User:AthiTrydhen/13-Hendrix diamond: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The '''13-Hendrix diamond''' is the tonality diamond generated from the ratios 1/1, 13/12, 5/4, 3/2 and 13/8.
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==
{| class="wikitable"
|-
! |
! |
! |
! |
! |
! |
|-
! |
| | 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 suspension]].


The symmetry group of the Hendrix diamond has 16 elements. Its generators are:
==Symmetry group==
* 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===
The symmetry group of the 13-Hendrix diamond has 16 elements. Its generators are:
[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;13-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, 13/12, 5/4, 3/2 and 13/8.&lt;br /&gt;


<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>


&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;13/12&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;13/8&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;td&gt;24/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/13&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;26/15&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;13/10&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;13/9&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;13/12&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;td&gt;16/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;24/13&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 1/1:13/12:5/4:3/2:13/8 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 Hendrix diamond has 16 elements. Its generators are:&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;3:2, 5:4, 13:8 → 13:12, 5:3, 13:9&lt;/li&gt;&lt;li&gt;3:2, 5:4, 13:8 → 3:2, 15:13, 18:13&lt;/li&gt;&lt;li&gt;3:2, 5:4, 13:8 → 4:3, 8:5, 16:13&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 05:46, 14 December 2024

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
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 suspension.

Symmetry group

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 → 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]

Retrieved from "https://en.xen.wiki/index.php?title=User:AthiTrydhen/13-Hendrix_diamond&oldid=170204"