User:AthiTrydhen/13-Hendrix diamond - Revision history

AthiTrydhen: AthiTrydhen moved page 13-Hendrix diamond to User:AthiTrydhen/13-Hendrix diamond

2024-12-14T05:46:54Z

AthiTrydhen moved page 13-Hendrix diamond to User:AthiTrydhen/13-Hendrix diamond

← Older revision	Revision as of 05:46, 14 December 2024
(No difference)

Fredg999 category edits: Misc. edit, categories

2022-08-05T02:09:26Z

Misc. edit, categories

← Older revision		Revision as of 02:09, 5 August 2022
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	The '''13-~~''''''~~Hendrix diamond''' is the tonality diamond generated from the ratios 1/1, 13/12, 5/4, 3/2 and 13/8.		The '''13-Hendrix diamond''' is the tonality diamond generated from the ratios 1/1, 13/12, 5/4, 3/2 and 13/8.

	{\| class="wikitable"		{\| class="wikitable"
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	===Orbits and Invariant Subsets===		===Orbits and Invariant Subsets===
	[to be included]		[to be included]

			[[Category:Diamond]]
			[[Category:Hendrix]]

Xenwolf: simplify links

2020-12-05T15:18:02Z

simplify links

← Older revision		Revision as of 15:18, 5 December 2020
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	\| \| 1/1		\| \| 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]].		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 suspension]].

	==Symmetry group==		==Symmetry group==

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>Praimhin: Imported revision 588772210 - Original comment:

2016-08-04T01:29:28Z

**Imported revision 588772210 - Original comment: **

Wikispaces>Praimhin: Imported revision 588772188 - Original comment:

2016-08-04T01:28:30Z

**Imported revision 588772188 - Original comment: **

← Older revision		Revision as of 01:28, 4 August 2016
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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 01:28:06 UTC</tt>.<br>		: This revision was by author [[User:Praimhin\|Praimhin]] and made on <tt>2016-08-04 01:28:30 UTC</tt>.<br>
	: The original revision id was <tt>~~588772180~~</tt>.<br>		: The original revision id was <tt>588772188</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 \|\| 13/9 \|\| 5/3 \|\| 1/1 \|\| 13/12 \|\|		\|\|~ \|\| 4/3 \|\| 13/9 \|\| 5/3 \|\| 1/1 \|\| 13/12 \|\|
	\|\|~ \|\| 16/13 \|\| 4/3 \|\| 20/13 \|\| 24/13 \|\| 1/1 \|\|		\|\|~ \|\| 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, because 1/1:13/12:5/4:3/2:13/8 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 1/1:13/12:5/4:3/2:13/8 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 1/1:13/12:5/4:3/2:13/8 is a 15-limit <a class="wiki_link" href="/Anomalous%20Saturated%20Suspensions">anomalous saturated suspension</a>.<br />		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 />
	<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>

Wikispaces>Praimhin: Imported revision 588772180 - Original comment:

2016-08-04T01:28:06Z

**Imported revision 588772180 - Original comment: **

New page

<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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 01:28:06 UTC</tt>.<br>
: The original revision id was <tt>588772180</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>
<h4>Original Wikitext content:</h4>
<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, 13/12, 5/4, 3/2 and 13/8.
||~ ||~ ||~ ||~ ||~ ||~ ||
||~ || 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, because 1/1:13/12:5/4:3/2:13/8 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, 13:8 → 13:12, 5:3, 13:9
* 3:2, 5:4, 13:8 → 3:2, 15:13, 18:13
* 3:2, 5:4, 13:8 → 4:3, 8:5, 16:13

===Orbits and Invariant Subsets===
[to be included]</pre></div>
<h4>Original HTML content:</h4>
<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>Hendrix diamond</strong> is the tonality diamond generated from the ratios 1/1, 13/12, 5/4, 3/2 and 13/8.<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>13/12<br />
</td>
<td>5/4<br />
</td>
<td>3/2<br />
</td>
<td>13/8<br />
</td>
</tr>
<tr>
<th><br />
</th>
<td>24/13<br />
</td>
<td>1/1<br />
</td>
<td>15/13<br />
</td>
<td>18/13<br />
</td>
<td>3/2<br />
</td>
</tr>
<tr>
<th><br />
</th>
<td>8/5<br />
</td>
<td>26/15<br />
</td>
<td>1/1<br />
</td>
<td>6/5<br />
</td>
<td>13/10<br />
</td>
</tr>
<tr>
<th><br />
</th>
<td>4/3<br />
</td>
<td>13/9<br />
</td>
<td>5/3<br />
</td>
<td>1/1<br />
</td>
<td>13/12<br />
</td>
</tr>
<tr>
<th><br />
</th>
<td>16/13<br />
</td>
<td>4/3<br />
</td>
<td>20/13<br />
</td>
<td>24/13<br />
</td>
<td>1/1<br />
</td>
</tr>
</table>

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 <a class="wiki_link" href="/Anomalous%20Saturated%20Suspensions">anomalous saturated suspension</a>.<br />
<br />
<h2 id="toc0"><a name="x-Symmetry group"></a>Symmetry group</h2>
<br />
The symmetry group of the Hendrix diamond has 16 elements. Its generators are:<br />
<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 />
<h3 id="toc1"><a name="x-Symmetry group-Orbits and Invariant Subsets"></a>Orbits and Invariant Subsets</h3>
[to be included]</body></html></pre></div>

← Older revision		Revision as of 01:29, 4 August 2016
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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 01:28~~:30~~ UTC</tt>.<br>		: This revision was by author [[User:Praimhin\|Praimhin]] and made on <tt>2016-08-04 01:29:28 UTC</tt>.<br>
	: The original revision id was <tt>~~588772188~~</tt>.<br>		: The original revision id was <tt>588772210</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>
	<h4>Original Wikitext content:</h4>		<h4>Original Wikitext content:</h4>
	<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, 13/12, 5/4, 3/2 and 13/8.		<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.
	\|\|~ \|\|~ \|\|~ \|\|~ \|\|~ \|\|~ \|\|		\|\|~ \|\|~ \|\|~ \|\|~ \|\|~ \|\|~ \|\|
	\|\|~ \|\| 1/1 \|\| 13/12 \|\| 5/4 \|\| 3/2 \|\| 13/8 \|\|		\|\|~ \|\| 1/1 \|\| 13/12 \|\| 5/4 \|\| 3/2 \|\| 13/8 \|\|
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	==Symmetry group==		==Symmetry group==

	The symmetry group of the 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		* 3:2, 5:4, 13:8 → 13:12, 5:3, 13:9
	* 3:2, 5:4, 13:8 → 3:2, 15:13, 18:13		* 3:2, 5:4, 13:8 → 3:2, 15:13, 18:13
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	[to be included]</pre></div>		[to be included]</pre></div>
	<h4>Original HTML content:</h4>		<h4>Original HTML content:</h4>
	<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>Hendrix diamond</strong> is the tonality diamond generated from the ratios 1/1, 13/12, 5/4, 3/2 and 13/8.<br />		<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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	<!-- 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>
	<br />		<br />
	The symmetry group of the Hendrix diamond has 16 elements. Its generators are:<br />		The symmetry group of the 13-Hendrix diamond has 16 elements. Its generators are:<br />
	<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 />		<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 />
	<!-- 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>		<!-- 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>
	[to be included]</body></html></pre></div>		[to be included]</body></html></pre></div>