Diaschismic rank three family: Difference between revisions

Revision as of 23:58, 31 December 2010

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These are the rank three temperaments tempering out the diaschisma, 2048/2025. 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.

==Julius==
Commas: 176/175, 896/891

Minimax tuning
[|1 0 0 0 0>, |11/8 1/2 -1/4 0 0>, |11/4 -1 1/2 0 0>, 
|-1/8 3/2 -5/4 0 1>, |11/8 -1/2 -1/4 0 1>]
Eigenmonzos: 2, 12/11, 10/9

Lattice basis: 3/2, 9/7
Map to lattice: [<0 1 -2 2 -2|, <0 0 0 -1 -1|]
Angle(3/2, 9/7) = 82.289 degrees

Map: [<2 0 11 0 14|, <0 1 -2 0 -4|, <0 0 0 1 1 |]
EDOs: 58, 68, 80, 126

Julius[22] [[Hobbits|hobbit]] [[transversal]]:
28/27, 16/15, 11/10, 9/8, 32/27, 6/5, 5/4, 9/7, 4/3, 15/11, 45/32, 22/15, 3/2, 14/9, 8/5, 5/3, 27/16, 16/9, 20/11, 15/8, 27/14, 2
Julius[24] hobbit transversal
28/27, 16/15, 11/10, 9/8, 7/6, 6/5, 40/33, 5/4, 9/7, 4/3, 15/11, 45/32, 16/11, 3/2, 14/9, 8/5, 33/20, 27/16, 7/4, 16/9, 20/11, 15/8, 27/14, 2

===13-limit===
Commas: 176/175, 325/324, 896/891

Map: [<2 0 11 0 14 -18|, <0 1 -2 0 -4 8|, <0 0 0 1 1 0|]
EDOs: 12, 46, 68, 80

==Augustus==
Commas: 385/384, 1232/1215

Minimax tuning
[|1 0 0 0 0>, |11/8 1/2 -1/4 0 0>, |11/4 -1 1/2 0 0>, 
|45/16 3/4 -3/8 1/2 -1/2>, |45/16 3/4 -3/8 -1/2 1/2>]
Eigenmonzos: 2, 10/9, 14/11

Map: [<2 0 11 0 3|, <0 1 -2 0 3|, <0 0 0 1 -1|]
EDOs: 46, 68, 114, 124

==Tiberius==
Commas: 2048/2025, 441/440

Minimax tuning
[|1 0 0 0 0>, |11/8 1/2 -1/4 0 0>, |11/4 -1 1/2 0 0>, 
|0 0 0 1 0>, |-3 2 -1 2 0>]
Eigenmonzos: 2, 9/5, 7

Map: [<2 0 11 0 -17|, <0 1 -2 0 4|, <0 0 0 1 2|]
EDOs: 58, 148, 160

==Claudius==
Commas: 2048/2025, 540/539

Minimax tuning
[|1 0 0 0 0>, |9/7 0 -3/7 2/7 1/7>, |41/14 0 6/7 -4/7 -2/7>,
|41/14 0 -1/7 3/7 -2/7>, |41/14 0 -1/7 -4/7 5/7>]
Eigenmonzos: 2, 7/5, 11/5

Map: [<2 0 11 0 15|, <0 1 -2 0 1|, <0 0 0 1 -2|]
EDOs: 58, 80

Original HTML content:

