Kleismic rank three family: Difference between revisions

Revision as of 22:44, 20 February 2012

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2012-02-20 22:44:05 UTC.

The original revision id was 303529768.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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[[toc|flat]]


These are the rank three temperaments tempering out the kleisma, 15625/15552. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.

7 and 9 limit minimax
[|1 0 0 0>, |0 1 0 0>, |1 5/6 0 0>, |0 0 0 1>]
[[Eigenmonzo|Eigenmonzos]]: 2, 7/6, 4/3

Map: [<1 0 1 0|, <0 6 5 0|, <0 0 0 1|]
[[Generator|Generators]]: 2, 6/5, 7
[[edo|Edos]]: [[15edo|15]], [[19edo|19]], [[23edo|23]], [[34edo|34]], [[53edo|53]], [[68edo|68]], [[72edo|72]], [[87edo|87]], [[121edo|121]], [[125edo|125]], [[140edo|140]], [[212edo|212]], 333, 405

=Enlil=
[[Comma|Commas]]: 385/384, 6250/6237

[[Minimax tuning]]
[|1 0 0 0 0>, |0 1 0 0 0>, |1 5/6 0 0 0>, 
|3 1/12 0 1/2 -1/2>, |3 1/12 0 -1/2 1/2>]
[[Eigenmonzo|Eigenmonzos]]: 2, 4/3, 14/11

Map: [<1 0 1 0 6|, <0 6 5 0 1|, <0 0 0 1 -1|]
[[Generator|Generators]]: 2, 6/5, 7
EDOs: 53, 68, 72, 140, 159, 212, 284
Badness: 0.000798

==13-limit==
[[Comma|Commas]]: 325/324, 385/384, 625/624

13 and 15 limit minimax tuning
[|1 0 0 0 0 0>, |4/3 0 0 -2/9 -2/9 4/9>, 
|19/9 0 0 -5/27 -5/27 10/27>, 
|28/9 0 0 13/27 -14/27 1/27>, 
|28/9 0 0 -14/27 13/27 1/27>, 
|28/9 0 0 -14/27 -14/27 28/27>]
[[Eigenmonzo|Eigenmonzos]]: 2, 13/11, 14/11

Map: [<1 0 1 0 6 0|, <0 6 5 0 1 14|, <0 0 0 1 -1 0|]
[[Generator|Generators]]: 2, 6/5, 7
[[edo|Edos]]: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[53edo|53]], [[57edo|57]], [[68edo|68]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[212edo|212]], [[284edo|284]], [[299edo|299]]
Badness: 0.000680

Scales: [[enlil19_13]]

=Enki=
[[Comma|Commas]]: 3025/3024, 4375/4356

[[Minimax tuning]]
[|1 0 0 0 0>, |-18/13 0 6/13 -6/13 12/13>, 
|-2/13 0 5/13 -5/13 10/13>, 
|-2/13 0 -8/13 8/13 10/13>, |0 0 0 0 1>]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/8, 7/5

Map: [<1 0 1 0 1|, <0 6 5 0 4|, <0 0 0 2 1|]
[[Generator|Generators]]: 2, 6/5, 66/25
[[edo|Edos]]: [[15edo|15]], [[49edo|49]], [[57edo|57]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[193edo|193]], [[231|231]], 265, 280, 337, 352, 439 
Badness: 0.00109

==13-limit==
[[Comma|Commas]]: 325/324, 364/363, 625/624

13 and 15 limit
[|1 0 0 0 0 0>, |2/3 0 -2/3 0 0 2/3>, 
|14/9 0 -5/9 0 0 5/9>, |0 0 0 1 0 0>, 
|13/9 0 -4/9 1/2 0 4/9>, 
|14/9 0 -14/9 0 0 14/9>]
[[Eigenmonzo|Eigenmonzos]]: 2, 8/7 13/10

Map: [<1 0 1 0 1 0|, <0 6 5 0 4 14|, <0 0 0 2 1 0|]
[[Generator|Generators]]: 2, 6/5, 66/25
[[edo|Edos]]: [[15edo|15]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[193edo|193]], 280, 439
Badness: 0.000874

=Isimud=
Commas: 4125/4096, 8019/8000

Map: [<1 0 1 0 9|, <0 6 5 0 -21|, <0 0 0 1 0|]
EDOs: 19, 53, 72, 197e, 269ce, 341ce, 375cde, 447cde, 519bcde
Badness: 0.003690

