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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | The '''Hendrix diamond''' is the tonality diamond generated from the ratios 1/1, 7/6, 5/4, 3/2 and 7/4. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:Praimhin|Praimhin]] and made on <tt>2016-08-04 00:11:12 UTC</tt>.<br>
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| : The original revision id was <tt>588770760</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <h4>Original Wikitext content:</h4>
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| <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;white-space: pre-wrap ! important" class="old-revision-html">The **Hendrix diamond** is the tonality diamond generated from the ratios 1/1, 7/6, 5/4, 3/2 and 7/4.
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| ||~ ||~ ||~ ||~ ||~ ||~ ||
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| ||~ || 1/1 || 7/6 || 5/4 || 3/2 || 7/4 ||
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| ||~ || 12/7 || 1/1 || 15/14 || 9/7 || 3/2 ||
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| ||~ || 8/5 || 28/15 || 1/1 || 6/5 || 7/5 ||
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| ||~ || 4/3 || 14/9 || 5/3 || 1/1 || 7/6 ||
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| ||~ || 8/7 || 4/3 || 10/7 || 12/7 || 1/1 ||
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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 [[Anomalous Saturated Suspensions|anomalous saturated suspension]].
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| ==Symmetry group== | | {| class="wikitable" |
| | |- |
| | ! | |
| | ! | |
| | ! | |
| | ! | |
| | ! | |
| | ! | |
| | |- |
| | ! | |
| | | | 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 suspension]]. |
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| The symmetry group of the Hendrix diamond has 8 elements. Its generators are:
| | ==Symmetry group== |
| * 3:2, 5:4, 7:4 → 7:6, 5:3, 14:9
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| * 3:2, 5:4, 7:4 → 3:2, 15:14, 9:7
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| * 3:2, 5:4, 7:4 → 4:3, 8:5, 8:7</pre></div>
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| <h4>Original HTML content:</h4>
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| <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"><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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| | The symmetry group of the Hendrix diamond has 16 elements. Its generators are: |
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| <table class="wiki_table">
| | <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> |
| <tr>
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| <th><br />
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| </th>
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| <th><br />
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| </th>
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| <th><br />
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| </th>
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| <th><br />
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| </th>
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| <th><br />
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| </th>
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| <th><br />
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| </th>
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| </tr>
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| <tr>
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| <th><br />
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| </th>
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| <td>1/1<br />
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| </td>
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| <td>7/6<br />
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| </td>
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| <td>5/4<br />
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| </td>
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| <td>3/2<br />
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| </td>
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| <td>7/4<br />
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| </td>
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| </tr>
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| <tr>
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| <th><br />
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| </th>
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| <td>12/7<br />
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| </td>
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| <td>1/1<br />
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| </td>
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| <td>15/14<br />
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| </td>
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| <td>9/7<br />
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| </td>
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| <td>3/2<br />
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| </td>
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| </tr>
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| <tr>
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| <th><br />
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| </th>
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| <td>8/5<br />
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| </td>
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| <td>28/15<br />
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| </td>
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| <td>1/1<br />
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| </td>
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| <td>6/5<br />
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| </td>
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| <td>7/5<br />
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| </td>
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| </tr>
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| <tr>
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| <th><br />
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| </th>
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| <td>4/3<br />
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| </td>
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| <td>14/9<br />
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| </td>
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| <td>5/3<br />
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| </td>
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| <td>1/1<br />
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| </td>
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| <td>7/6<br />
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| </td>
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| </tr>
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| <tr>
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| <th><br />
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| </th>
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| <td>8/7<br />
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| </td>
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| <td>4/3<br />
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| </td>
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| <td>10/7<br />
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| </td>
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| <td>12/7<br />
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| </td>
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| <td>1/1<br />
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| </td>
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| </tr>
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| </table>
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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 />
| | ===Orbits and Invariant Subsets=== |
| <br />
| | [to be included] |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Symmetry group"></a><!-- ws:end:WikiTextHeadingRule:0 -->Symmetry group</h2>
| | [[Category:Just intonation scales]] |
| <br />
| | [[Category:Diamond]] |
| The symmetry group of the Hendrix diamond has 8 elements. Its generators are:<br />
| | [[Category:Tables]] |
| <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></pre></div>
| | [[Category:Todo:expand]] |