User:AthiTrydhen/11-Hendrix diamond

From Xenharmonic Wiki
< User:AthiTrydhen
Revision as of 01:26, 4 August 2016 by Wikispaces>Praimhin (**Imported revision 588772154 - Original comment: **)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search

IMPORTED REVISION FROM WIKISPACES

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 01:26:20 UTC.
The original revision id was 588772154.
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 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 />


<table class="wiki_table">
    <tr>
        <th><br />
</th>
        <th><br />
</th>
        <th><br />
</th>
        <th><br />
</th>
        <th><br />
</th>
        <th><br />
</th>
    </tr>
    <tr>
        <th><br />
</th>
        <td>1/1<br />
</td>
        <td>5/4<br />
</td>
        <td>11/8<br />
</td>
        <td>3/2<br />
</td>
        <td>11/6<br />
</td>
    </tr>
    <tr>
        <th><br />
</th>
        <td>8/5<br />
</td>
        <td>1/1<br />
</td>
        <td>11/10<br />
</td>
        <td>6/5<br />
</td>
        <td>22/15<br />
</td>
    </tr>
    <tr>
        <th><br />
</th>
        <td>16/11<br />
</td>
        <td>20/11<br />
</td>
        <td>1/1<br />
</td>
        <td>12/11<br />
</td>
        <td>4/3<br />
</td>
    </tr>
    <tr>
        <th><br />
</th>
        <td>4/3<br />
</td>
        <td>5/3<br />
</td>
        <td>11/6<br />
</td>
        <td>1/1<br />
</td>
        <td>11/9<br />
</td>
    </tr>
    <tr>
        <th><br />
</th>
        <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 15-limit tonality diamond, 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 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>
Retrieved from "https://en.xen.wiki/index.php?title=User:AthiTrydhen/11-Hendrix_diamond&oldid=4257"