User:AthiTrydhen/Hendrix diamond: Difference between revisions

Revision as of 01:12, 4 August 2016

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 01:12:28 UTC.

The original revision id was 588772062.

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 **Hendrix diamond** is the tonality diamond generated from the ratios 1/1, 7/6, 5/4, 3/2 and 7/4.
||~   ||~   ||~   ||~   ||~   ||~   ||
||~   || 1/1 || 7/6 || 5/4 || 3/2 || 7/4 ||
||~   || 12/7 || 1/1 || 15/14 || 9/7 || 3/2 ||
||~   || 8/5 || 28/15 || 1/1 || 6/5 || 7/5 ||
||~   || 4/3 || 14/9 || 5/3 || 1/1 || 7/6 ||
||~   || 8/7 || 4/3 || 10/7 || 12/7 || 1/1 ||
All notes in the Hendrix diamond are also found in the 15-limit tonality diamond, because 1/1:7/6:5/4:3/2:7/4 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, 7:4 → 7:6, 5:3, 14:9
* 3:2, 5:4, 7:4 → 3:2, 15:14, 9:7
* 3:2, 5:4, 7:4 → 4:3, 8:5, 8:7

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

Original HTML content:

<html><head><title>Hendrix diamond</title></head><body>The <strong>Hendrix diamond</strong> is the tonality diamond generated from the ratios 1/1, 7/6, 5/4, 3/2 and 7/4.<br />


<table class="wiki_table">
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        <td>1/1<br />
</td>
        <td>7/6<br />
</td>
        <td>5/4<br />
</td>
        <td>3/2<br />
</td>
        <td>7/4<br />
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        <td>12/7<br />
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        <td>1/1<br />
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        <td>15/14<br />
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        <td>9/7<br />
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        <td>3/2<br />
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        <td>8/5<br />
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        <td>28/15<br />
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        <td>1/1<br />
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        <td>6/5<br />
</td>
        <td>7/5<br />
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    </tr>
    <tr>
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        <td>4/3<br />
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        <td>14/9<br />
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        <td>5/3<br />
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        <td>1/1<br />
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        <td>7/6<br />
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    </tr>
    <tr>
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        <td>8/7<br />
</td>
        <td>4/3<br />
</td>
        <td>10/7<br />
</td>
        <td>12/7<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 1/1:7/6:5/4:3/2:7/4 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, 7:4 → 7:6, 5:3, 14:9</li><li>3:2, 5:4, 7:4 → 3:2, 15:14, 9:7</li><li>3:2, 5:4, 7:4 → 4:3, 8:5, 8:7</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>

@@ 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:Praimhin|Praimhin]] and made on <tt>2016-08-04 00:55:52 UTC</tt>.<br>
+: This revision was by author [[User:Praimhin|Praimhin]] and made on <tt>2016-08-04 01:12:28 UTC</tt>.<br>
-: The original revision id was <tt>588771850</tt>.<br>
+: The original revision id was <tt>588772062</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 20: / Line 20: @@
 * 3:2, 5:4, 7:4 → 7:6, 5:3, 14:9
 * 3:2, 5:4, 7:4 → 3:2, 15:14, 9:7
-* 3:2, 5:4, 7:4 → 4:3, 8:5, 8:7</pre></div>
+* 3:2, 5:4, 7:4 → 4:3, 8:5, 8:7
+===Orbits and Invariant Subsets===
+[to be included]</pre></div>
 <h4>Original HTML content:</h4>
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Hendrix diamond&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;strong&gt;Hendrix diamond&lt;/strong&gt; is the tonality diamond generated from the ratios 1/1, 7/6, 5/4, 3/2 and 7/4.&lt;br /&gt;
@@ Line 117: / Line 120: @@
   &lt;br /&gt;
 The symmetry group of the Hendrix diamond has 16 elements. Its generators are:&lt;br /&gt;
-&lt;ul&gt;&lt;li&gt;3:2, 5:4, 7:4 → 7:6, 5:3, 14:9&lt;/li&gt;&lt;li&gt;3:2, 5:4, 7:4 → 3:2, 15:14, 9:7&lt;/li&gt;&lt;li&gt;3:2, 5:4, 7:4 → 4:3, 8:5, 8:7&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+&lt;ul&gt;&lt;li&gt;3:2, 5:4, 7:4 → 7:6, 5:3, 14:9&lt;/li&gt;&lt;li&gt;3:2, 5:4, 7:4 → 3:2, 15:14, 9:7&lt;/li&gt;&lt;li&gt;3:2, 5:4, 7:4 → 4:3, 8:5, 8:7&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/Hendrix diamond: Difference between revisions

Revision as of 01:12, 4 August 2016

IMPORTED REVISION FROM WIKISPACES

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