~~: The original revision id was <tt>400169386</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> of 4.503 cents.

=Keenanismic=

Comma: 385/384

Minimax tuning

[|1 0 0 0 0>, |0 1 0 0 0>, |7/3 1/3 2/3 -1/3 -1/3>,

|7/3 1/3 -1/3 2/3 -1/3>, |7/3 1/3 -1/3 -1/3 2/3>]

Eigenmonzos: 2, 3, 7/5, 11/5

Map: [<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=

Commas: 385/384, 325/324

Line 28:

Line 26:

||1 0 0 0 0 0>, |0 1 0 0 0 0>, |2/3 4/3 1/3 0 0 -1/3>,

|17/3 -5/3 1/3 0 -1 2/3>, |2/3 4/3 -2/3 0 1 -1/3>, |2/3 4/3 -2/3 0 0 2/3>]

Eigenmonzos: 2, 3, 11/5, 13/5

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

Transpose: [2 3 5 7 385/35 324/25]

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]]

10^6*Badness: 2.206

=Ancient=

Commas: 385/384, 625/624

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

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]]

~~10^6*Badness: 2.573</pre></div>~~

~~<h4>Original HTML content:</h4>~~

10^6*Badness: 2.573

<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"><html><head><title>Keenanismic family</title></head><body><a href="#Keenanismic">Keenanismic</a> | <a href="#Martwin">Martwin</a> | <a href="#Ancient">Ancient</a>

The keenanismic family of rank four temperaments tempers out the <a class="wiki_link" href="/385_384">keenanisma</a>, the 11-limit comma 385/384 = |-7 -1 1 1 1&gt; of 4.503 cents.<br />

~~<br />~~

~~<h1 id="toc0"><a name="Keenanismic"></a>Keenanismic</h1>~~

~~Comma: 385/384<br />~~

~~<br />~~

~~Minimax tuning<br />~~

~~[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;, |7/3 1/3 2/3 -1/3 -1/3&gt;,<br />~~

~~|7/3 1/3 -1/3 2/3 -1/3&gt;, |7/3 1/3 -1/3 -1/3 2/3&gt;]<br />~~

~~Eigenmonzos: 2, 3, 7/5, 11/5<br />~~

~~<br />~~

~~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|]<br />~~

~~Transpose: [2 3 5 7 385/35]<br />~~

EDOs: <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/41edo">41</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/68edo">53</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/118edo">118</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/190edo">190</a>, <a class="wiki_link" href="/212edo">212</a> and <a class="wiki_link" href="/284edo">284</a><br />

~~10^9*Badness: 15.159<br />~~

~~<br />~~

~~<h1 id="toc1"><a name="Martwin"></a>Martwin</h1>~~

~~Commas: 385/384, 325/324<br />~~

~~<br />~~

~~Minimax tuning<br />~~

~~||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;,<br />~~

~~|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;]<br />~~

~~Eigenmonzos: 2, 3, 11/5, 13/5<br />~~

~~<br />~~

~~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|]<br />~~

~~Transpose: [2 3 5 7 385/35 324/25]<br />~~

EDOs: <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/26edo">26</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/41edo">41</a>, <a class="wiki_link" href="/46edo">46</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/212edo">212</a> and<a class="wiki_link" href="/299edo">299</a><br />

~~10^6*Badness: 2.206<br />~~

~~<br />~~

~~<h1 id="toc2"><a name="Ancient"></a>Ancient</h1>~~

~~Commas: 385/384, 625/624<br />~~

~~<br />~~

~~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|]<br />~~

~~Transpose: [2 3 5 7 385/35 625/48]<br />~~

EDOs: <a class="wiki_link" href="/6edo">6</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/50edo">50</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/103edo">103</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/190edo">190</a><br />

10^6*Badness: 2.573~~</body></html></pre></div>~~

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+__FORCETOC__
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+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.
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-01-21 13:23:17 UTC</tt>.<br>
-: The original revision id was <tt>400169386</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=
 Comma: 385/384
 Minimax tuning
 [|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|]
 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]]
 ^9*Badness: 15.159
 =Martwin=
 Commas: 385/384, 325/324
@@ Line 28: / Line 26: @@
 ||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|]
 Transpose: [2 3 5 7 385/35 324/25]
 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]]
 ^6*Badness: 2.206
 =Ancient=
 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|]
 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]]
-^6*Badness: 2.573</pre></div>
-<h4>Original HTML content:</h4>
+^6*Badness: 2.573
-<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;
-&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;
-&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;
-&lt;br /&gt;
-Minimax tuning&lt;br /&gt;
-[|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;
-|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;
-Eigenmonzos: 2, 3, 7/5, 11/5&lt;br /&gt;
-&lt;br /&gt;
-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;
-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;
-^9*Badness: 15.159&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="Martwin"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Martwin&lt;/h1&gt;
- Commas: 385/384, 325/324&lt;br /&gt;
-&lt;br /&gt;
-Minimax tuning&lt;br /&gt;
-||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;
-Eigenmonzos: 2, 3, 11/5, 13/5&lt;br /&gt;
-&lt;br /&gt;
-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;
-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;
-^6*Badness: 2.206&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="Ancient"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Ancient&lt;/h1&gt;
- Commas: 385/384, 625/624&lt;br /&gt;
-&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;
-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;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &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;
-^6*Badness: 2.573&lt;/body&gt;&lt;/html&gt;</pre></div>