Kleismic rank three family: Difference between revisions

Revision as of 00:35, 24 October 2011

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 2011-10-24 00:35:22 UTC.

The original revision id was 267786952.

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.

Original Wikitext content:

[[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]], 284, 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

Original HTML content:

<html><head><title>Kleismic rank three family</title></head><body><!-- ws:start:WikiTextTocRule:8:&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:8 --><!-- ws:start:WikiTextTocRule:9: --><a href="#Enlil">Enlil</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --><!-- ws:end:WikiTextTocRule:10 --><!-- ws:start:WikiTextTocRule:11: --> | <a href="#Enki">Enki</a><!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: -->
<!-- ws:end:WikiTextTocRule:13 --><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>, 284, 299<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</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>2011-01-03 22:09:50 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-24 00:35:22 UTC</tt>.<br>
-: The original revision id was <tt>190776398</tt>.<br>
+: The original revision id was <tt>267786952</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">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.
+<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]]
+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.
 and 9 limit minimax
@@ Line 16: / Line 19: @@
 [[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==
+=Enlil=
-[[Comma|Commas]]: 15625/15552, 385/384
+[[Comma|Commas]]: 385/384, 6250/6237
 [[Minimax tuning]]
@@ Line 29: / Line 32: @@
 Badness: 0.000798
-===13-limit===
+==13-limit==
 [[Comma|Commas]]: 325/324, 385/384, 625/624
@@ Line 47: / Line 50: @@
 Scales: [[enlil19_13]]
-==Enki==
+=Enki=
 [[Comma|Commas]]: 3025/3024, 4375/4356
@@ Line 61: / Line 64: @@
 Badness: 0.00109
-===13-limit===
+==13-limit==
 [[Comma|Commas]]: 325/324, 364/363, 625/624
@@ Line 76: / Line 79: @@
 Badness: 0.000874</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;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;
+<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;
+&lt;!-- ws:end:WikiTextTocRule:13 --&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;
 &lt;br /&gt;
 and 9 limit minimax&lt;br /&gt;
@@ Line 86: / Line 92: @@
 &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="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/23edo"&gt;23&lt;/a&gt;, &lt;a class="wiki_link" href="/34edo"&gt;34&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/68edo"&gt;68&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="/121edo"&gt;121&lt;/a&gt;, &lt;a class="wiki_link" href="/125edo"&gt;125&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140&lt;/a&gt;, &lt;a class="wiki_link" href="/212edo"&gt;212&lt;/a&gt;, 333, 405&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Enlil"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Enlil&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Enlil"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Enlil&lt;/h1&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 15625/15552, 385/384&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 385/384, 6250/6237&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/Minimax%20tuning"&gt;Minimax tuning&lt;/a&gt;&lt;br /&gt;
@@ Line 99: / Line 105: @@
 Badness: 0.000798&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Enlil-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;13-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Enlil-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;13-limit&lt;/h2&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 325/324, 385/384, 625/624&lt;br /&gt;
 &lt;br /&gt;
@@ Line 117: / Line 123: @@
 Scales: &lt;a class="wiki_link" href="/enlil19_13"&gt;enlil19_13&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Enki"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Enki&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Enki"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Enki&lt;/h1&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 3025/3024, 4375/4356&lt;br /&gt;
 &lt;br /&gt;
@@ Line 131: / Line 137: @@
 Badness: 0.00109&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Enki-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Enki-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 325/324, 364/363, 625/624&lt;br /&gt;
 &lt;br /&gt;

Kleismic rank three family: Difference between revisions

Revision as of 00:35, 24 October 2011

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