Marveltwin: Difference between revisions

Revision as of 15:00, 21 June 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 2011-06-21 15:00:02 UTC.

The original revision id was 238014607.

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]]

=Marveltwin and Marvel=
The //marveltwin comma//, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the [[11-limit]] version of marvel, which tempers out 225/224 and 385/384, to get [[13-limit]] marvel. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15.

=Rank five=
Comma: 325/324

13 and 15 limit minimax tuning
|| [1 0 0 0 0 0> ||
|| [0 1 0 0 0 0> ||
|| [2/3 4/3 1/3 0 0 -1/3> ||
|| [2/3 4/3 -2/3 1 0 -1/3> ||
|| [2/3 4/3 -2/3 0 1 -1/3> ||
|| [2/3 4/3 -2/3 0 0 2/3> ||

Eigenmonzo subgroup: 2.3.7/5.11/5.13/5

Map: 
|| <1 0 0 0 0 2] ||
|| <0 1 0 0 0 4] ||
|| <0 0 1 0 0 -2] || 
|| <0 0 0 1 0 0] ||
|| <0 0 0 0 1 0] ||

Edos: 7, 12, 15, 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 299, 333

Original HTML content:

<html><head><title>Marveltwin</title></head><body><!-- ws:start:WikiTextTocRule:4:&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:4 --><!-- ws:start:WikiTextTocRule:5: --><a href="#Marveltwin and Marvel">Marveltwin and Marvel</a><!-- ws:end:WikiTextTocRule:5 --><!-- ws:start:WikiTextTocRule:6: --> | <a href="#Rank five">Rank five</a><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: -->
<!-- ws:end:WikiTextTocRule:7 --><br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Marveltwin and Marvel"></a><!-- ws:end:WikiTextHeadingRule:0 -->Marveltwin and Marvel</h1>
The <em>marveltwin comma</em>, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the <a class="wiki_link" href="/11-limit">11-limit</a> version of marvel, which tempers out 225/224 and 385/384, to get <a class="wiki_link" href="/13-limit">13-limit</a> marvel. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Rank five"></a><!-- ws:end:WikiTextHeadingRule:2 -->Rank five</h1>
Comma: 325/324<br />
<br />
13 and 15 limit minimax tuning<br />


<table class="wiki_table">
    <tr>
        <td>[1 0 0 0 0 0&gt;<br />
</td>
    </tr>
    <tr>
        <td>[0 1 0 0 0 0&gt;<br />
</td>
    </tr>
    <tr>
        <td>[2/3 4/3 1/3 0 0 -1/3&gt;<br />
</td>
    </tr>
    <tr>
        <td>[2/3 4/3 -2/3 1 0 -1/3&gt;<br />
</td>
    </tr>
    <tr>
        <td>[2/3 4/3 -2/3 0 1 -1/3&gt;<br />
</td>
    </tr>
    <tr>
        <td>[2/3 4/3 -2/3 0 0 2/3&gt;<br />
</td>
    </tr>
</table>

<br />
Eigenmonzo subgroup: 2.3.7/5.11/5.13/5<br />
<br />
Map: <br />


<table class="wiki_table">
    <tr>
        <td>&lt;1 0 0 0 0 2]<br />
</td>
    </tr>
    <tr>
        <td>&lt;0 1 0 0 0 4]<br />
</td>
    </tr>
    <tr>
        <td>&lt;0 0 1 0 0 -2]<br />
</td>
        <td><br />
</td>
        <td>&lt;0 0 0 1 0 0]<br />
</td>
    </tr>
    <tr>
        <td>&lt;0 0 0 0 1 0]<br />
</td>
    </tr>
</table>

<br />
Edos: 7, 12, 15, 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 299, 333</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>2011-06-21 14:49:27 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-21 15:00:02 UTC</tt>.<br>
-: The original revision id was <tt>238012277</tt>.<br>
+: The original revision id was <tt>238014607</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 9: / Line 9: @@
 =Marveltwin and Marvel=
-The //marveltwin comma//, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the 11-limit
+The //marveltwin comma//, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the [[11-limit]] version of marvel, which tempers out 225/224 and 385/384, to get [[13-limit]] marvel. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15.
-version of marvel, tempering out 225/224 and 385/384 to get 13-limit marvel. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15.
 =Rank five=
 Comma: 325/324
+and 15 limit minimax tuning
+|| [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; ||
+|| [2/3 4/3 -2/3 1 0 -1/3&gt; ||
+|| [2/3 4/3 -2/3 0 1 -1/3&gt; ||
+|| [2/3 4/3 -2/3 0 0 2/3&gt; ||
+Eigenmonzo subgroup: 2.3.7/5.11/5.13/5
 Map:
@@ Line 28: / Line 37: @@
 &lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Marveltwin and Marvel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Marveltwin and Marvel&lt;/h1&gt;
-The &lt;em&gt;marveltwin comma&lt;/em&gt;, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the 11-limit&lt;br /&gt;
+The &lt;em&gt;marveltwin comma&lt;/em&gt;, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; version of marvel, which tempers out 225/224 and 385/384, to get &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; marvel. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15.&lt;br /&gt;
-version of marvel, tempering out 225/224 and 385/384 to get 13-limit marvel. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15.&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="Rank five"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Rank five&lt;/h1&gt;
 Comma: 325/324&lt;br /&gt;
+&lt;br /&gt;
+and 15 limit minimax tuning&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;td&gt;[1 0 0 0 0 0&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;[0 1 0 0 0 0&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;[2/3 4/3 1/3 0 0 -1/3&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;[2/3 4/3 -2/3 1 0 -1/3&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;[2/3 4/3 -2/3 0 1 -1/3&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;[2/3 4/3 -2/3 0 0 2/3&amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;br /&gt;
+Eigenmonzo subgroup: 2.3.7/5.11/5.13/5&lt;br /&gt;
 &lt;br /&gt;
 Map: &lt;br /&gt;

Marveltwin: Difference between revisions

Revision as of 15:00, 21 June 2011

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

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