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User:AthiTrydhen/13-Hendrix diamond

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Revision as of 01:29, 4 August 2016 by Wikispaces>Praimhin (**Imported revision 588772210 - Original comment: **)

IMPORTED REVISION FROM WIKISPACES

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This revision was by author Praimhin and made on 2016-08-04 01:29:28 UTC.
The original revision id was 588772210.
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 **13-****Hendrix diamond** is the tonality diamond generated from the ratios 1/1, 13/12, 5/4, 3/2 and 13/8.
||~   ||~   ||~   ||~   ||~   ||~   ||
||~   || 1/1 || 13/12 || 5/4 || 3/2 || 13/8 ||
||~   || 24/13 || 1/1 || 15/13 || 18/13 || 3/2 ||
||~   || 8/5 || 26/15 || 1/1 || 6/5 || 13/10 ||
||~   || 4/3 || 13/9 || 5/3 || 1/1 || 13/12 ||
||~   || 16/13 || 4/3 || 20/13 || 24/13 || 1/1 ||
All notes in the Hendrix diamond are also found in the [[15-limit tonality diamond]], because 1/1:13/12:5/4:3/2:13/8 is a 15-limit [[Anomalous Saturated Suspensions|anomalous saturated suspension]].

==Symmetry group== 

The symmetry group of the 13-Hendrix diamond has 16 elements. Its generators are:
* 3:2, 5:4, 13:8 → 13:12, 5:3, 13:9
* 3:2, 5:4, 13:8 → 3:2, 15:13, 18:13
* 3:2, 5:4, 13:8 → 4:3, 8:5, 16:13

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

Original HTML content:

<html><head><title>13-Hendrix diamond</title></head><body>The <strong>13-</strong><strong>Hendrix diamond</strong> is the tonality diamond generated from the ratios 1/1, 13/12, 5/4, 3/2 and 13/8.<br />


<table class="wiki_table">
    <tr>
        <th><br />
</th>
        <th><br />
</th>
        <th><br />
</th>
        <th><br />
</th>
        <th><br />
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    </tr>
    <tr>
        <th><br />
</th>
        <td>1/1<br />
</td>
        <td>13/12<br />
</td>
        <td>5/4<br />
</td>
        <td>3/2<br />
</td>
        <td>13/8<br />
</td>
    </tr>
    <tr>
        <th><br />
</th>
        <td>24/13<br />
</td>
        <td>1/1<br />
</td>
        <td>15/13<br />
</td>
        <td>18/13<br />
</td>
        <td>3/2<br />
</td>
    </tr>
    <tr>
        <th><br />
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        <td>8/5<br />
</td>
        <td>26/15<br />
</td>
        <td>1/1<br />
</td>
        <td>6/5<br />
</td>
        <td>13/10<br />
</td>
    </tr>
    <tr>
        <th><br />
</th>
        <td>4/3<br />
</td>
        <td>13/9<br />
</td>
        <td>5/3<br />
</td>
        <td>1/1<br />
</td>
        <td>13/12<br />
</td>
    </tr>
    <tr>
        <th><br />
</th>
        <td>16/13<br />
</td>
        <td>4/3<br />
</td>
        <td>20/13<br />
</td>
        <td>24/13<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 1/1:13/12:5/4:3/2:13/8 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 13-Hendrix diamond has 16 elements. Its generators are:<br />
<ul><li>3:2, 5:4, 13:8 → 13:12, 5:3, 13:9</li><li>3:2, 5:4, 13:8 → 3:2, 15:13, 18:13</li><li>3:2, 5:4, 13:8 → 4:3, 8:5, 16:13</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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