User:AthiTrydhen/Hendrix diamond: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The '''Hendrix diamond''' is the tonality diamond generated from the ratios 1/1, 7/6, 5/4, 3/2 and 7/4.
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>
: The original revision id was <tt>588771850</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==  
{| class="wikitable"
|-
! |
! |
! |
! |
! |
! |
|-
! |
| | 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 suspension]].
 
==Symmetry group==


The symmetry group of the Hendrix diamond has 16 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 → 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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Hendrix diamond&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;strong&gt;Hendrix diamond&lt;/strong&gt; is the tonality diamond generated from the ratios 1/1, 7/6, 5/4, 3/2 and 7/4.&lt;br /&gt;


&lt;table class="wiki_table"&gt;
<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>
    &lt;tr&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;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;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;td&gt;12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&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;28/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/5&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;14/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;td&gt;8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/7&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 15-limit tonality diamond, because 1/1:7/6:5/4:3/2:7/4 is a 15-limit &lt;a class="wiki_link" href="/Anomalous%20Saturated%20Suspensions"&gt;anomalous saturated suspension&lt;/a&gt;.&lt;br /&gt;
===Orbits and Invariant Subsets===
&lt;br /&gt;
[to be included]
&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;
[[Category:Just intonation scales]]
&lt;br /&gt;
[[Category:Diamond]]
The symmetry group of the Hendrix diamond has 16 elements. Its generators are:&lt;br /&gt;
[[Category:Tables]]
&lt;ul&gt;&lt;li&gt;3:2, 5:4, 7:4 → 7:6, 5:3, 14:9&lt;/li&gt;&lt;li&gt;3:2, 5:4, 7:4 → 3:2, 15:14, 9:7&lt;/li&gt;&lt;li&gt;3:2, 5:4, 7:4 → 4:3, 8:5, 8:7&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Category:Todo:expand]]

Latest revision as of 05:46, 14 December 2024

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 suspension.

Symmetry group

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 → 3:2, 15:14, 9:7
  • 3:2, 5:4, 7:4 → 4:3, 8:5, 8:7

Orbits and Invariant Subsets

[to be included]

Retrieved from "https://en.xen.wiki/index.php?title=User:AthiTrydhen/Hendrix_diamond&oldid=170202"