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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | The '''13-''''''Hendrix diamond''' is the tonality diamond generated from the ratios 1/1, 13/12, 5/4, 3/2 and 13/8. |
| 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 01:29:28 UTC</tt>.<br>
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| : The original revision id was <tt>588772210</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 **13-****Hendrix diamond** is the tonality diamond generated from the ratios 1/1, 13/12, 5/4, 3/2 and 13/8.
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| ||~ ||~ ||~ ||~ ||~ ||~ ||
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| ||~ || 1/1 || 13/12 || 5/4 || 3/2 || 13/8 ||
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| ||~ || 24/13 || 1/1 || 15/13 || 18/13 || 3/2 ||
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| ||~ || 8/5 || 26/15 || 1/1 || 6/5 || 13/10 ||
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| ||~ || 4/3 || 13/9 || 5/3 || 1/1 || 13/12 ||
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| ||~ || 16/13 || 4/3 || 20/13 || 24/13 || 1/1 ||
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| 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]].
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| ==Symmetry group== | | {| class="wikitable" |
| | |- |
| | ! | |
| | ! | |
| | ! | |
| | ! | |
| | ! | |
| | ! | |
| | |- |
| | ! | |
| | | | 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|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]]. |
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| | ==Symmetry group== |
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| The symmetry group of the 13-Hendrix diamond has 16 elements. Its generators are: | | The symmetry group of the 13-Hendrix diamond has 16 elements. Its generators are: |
| * 3:2, 5:4, 13:8 → 13:12, 5:3, 13:9
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| * 3:2, 5:4, 13:8 → 3:2, 15:13, 18:13
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| * 3:2, 5:4, 13:8 → 4:3, 8:5, 16:13
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| ===Orbits and Invariant Subsets===
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| [to be included]</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>13-Hendrix diamond</title></head><body>The <strong>13-</strong><strong>Hendrix diamond</strong> is the tonality diamond generated from the ratios 1/1, 13/12, 5/4, 3/2 and 13/8.<br />
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| <table class="wiki_table">
| | <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> |
| <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>13/12<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>13/8<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>24/13<br />
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| </td>
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| <td>1/1<br />
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| </td>
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| <td>15/13<br />
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| </td>
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| <td>18/13<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>26/15<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>13/10<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>13/9<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>13/12<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>16/13<br />
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| </td>
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| <td>4/3<br />
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| </td>
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| <td>20/13<br />
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| </td>
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| <td>24/13<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 <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 />
| | ===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>
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| <br />
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| The symmetry group of the 13-Hendrix diamond has 16 elements. Its generators are:<br />
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| <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 />
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| <!-- 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>
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| [to be included]</body></html></pre></div>
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