User:AthiTrydhen/13-Hendrix diamond: Difference between revisions
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Wikispaces>Praimhin **Imported revision 588772180 - Original comment: ** |
Wikispaces>Praimhin **Imported revision 588772188 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | 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 01:28: | : This revision was by author [[User:Praimhin|Praimhin]] and made on <tt>2016-08-04 01:28:30 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>588772188</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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||~ || 4/3 || 13/9 || 5/3 || 1/1 || 13/12 || | ||~ || 4/3 || 13/9 || 5/3 || 1/1 || 13/12 || | ||
||~ || 16/13 || 4/3 || 20/13 || 24/13 || 1/1 || | ||~ || 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]]. | 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== | ==Symmetry group== | ||
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</table> | </table> | ||
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 <a class="wiki_link" href="/Anomalous%20Saturated%20Suspensions">anomalous saturated suspension</a>.<br /> | 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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Symmetry group"></a><!-- ws:end:WikiTextHeadingRule:0 -->Symmetry group</h2> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Symmetry group"></a><!-- ws:end:WikiTextHeadingRule:0 -->Symmetry group</h2> | ||
Revision as of 01:28, 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 01:28:30 UTC.
- The original revision id was 588772188.
- 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, 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 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>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 />
</th>
<th><br />
</th>
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<tr>
<th><br />
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<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 />
</th>
<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>
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</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:<h2> --><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, 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:<h3> --><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>