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Cuthbert chords: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
'''Cuthbert chords''' are [[essentially tempered dyadic chord]]s tempered by the cuthbert comma, [[847/845]].
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
 
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-28 01:33:06 UTC</tt>.<br>
Cuthbert chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1a]] in the 2.5.7.11.13 [[subgroup]] [[13-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.  
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The most basic cuthbert triad is a palindrome, consisting of two [[13/11]]'s making up [[7/5]], which implies tempering by cuthbert, the 847/845 comma. It is, in other words, the 847/845-tempered version of  
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
* 1–13/11–7/5 chord with steps of 13/11, 13/11, 10/7.
<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 //cuthbert triad// is an [[dyadic chord|essentially tempered dyadic triad]] which consists of two 13/11 thirds making up a 7/5, which implies tempering by cuthbert, the 847/845 comma. It is, in other words, the 847/845-tempered version of 1-13/11-7/5. Equal temperaments with cuthbert triads include 29, 33, 37, 41, 46, 50, 53, 58, 70, 87, 94, 99, 103, 111, 140, 190, 227, 264 and 388. </pre></div>
There is an inversely related pair which is more squeezed and fit for a sort of secundal harmony:
<h4>Original HTML content:</h4>
* 1–11/10–13/11 with steps of 11/10, 14/13, 22/13, and its inverse
<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;cuthbert triad&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;cuthbert triad&lt;/em&gt; is an &lt;a class="wiki_link" href="/dyadic%20chord"&gt;essentially tempered dyadic triad&lt;/a&gt; which consists of two 13/11 thirds making up a 7/5, which implies tempering by cuthbert, the 847/845 comma. It is, in other words, the 847/845-tempered version of 1-13/11-7/5. Equal temperaments with cuthbert triads include 29, 33, 37, 41, 46, 50, 53, 58, 70, 87, 94, 99, 103, 111, 140, 190, 227, 264 and 388.&lt;/body&gt;&lt;/html&gt;</pre></div>
* 1–14/13–13/11 with steps of 14/13, 11/10, 22/13.
 
They can be extended to the following tetrads, with two palindromic chords and two pairs of chords in inverse relationship. The palindromic tetrads are
* 1–11/10–13/11–13/10 chord with steps of 11/10, 14/13, 11/10, 20/13;
* 1–14/13–13/11–14/11 chord with steps of 14/13, 11/10, 14/13, 11/7.
 
The inversely related pairs of tetrads are
* 1–13/11–14/11–7/5 with steps of 13/11, 14/13, 11/10, 10/7, and its inverse
* 1–11/10–13/11–7/5 with steps of 11/10, 14/13, 13/11, 10/7;  
* 1–13/11–13/10–7/5 with steps of 13/11, 11/10, 14/13, 10/7, and its inverse
* 1–14/13–13/11–7/5 with steps of 14/13, 11/10, 13/11, 10/7.  
 
Then there is an inversely related pair of pentads:
* 1–11/10–13/11–13/10–7/5 with steps of 11/10, 14/13, 11/10, 14/13, 10/7, and its inverse
* 1–14/13–13/11–14/11–7/5 with steps of 14/13, 11/10, 14/13, 11/10, 10/7.  
 
Equal temperaments with cuthbert triads include {{Optimal ET sequence| 29, 33, 37, 41, 46, 50, 53, 58, 70, 87, 94, 99, 103, 111, 128, 140, 149, 177, 190, 198, 205, 227, 264, 284 and 388 }}.
 
== Garibert tetrad ==
The first cuthbert triad can be extended to the '''garibert tetrad''', which is the {[[275/273]], 847/845} garibert tempering of a tetrad,
* 1–13/11–7/5–[[5/3]] with steps of size 13/11, 13/11, 13/11, [[6/5]].
 
Equal temperaments with the garibert tetrad include {{Optimal ET sequence| 16, 29, 37, 41, 53 and 94 }}; and it is a characteristic chord of [[13-limit]] [[garibaldi temperament]].
 
[[Category:13-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Cuthbert]]
[[Category:Garibaldi]]
[[Category:Garibert]]
[[Category:Gassormic]]
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