User:AthiTrydhen/11-Hendrix diamond: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The '''11-Hendrix diamond''' is the tonality diamond generated from the ratios 1/1, 5/4, 11/8, 3/2 and 11/6.
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 01:29:42 UTC</tt>.<br>
: The original revision id was <tt>588772216</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 **11-****Hendrix diamond** is the tonality diamond generated from the ratios 1/1, 5/4, 11/8, 3/2 and 11/6.
||~  ||~  ||~  ||~  ||~  ||~  ||
||~  || 1/1 || 5/4 || 11/8 || 3/2 || 11/6 ||
||~  || 8/5 || 1/1 || 11/10 || 6/5 || 22/15 ||
||~  || 16/11 || 20/11 || 1/1 || 12/11 || 4/3 ||
||~  || 4/3 || 5/3 || 11/6 || 1/1 || 11/9 ||
||~  || 12/11 || 15/11 || 3/2 || 18/11 || 1/1 ||
All notes in the Hendrix diamond are also found in the [[15-limit tonality diamond]], because 1/1:5/4:11/8:3/2:11/6 is a 15-limit [[Anomalous Saturated Suspensions|anomalous saturated suspension]].


==Symmetry group==  
{| class="wikitable"
|-
! |
! |
! |
! |
! |
! |
|-
! |
| | 1/1
| | 5/4
| | 11/8
| | 3/2
| | 11/6
|-
! |
| | 8/5
| | 1/1
| | 11/10
| | 6/5
| | 22/15
|-
! |
| | 16/11
| | 20/11
| | 1/1
| | 12/11
| | 4/3
|-
! |
| | 4/3
| | 5/3
| | 11/6
| | 1/1
| | 11/9
|-
! |
| | 12/11
| | 15/11
| | 3/2
| | 18/11
| | 1/1
|}
All notes in the Hendrix diamond are also found in the [[15-limit tonality diamond]], because 1/1:5/4:11/8:3/2:11/6 is a 15-limit [[anomalous saturated suspension]].
 
==Symmetry group==


The symmetry group of the 11-Hendrix diamond has 16 elements. Its generators are:
The symmetry group of the 11-Hendrix diamond has 16 elements. Its generators are:
* 3:2, 5:4, 11:8 → 11:6, 5:3, 11:9
* 3:2, 5:4, 11:8 → 3:2, 15:11, 18:11
* 3:2, 5:4, 11:8 → 4:3, 8:5, 16:11
===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">&lt;html&gt;&lt;head&gt;&lt;title&gt;11-Hendrix diamond&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;strong&gt;11-&lt;/strong&gt;&lt;strong&gt;Hendrix diamond&lt;/strong&gt; is the tonality diamond generated from the ratios 1/1, 5/4, 11/8, 3/2 and 11/6.&lt;br /&gt;


<ul><li>3:2, 5:4, 11:8 → 11:6, 5:3, 11:9</li><li>3:2, 5:4, 11:8 → 3:2, 15:11, 18:11</li><li>3:2, 5:4, 11:8 → 4:3, 8:5, 16:11</li></ul>


&lt;table class="wiki_table"&gt;
===Orbits and Invariant Subsets===
    &lt;tr&gt;
[to be included]
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/6&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;td&gt;8/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;22/15&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;td&gt;16/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;td&gt;12/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


All notes in the Hendrix diamond are also found in the &lt;a class="wiki_link" href="/15-limit%20tonality%20diamond"&gt;15-limit tonality diamond&lt;/a&gt;, because 1/1:5/4:11/8:3/2:11/6 is a 15-limit &lt;a class="wiki_link" href="/Anomalous%20Saturated%20Suspensions"&gt;anomalous saturated suspension&lt;/a&gt;.&lt;br /&gt;
[[Category:Diamond]]
&lt;br /&gt;
[[Category:Hendrix]]
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Symmetry group"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Symmetry group&lt;/h2&gt;
&lt;br /&gt;
The symmetry group of the 11-Hendrix diamond has 16 elements. Its generators are:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;3:2, 5:4, 11:8 → 11:6, 5:3, 11:9&lt;/li&gt;&lt;li&gt;3:2, 5:4, 11:8 → 3:2, 15:11, 18:11&lt;/li&gt;&lt;li&gt;3:2, 5:4, 11:8 → 4:3, 8:5, 16:11&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Symmetry group-Orbits and Invariant Subsets"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Orbits and Invariant Subsets&lt;/h3&gt;
[to be included]&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 05:47, 14 December 2024

The 11-Hendrix diamond is the tonality diamond generated from the ratios 1/1, 5/4, 11/8, 3/2 and 11/6.

1/1 5/4 11/8 3/2 11/6
8/5 1/1 11/10 6/5 22/15
16/11 20/11 1/1 12/11 4/3
4/3 5/3 11/6 1/1 11/9
12/11 15/11 3/2 18/11 1/1

All notes in the Hendrix diamond are also found in the 15-limit tonality diamond, because 1/1:5/4:11/8:3/2:11/6 is a 15-limit anomalous saturated suspension.

Symmetry group

The symmetry group of the 11-Hendrix diamond has 16 elements. Its generators are:

  • 3:2, 5:4, 11:8 → 11:6, 5:3, 11:9
  • 3:2, 5:4, 11:8 → 3:2, 15:11, 18:11
  • 3:2, 5:4, 11:8 → 4:3, 8:5, 16:11

Orbits and Invariant Subsets

[to be included]

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