==13-limit==
Commas: 325/324, 625/624, 1287/1280

Map: [<1 0 1 0 9 0|, <0 6 5 0 -21 14|, <0 0 0 1 0 0|]
EDOs: 19, 53, 72, 178def, 197ef, 231ef, 250def, 303cdef
Badness: 0.002273

Original HTML content:

<html><head><title>Kleismic rank three family</title></head><body><!-- ws:start:WikiTextTocRule:12:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --><a href="#Enlil">Enlil</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --> | <a href="#Enki">Enki</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Isimud">Isimud</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: -->
<!-- ws:end:WikiTextTocRule:19 --><br />
<br />
These are the rank three temperaments tempering out the kleisma, 15625/15552. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.<br />
<br />
7 and 9 limit minimax<br />
[|1 0 0 0&gt;, |0 1 0 0&gt;, |1 5/6 0 0&gt;, |0 0 0 1&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/6, 4/3<br />
<br />
Map: [&lt;1 0 1 0|, &lt;0 6 5 0|, &lt;0 0 0 1|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 6/5, 7<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/23edo">23</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/121edo">121</a>, <a class="wiki_link" href="/125edo">125</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/212edo">212</a>, 333, 405<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Enlil"></a><!-- ws:end:WikiTextHeadingRule:0 -->Enlil</h1>
<a class="wiki_link" href="/Comma">Commas</a>: 385/384, 6250/6237<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br />
[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;, |1 5/6 0 0 0&gt;, <br />
|3 1/12 0 1/2 -1/2&gt;, |3 1/12 0 -1/2 1/2&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 4/3, 14/11<br />
<br />
Map: [&lt;1 0 1 0 6|, &lt;0 6 5 0 1|, &lt;0 0 0 1 -1|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 6/5, 7<br />
EDOs: 53, 68, 72, 140, 159, 212, 284<br />
Badness: 0.000798<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Enlil-13-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->13-limit</h2>
<a class="wiki_link" href="/Comma">Commas</a>: 325/324, 385/384, 625/624<br />
<br />
13 and 15 limit minimax tuning<br />
[|1 0 0 0 0 0&gt;, |4/3 0 0 -2/9 -2/9 4/9&gt;, <br />
|19/9 0 0 -5/27 -5/27 10/27&gt;, <br />
|28/9 0 0 13/27 -14/27 1/27&gt;, <br />
|28/9 0 0 -14/27 13/27 1/27&gt;, <br />
|28/9 0 0 -14/27 -14/27 28/27&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 13/11, 14/11<br />
<br />
Map: [&lt;1 0 1 0 6 0|, &lt;0 6 5 0 1 14|, &lt;0 0 0 1 -1 0|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 6/5, 7<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/57edo">57</a>, <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/212edo">212</a>, <a class="wiki_link" href="/284edo">284</a>, <a class="wiki_link" href="/299edo">299</a><br />
Badness: 0.000680<br />
<br />
Scales: <a class="wiki_link" href="/enlil19_13">enlil19_13</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Enki"></a><!-- ws:end:WikiTextHeadingRule:4 -->Enki</h1>
<a class="wiki_link" href="/Comma">Commas</a>: 3025/3024, 4375/4356<br />
<br />
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a><br />
[|1 0 0 0 0&gt;, |-18/13 0 6/13 -6/13 12/13&gt;, <br />
|-2/13 0 5/13 -5/13 10/13&gt;, <br />
|-2/13 0 -8/13 8/13 10/13&gt;, |0 0 0 0 1&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/8, 7/5<br />
<br />
Map: [&lt;1 0 1 0 1|, &lt;0 6 5 0 4|, &lt;0 0 0 2 1|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 6/5, 66/25<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/49edo">49</a>, <a class="wiki_link" href="/57edo">57</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/193edo">193</a>, <a class="wiki_link" href="/231">231</a>, 265, 280, 337, 352, 439 <br />
Badness: 0.00109<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Enki-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2>
<a class="wiki_link" href="/Comma">Commas</a>: 325/324, 364/363, 625/624<br />
<br />
13 and 15 limit<br />
[|1 0 0 0 0 0&gt;, |2/3 0 -2/3 0 0 2/3&gt;, <br />
|14/9 0 -5/9 0 0 5/9&gt;, |0 0 0 1 0 0&gt;, <br />
|13/9 0 -4/9 1/2 0 4/9&gt;, <br />
|14/9 0 -14/9 0 0 14/9&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 8/7 13/10<br />
<br />
