User:AthiTrydhen/15-limit tonality 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 01:11:33 UTC.
- The original revision id was 588772052.
- 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 **15-limit tonality diamond** has the following notes: || 1/1 || 9/8 || 5/4 || 11/8 || 3/2 || 13/8 || 7/4 || 15/8 || || 16/9 || 1/1 || 10/9 || 11/9 || 4/3 || 13/9 || 14/9 || 5/3 || || 8/5 || 9/5 || 1/1 || 11/10 || 6/5 || 13/10 || 7/5 || 3/2 || || 16/11 || 18/11 || 20/11 || 1/1 || 12/11 || 13/11 || 14/11 || 15/11 || || 4/3 || 3/2 || 5/3 || 11/6 || 1/1 || 13/12 || 7/6 || 5/4 || || 16/13 || 18/13 || 20/13 || 22/13 || 24/13 || 1/1 || 14/13 || 15/13 || || 8/7 || 9/7 || 10/7 || 11/7 || 12/7 || 13/7 || 1/1 || 15/14 || || 16/15 || 6/5 || 4/3 || 22/15 || 8/5 || 26/15 || 28/15 || 1/1 || ==Symmetry group== The symmetry group of the 15-limit tonality diamond has 24 elements. The following are its generators: * 3:2, 5:4, 7:4, 11:8, 13:8 -> 4:3, 5:3, 14:9, 11:9, 13:9 * 3:2, 5:4, 7:4, 11:8, 13:8 -> 3:2, 5:4, 11:8, 7:4, 13:8 * 3:2, 5:4, 7:4, 11:8, 13:8 -> 3:2, 5:4, 7:4, 13:8, 11:8 * 3:2, 5:4, 7:4, 11:8, 13:8 -> 4:3, 8:5, 8:7, 16:11, 16:13 ===Orbits=== [to be included]
Original HTML content:
<html><head><title>15-limit tonality diamond</title></head><body>The <strong>15-limit tonality diamond</strong> has the following notes:<br />
<br />
<table class="wiki_table">
<tr>
<td>1/1<br />
</td>
<td>9/8<br />
</td>
<td>5/4<br />
</td>
<td>11/8<br />
</td>
<td>3/2<br />
</td>
<td>13/8<br />
</td>
<td>7/4<br />
</td>
<td>15/8<br />
</td>
</tr>
<tr>
<td>16/9<br />
</td>
<td>1/1<br />
</td>
<td>10/9<br />
</td>
<td>11/9<br />
</td>
<td>4/3<br />
</td>
<td>13/9<br />
</td>
<td>14/9<br />
</td>
<td>5/3<br />
</td>
</tr>
<tr>
<td>8/5<br />
</td>
<td>9/5<br />
</td>
<td>1/1<br />
</td>
<td>11/10<br />
</td>
<td>6/5<br />
</td>
<td>13/10<br />
</td>
<td>7/5<br />
</td>
<td>3/2<br />
</td>
</tr>
<tr>
<td>16/11<br />
</td>
<td>18/11<br />
</td>
<td>20/11<br />
</td>
<td>1/1<br />
</td>
<td>12/11<br />
</td>
<td>13/11<br />
</td>
<td>14/11<br />
</td>
<td>15/11<br />
</td>
</tr>
<tr>
<td>4/3<br />
</td>
<td>3/2<br />
</td>
<td>5/3<br />
</td>
<td>11/6<br />
</td>
<td>1/1<br />
</td>
<td>13/12<br />
</td>
<td>7/6<br />
</td>
<td>5/4<br />
</td>
</tr>
<tr>
<td>16/13<br />
</td>
<td>18/13<br />
</td>
<td>20/13<br />
</td>
<td>22/13<br />
</td>
<td>24/13<br />
</td>
<td>1/1<br />
</td>
<td>14/13<br />
</td>
<td>15/13<br />
</td>
</tr>
<tr>
<td>8/7<br />
</td>
<td>9/7<br />
</td>
<td>10/7<br />
</td>
<td>11/7<br />
</td>
<td>12/7<br />
</td>
<td>13/7<br />
</td>
<td>1/1<br />
</td>
<td>15/14<br />
</td>
</tr>
<tr>
<td>16/15<br />
</td>
<td>6/5<br />
</td>
<td>4/3<br />
</td>
<td>22/15<br />
</td>
<td>8/5<br />
</td>
<td>26/15<br />
</td>
<td>28/15<br />
</td>
<td>1/1<br />
</td>
</tr>
</table>
<!-- 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 15-limit tonality diamond has 24 elements. The following are its generators:<br />
<ul><li>3:2, 5:4, 7:4, 11:8, 13:8 -> 4:3, 5:3, 14:9, 11:9, 13:9</li><li>3:2, 5:4, 7:4, 11:8, 13:8 -> 3:2, 5:4, 11:8, 7:4, 13:8</li><li>3:2, 5:4, 7:4, 11:8, 13:8 -> 3:2, 5:4, 7:4, 13:8, 11:8</li><li>3:2, 5:4, 7:4, 11:8, 13:8 -> 4:3, 8:5, 8:7, 16:11, 16:13</li></ul><br />
<!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x-Symmetry group-Orbits"></a><!-- ws:end:WikiTextHeadingRule:2 -->Orbits</h3>
[to be included]</body></html>