User:AthiTrydhen/11-Hendrix diamond: Difference between revisions

Revision as of 01:29, 4 August 2016

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

This revision was by author Praimhin and made on 2016-08-04 01:29:42 UTC.

The original revision id was 588772216.

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:

The **11-****Hendrix diamond** is the tonality diamond generated from the ratios 1/1, 5/4, 11/8, 3/2 and 11/6.
||~   ||~   ||~   ||~   ||~   ||~   ||
||~   || 1/1 || 5/4 || 11/8 || 3/2 || 11/6 ||
||~   || 8/5 || 1/1 || 11/10 || 6/5 || 22/15 ||
||~   || 16/11 || 20/11 || 1/1 || 12/11 || 4/3 ||
||~   || 4/3 || 5/3 || 11/6 || 1/1 || 11/9 ||
||~   || 12/11 || 15/11 || 3/2 || 18/11 || 1/1 ||
All notes in the Hendrix diamond are also found in the [[15-limit tonality diamond]], because 1/1:5/4:11/8:3/2:11/6 is a 15-limit [[Anomalous Saturated Suspensions|anomalous saturated suspension]].

==Symmetry group== 

The symmetry group of the 11-Hendrix diamond has 16 elements. Its generators are:
* 3:2, 5:4, 11:8 → 11:6, 5:3, 11:9
* 3:2, 5:4, 11:8 → 3:2, 15:11, 18:11
* 3:2, 5:4, 11:8 → 4:3, 8:5, 16:11

===Orbits and Invariant Subsets=== 
[to be included]

Original HTML content:

<html><head><title>11-Hendrix diamond</title></head><body>The <strong>11-</strong><strong>Hendrix diamond</strong> is the tonality diamond generated from the ratios 1/1, 5/4, 11/8, 3/2 and 11/6.<br />


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        <td>1/1<br />
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        <td>5/4<br />
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        <td>11/8<br />
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        <td>3/2<br />
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        <td>11/6<br />
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        <td>8/5<br />
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        <td>1/1<br />
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        <td>6/5<br />
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        <td>22/15<br />
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        <td>16/11<br />
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        <td>20/11<br />
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        <td>1/1<br />
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        <td>12/11<br />
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        <td>4/3<br />
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        <td>4/3<br />
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        <td>5/3<br />
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        <td>11/6<br />
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        <td>1/1<br />
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        <td>11/9<br />
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    </tr>
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        <td>12/11<br />
</td>
        <td>15/11<br />
</td>
        <td>3/2<br />
</td>
        <td>18/11<br />
</td>
        <td>1/1<br />
</td>
    </tr>
</table>

All notes in the Hendrix diamond are also found in the <a class="wiki_link" href="/15-limit%20tonality%20diamond">15-limit tonality diamond</a>, because 1/1:5/4:11/8:3/2:11/6 is a 15-limit <a class="wiki_link" href="/Anomalous%20Saturated%20Suspensions">anomalous saturated suspension</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Symmetry group"></a><!-- ws:end:WikiTextHeadingRule:0 -->Symmetry group</h2>
 <br />
The symmetry group of the 11-Hendrix diamond has 16 elements. Its generators are:<br />
<ul><li>3:2, 5:4, 11:8 → 11:6, 5:3, 11:9</li><li>3:2, 5:4, 11:8 → 3:2, 15:11, 18:11</li><li>3:2, 5:4, 11:8 → 4:3, 8:5, 16:11</li></ul><br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-Symmetry group-Orbits and Invariant Subsets"></a><!-- ws:end:WikiTextHeadingRule:2 -->Orbits and Invariant Subsets</h3>
 [to be included]</body></html>

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 <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:Praimhin|Praimhin]] and made on <tt>2016-08-04 01:29:04 UTC</tt>.<br>
+: This revision was by author [[User:Praimhin|Praimhin]] and made on <tt>2016-08-04 01:29:42 UTC</tt>.<br>
-: The original revision id was <tt>588772204</tt>.<br>
+: The original revision id was <tt>588772216</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 17: / Line 17: @@
 ==Symmetry group==
-The symmetry group of the Hendrix diamond has 16 elements. Its generators are:
+The symmetry group of the 11-Hendrix diamond has 16 elements. Its generators are:
 * 3:2, 5:4, 11:8 → 11:6, 5:3, 11:9
 * 3:2, 5:4, 11:8 → 3:2, 15:11, 18:11
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 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Symmetry group"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Symmetry group&lt;/h2&gt;
   &lt;br /&gt;
-The symmetry group of the Hendrix diamond has 16 elements. Its generators are:&lt;br /&gt;
+The symmetry group of the 11-Hendrix diamond has 16 elements. Its generators are:&lt;br /&gt;
 &lt;ul&gt;&lt;li&gt;3:2, 5:4, 11:8 → 11:6, 5:3, 11:9&lt;/li&gt;&lt;li&gt;3:2, 5:4, 11:8 → 3:2, 15:11, 18:11&lt;/li&gt;&lt;li&gt;3:2, 5:4, 11:8 → 4:3, 8:5, 16:11&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Symmetry group-Orbits and Invariant Subsets"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Orbits and Invariant Subsets&lt;/h3&gt;
   [to be included]&lt;/body&gt;&lt;/html&gt;</pre></div>

User:AthiTrydhen/11-Hendrix diamond: Difference between revisions

Revision as of 01:29, 4 August 2016

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