User:AthiTrydhen/Hendrix diamond
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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 00:55:52 UTC.
- The original revision id was 588771850.
- 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
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 />
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<td>1/1<br />
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<td>7/6<br />
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<td>5/4<br />
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<td>3/2<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>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>8/7<br />
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<td>4/3<br />
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<td>10/7<br />
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<td>12/7<br />
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<td>1/1<br />
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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 />
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<!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Symmetry group"></a><!-- ws:end:WikiTextHeadingRule:0 -->Symmetry group</h2>
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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></body></html>