Map: [&lt;1 0 1 0 1 0|, &lt;0 6 5 0 4 14|, &lt;0 0 0 2 1 0|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 6/5, 66/25<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/193edo">193</a>, 280, 439<br />
Badness: 0.000874<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Isimud"></a><!-- ws:end:WikiTextHeadingRule:8 -->Isimud</h1>
Commas: 4125/4096, 8019/8000<br />
<br />
Map: [&lt;1 0 1 0 9|, &lt;0 6 5 0 -21|, &lt;0 0 0 1 0|]<br />
EDOs: 19, 53, 72, 197e, 269ce, 341ce, 375cde, 447cde, 519bcde<br />
Badness: 0.003690<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Isimud-13-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->13-limit</h2>
Commas: 325/324, 625/624, 1287/1280<br />
<br />
Map: [&lt;1 0 1 0 9 0|, &lt;0 6 5 0 -21 14|, &lt;0 0 0 1 0 0|]<br />
EDOs: 19, 53, 72, 178def, 197ef, 231ef, 250def, 303cdef<br />
Badness: 0.002273</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2011-10-24 00:46:27 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-20 22:44:05 UTC</tt>.<br>
-: The original revision id was <tt>267788536</tt>.<br>
+: The original revision id was <tt>303529768</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>
@@ Line 77: / Line 77: @@
 [[Generator|Generators]]: 2, 6/5, 66/25
 [[edo|Edos]]: [[15edo|15]], [[72edo|72]], [[87edo|87]], [[159edo|159]], [[193edo|193]], 280, 439
-Badness: 0.000874</pre></div>
+Badness: 0.000874
+=Isimud=
+Commas: 4125/4096, 8019/8000
+Map: [&lt;1 0 1 0 9|, &lt;0 6 5 0 -21|, &lt;0 0 0 1 0|]
+EDOs: 19, 53, 72, 197e, 269ce, 341ce, 375cde, 447cde, 519bcde
+Badness: 0.003690
+==13-limit==
+Commas: 325/324, 625/624, 1287/1280
+Map: [&lt;1 0 1 0 9 0|, &lt;0 6 5 0 -21 14|, &lt;0 0 0 1 0 0|]
+EDOs: 19, 53, 72, 178def, 197ef, 231ef, 250def, 303cdef
+Badness: 0.002273
+</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;Kleismic rank three family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:8:&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:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt;&lt;a href="#Enlil"&gt;Enlil&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;!-- ws:start:WikiTextTocRule:11: --&gt; | &lt;a href="#Enki"&gt;Enki&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;
+<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;Kleismic rank three family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:12:&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:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;a href="#Enlil"&gt;Enlil&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt; | &lt;a href="#Enki"&gt;Enki&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt; | &lt;a href="#Isimud"&gt;Isimud&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 These are the rank three temperaments tempering out the kleisma, 15625/15552. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.&lt;br /&gt;
@@ Line 150: / Line 167: @@
 &lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 6/5, 66/25&lt;br /&gt;
 &lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/15edo"&gt;15&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="/159edo"&gt;159&lt;/a&gt;, &lt;a class="wiki_link" href="/193edo"&gt;193&lt;/a&gt;, 280, 439&lt;br /&gt;
-Badness: 0.000874&lt;/body&gt;&lt;/html&gt;</pre></div>
+Badness: 0.000874&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Isimud"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Isimud&lt;/h1&gt;
+Commas: 4125/4096, 8019/8000&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 0 1 0 9|, &amp;lt;0 6 5 0 -21|, &amp;lt;0 0 0 1 0|]&lt;br /&gt;
+EDOs: 19, 53, 72, 197e, 269ce, 341ce, 375cde, 447cde, 519bcde&lt;br /&gt;
+Badness: 0.003690&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="Isimud-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit&lt;/h2&gt;
+Commas: 325/324, 625/624, 1287/1280&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 0 1 0 9 0|, &amp;lt;0 6 5 0 -21 14|, &amp;lt;0 0 0 1 0 0|]&lt;br /&gt;
+EDOs: 19, 53, 72, 178def, 197ef, 231ef, 250def, 303cdef&lt;br /&gt;
+Badness: 0.002273&lt;/body&gt;&lt;/html&gt;</pre></div>

Kleismic rank three family: Difference between revisions

Revision as of 22:44, 20 February 2012

IMPORTED REVISION FROM WIKISPACES

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