<html><head><title>Diaschismic rank three family</title></head><body>These are the rank three temperaments tempering out the diaschisma, 2048/2025. 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 />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Julius"></a><!-- ws:end:WikiTextHeadingRule:0 -->Julius</h2>
Commas: 176/175, 896/891<br />
<br />
Minimax tuning<br />
[|1 0 0 0 0&gt;, |11/8 1/2 -1/4 0 0&gt;, |11/4 -1 1/2 0 0&gt;, <br />
|-1/8 3/2 -5/4 0 1&gt;, |11/8 -1/2 -1/4 0 1&gt;]<br />
Eigenmonzos: 2, 12/11, 10/9<br />
<br />
Lattice basis: 3/2, 9/7<br />
Map to lattice: [&lt;0 1 -2 2 -2|, &lt;0 0 0 -1 -1|]<br />
Angle(3/2, 9/7) = 82.289 degrees<br />
<br />
Map: [&lt;2 0 11 0 14|, &lt;0 1 -2 0 -4|, &lt;0 0 0 1 1 |]<br />
EDOs: 58, 68, 80, 126<br />
<br />
Julius[22] <a class="wiki_link" href="/Hobbits">hobbit</a> <a class="wiki_link" href="/transversal">transversal</a>:<br />
28/27, 16/15, 11/10, 9/8, 32/27, 6/5, 5/4, 9/7, 4/3, 15/11, 45/32, 22/15, 3/2, 14/9, 8/5, 5/3, 27/16, 16/9, 20/11, 15/8, 27/14, 2<br />
Julius[24] hobbit transversal<br />
28/27, 16/15, 11/10, 9/8, 7/6, 6/5, 40/33, 5/4, 9/7, 4/3, 15/11, 45/32, 16/11, 3/2, 14/9, 8/5, 33/20, 27/16, 7/4, 16/9, 20/11, 15/8, 27/14, 2<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-Julius-13-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->13-limit</h3>
Commas: 176/175, 325/324, 896/891<br />
<br />
Map: [&lt;2 0 11 0 14 -18|, &lt;0 1 -2 0 -4 8|, &lt;0 0 0 1 1 0|]<br />
EDOs: 12, 46, 68, 80<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Augustus"></a><!-- ws:end:WikiTextHeadingRule:4 -->Augustus</h2>
Commas: 385/384, 1232/1215<br />
<br />
Minimax tuning<br />
[|1 0 0 0 0&gt;, |11/8 1/2 -1/4 0 0&gt;, |11/4 -1 1/2 0 0&gt;, <br />
|45/16 3/4 -3/8 1/2 -1/2&gt;, |45/16 3/4 -3/8 -1/2 1/2&gt;]<br />
Eigenmonzos: 2, 10/9, 14/11<br />
<br />
Map: [&lt;2 0 11 0 3|, &lt;0 1 -2 0 3|, &lt;0 0 0 1 -1|]<br />
EDOs: 46, 68, 114, 124<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Tiberius"></a><!-- ws:end:WikiTextHeadingRule:6 -->Tiberius</h2>
Commas: 2048/2025, 441/440<br />
<br />
Minimax tuning<br />
[|1 0 0 0 0&gt;, |11/8 1/2 -1/4 0 0&gt;, |11/4 -1 1/2 0 0&gt;, <br />
|0 0 0 1 0&gt;, |-3 2 -1 2 0&gt;]<br />
Eigenmonzos: 2, 9/5, 7<br />
<br />
Map: [&lt;2 0 11 0 -17|, &lt;0 1 -2 0 4|, &lt;0 0 0 1 2|]<br />
EDOs: 58, 148, 160<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x-Claudius"></a><!-- ws:end:WikiTextHeadingRule:8 -->Claudius</h2>
Commas: 2048/2025, 540/539<br />
<br />
Minimax tuning<br />
[|1 0 0 0 0&gt;, |9/7 0 -3/7 2/7 1/7&gt;, |41/14 0 6/7 -4/7 -2/7&gt;,<br />
|41/14 0 -1/7 3/7 -2/7&gt;, |41/14 0 -1/7 -4/7 5/7&gt;]<br />
Eigenmonzos: 2, 7/5, 11/5<br />
<br />
Map: [&lt;2 0 11 0 15|, &lt;0 1 -2 0 1|, &lt;0 0 0 1 -2|]<br />
EDOs: 58, 80</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>2010-12-12 17:00:17 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-31 23:58:47 UTC</tt>.<br>
-: The original revision id was <tt>187536311</tt>.<br>
+: The original revision id was <tt>190387702</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 27: / Line 27: @@
 Julius[24] hobbit transversal
 /27, 16/15, 11/10, 9/8, 7/6, 6/5, 40/33, 5/4, 9/7, 4/3, 15/11, 45/32, 16/11, 3/2, 14/9, 8/5, 33/20, 27/16, 7/4, 16/9, 20/11, 15/8, 27/14, 2
+===13-limit===
+Commas: 176/175, 325/324, 896/891
+Map: [&lt;2 0 11 0 14 -18|, &lt;0 1 -2 0 -4 8|, &lt;0 0 0 1 1 0|]
+EDOs: 12, 46, 68, 80
 ==Augustus==
@@ Line 83: / Line 89: @@
 /27, 16/15, 11/10, 9/8, 7/6, 6/5, 40/33, 5/4, 9/7, 4/3, 15/11, 45/32, 16/11, 3/2, 14/9, 8/5, 33/20, 27/16, 7/4, 16/9, 20/11, 15/8, 27/14, 2&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Augustus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Augustus&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Julius-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;13-limit&lt;/h3&gt;
+Commas: 176/175, 325/324, 896/891&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;2 0 11 0 14 -18|, &amp;lt;0 1 -2 0 -4 8|, &amp;lt;0 0 0 1 1 0|]&lt;br /&gt;
+EDOs: 12, 46, 68, 80&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-Augustus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Augustus&lt;/h2&gt;
 Commas: 385/384, 1232/1215&lt;br /&gt;
 &lt;br /&gt;
@@ Line 94: / Line 106: @@
 EDOs: 46, 68, 114, 124&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-Tiberius"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Tiberius&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-Tiberius"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Tiberius&lt;/h2&gt;
 Commas: 2048/2025, 441/440&lt;br /&gt;
 &lt;br /&gt;
@@ Line 105: / Line 117: @@
 EDOs: 58, 148, 160&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-Claudius"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Claudius&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x-Claudius"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Claudius&lt;/h2&gt;
 Commas: 2048/2025, 540/539&lt;br /&gt;
 &lt;br /&gt;

Diaschismic rank three family: Difference between revisions

Revision as of 23:58, 31 December 2010

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