User:AthiTrydhen/Hendrix diamond - Revision history

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

2024-12-14T05:46:39Z

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

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

BudjarnLambeth at 00:25, 27 April 2023

2023-04-27T00:25:43Z

← Older revision		Revision as of 00:25, 27 April 2023
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	[[Category:Diamond]]		[[Category:Diamond]]
	[[Category:Tables]]		[[Category:Tables]]
			[[Category:Todo:expand]]

BudjarnLambeth: Categorised this uncategorised page

2023-04-27T00:25:25Z

Categorised this uncategorised page

← Older revision		Revision as of 00:25, 27 April 2023
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	===Orbits and Invariant Subsets===		===Orbits and Invariant Subsets===
	[to be included]		[to be included]
			[[Category:Just intonation scales]]
			[[Category:Diamond]]
			[[Category:Tables]]

Xenwolf: simplify links

2020-12-05T15:19:15Z

simplify links

← Older revision		Revision as of 15:19, 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 1/1:7/6:5/4:3/2:7/4 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 1/1:7/6:5/4:3/2:7/4 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 588772194 - Original comment:

2016-08-04T01:28:47Z

**Imported revision 588772194 - 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 01:12:28 UTC</tt>.<br>		: This revision was by author [[User:Praimhin\|Praimhin]] and made on <tt>2016-08-04 01:28:47 UTC</tt>.<br>
	: The original revision id was <tt>~~588772062~~</tt>.<br>		: The original revision id was <tt>588772194</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 \|\| 14/9 \|\| 5/3 \|\| 1/1 \|\| 7/6 \|\|		\|\|~ \|\| 4/3 \|\| 14/9 \|\| 5/3 \|\| 1/1 \|\| 7/6 \|\|
	\|\|~ \|\| 8/7 \|\| 4/3 \|\| 10/7 \|\| 12/7 \|\| 1/1 \|\|		\|\|~ \|\| 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]].		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==		==Symmetry group==
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	</table>		</table>

	All notes in the Hendrix diamond are also found in the 15-limit tonality diamond, because 1/1:7/6:5/4:3/2:7/4 is a 15-limit <a class="wiki_link" href="/Anomalous%20Saturated%20Suspensions">anomalous saturated suspension</a>.<br />		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 1/1:7/6:5/4:3/2:7/4 is a 15-limit <a class="wiki_link" href="/Anomalous%20Saturated%20Suspensions">anomalous saturated suspension</a>.<br />
	<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 588772062 - Original comment:

2016-08-04T01:12:28Z

**Imported revision 588772062 - Original comment: **

← Older revision		Revision as of 01:12, 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 00:55:52 UTC</tt>.<br>		: This revision was by author [[User:Praimhin\|Praimhin]] and made on <tt>2016-08-04 01:12:28 UTC</tt>.<br>
	: The original revision id was <tt>~~588771850~~</tt>.<br>		: The original revision id was <tt>588772062</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>
Line 20:		Line 20:
	* 3:2, 5:4, 7:4 → 7:6, 5:3, 14:9		* 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 → 3:2, 15:14, 9:7
	* 3:2, 5:4, 7:4 → 4:3, 8:5, 8:7</pre></div>		* 3:2, 5:4, 7:4 → 4:3, 8:5, 8:7

			===Orbits and Invariant Subsets===
			[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>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 />		<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 />
Line 117:		Line 120:
	<br />		<br />
	The symmetry group of the Hendrix diamond has 16 elements. Its generators are:<br />		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></pre></div>		<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><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>
			[to be included]</body></html></pre></div>

Wikispaces>Praimhin: Imported revision 588771850 - Original comment:

2016-08-04T00:55:52Z

**Imported revision 588771850 - Original comment: **

Wikispaces>Praimhin: Imported revision 588770760 - Original comment:

2016-08-04T00:11:12Z

**Imported revision 588770760 - 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 00:11:12 UTC</tt>.<br>
: The original revision id was <tt>588770760</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, 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 8 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</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>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 />

<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>7/6<br />
</td>
<td>5/4<br />
</td>
<td>3/2<br />
</td>
<td>7/4<br />
</td>
</tr>
<tr>
<th><br />
</th>
<td>12/7<br />
</td>
<td>1/1<br />
</td>
<td>15/14<br />
</td>
<td>9/7<br />
</td>
<td>3/2<br />
</td>
</tr>
<tr>
<th><br />
</th>
<td>8/5<br />
</td>
<td>28/15<br />
</td>
<td>1/1<br />
</td>
<td>6/5<br />
</td>
<td>7/5<br />
</td>
</tr>
<tr>
<th><br />
</th>
<td>4/3<br />
</td>
<td>14/9<br />
</td>
<td>5/3<br />
</td>
<td>1/1<br />
</td>
<td>7/6<br />
</td>
</tr>
<tr>
<th><br />
</th>
<td>8/7<br />
</td>
<td>4/3<br />
</td>
<td>10/7<br />
</td>
<td>12/7<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 1/1:7/6:5/4:3/2:7/4 is a 15-limit <a class="wiki_link" href="/Anomalous%20Saturated%20Suspensions">anomalous saturated suspension</a>.<br />
<br />
<h2 id="toc0"><a name="x-Symmetry group"></a>Symmetry group</h2>
<br />
The symmetry group of the Hendrix diamond has 8 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></pre></div>

← Older revision		Revision as of 00:55, 4 August 2016
Line 1:		Line 1:
	<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 00:11:12 UTC</tt>.<br>		: This revision was by author [[User:Praimhin\|Praimhin]] and made on <tt>2016-08-04 00:55:52 UTC</tt>.<br>
	: The original revision id was <tt>~~588770760~~</tt>.<br>		: The original revision id was <tt>588771850</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>
Line 17:		Line 17:
	==Symmetry group==		==Symmetry group==

	The symmetry group of the Hendrix diamond has 8 elements. Its generators are:		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 → 7:6, 5:3, 14:9
	* 3:2, 5:4, 7:4 → 3:2, 15:14, 9:7		* 3:2, 5:4, 7:4 → 3:2, 15:14, 9:7
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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 8 elements. Its generators are:<br />		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></pre></div>		<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>