User:AthiTrydhen/11-Hendrix diamond: Difference between revisions
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Wikispaces>Praimhin **Imported revision 588772154 - Original comment: ** |
Wikispaces>Praimhin **Imported revision 588772204 - 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: | : This revision was by author [[User:Praimhin|Praimhin]] and made on <tt>2016-08-04 01:29:04 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>588772204</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 || 5/3 || 11/6 || 1/1 || 11/9 || | ||~ || 4/3 || 5/3 || 11/6 || 1/1 || 11/9 || | ||
||~ || 12/11 || 15/11 || 3/2 || 18/11 || 1/1 || | ||~ || 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]]. | 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== | ==Symmetry group== | ||
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</table> | </table> | ||
All notes in the Hendrix diamond are also found in the 15-limit tonality diamond, because 1/1:5/4:11/8:3/2:11/6 is a 15-limit <a class="wiki_link" href="/Anomalous%20Saturated%20Suspensions">anomalous saturated suspension</a>.<br /> | 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 /> | <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 01:29, 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 01:29:04 UTC.
- The original revision id was 588772204.
- 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>
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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:<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, 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:<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>