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'''Cuthbert chords''' are [[essentially tempered dyadic chord]]s tempered by the cuthbert comma, [[847/845]].  
'''Cuthbert chords''' are [[essentially tempered dyadic chord]]s tempered by the cuthbert comma, [[847/845]].  


The most typical cuthbert triad is a palindrome in the 2.5.7.11.13 [[subgroup]] [[13-odd-limit]], 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  
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.  
* 1-13/11-7/5 with steps 13/11-13/11-10/7.


There is an inversely related pair which are more squeezed and fit for a sort of secundal harmony:
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
* 1-11/10-13/11 with steps 11/10-14/13-22/13, and its inverse,  
* 1–13/11–7/5 chord with steps of 13/11, 13/11, 10/7.  
* 1-14/13-13/11 with steps 14/13-11/10-22/13.  


They can be extended to the following inversely related tetrads:  
There is an inversely related pair which is more squeezed and fit for a sort of secundal harmony:  
* 1-13/11-14/11-7/5 with steps 13/11-14/13-11/10-10/7, and its inverse,
* 1–11/10–13/11 with steps of 11/10, 14/13, 22/13, and its inverse  
* 1-11/10-13/11-7/5 with steps 11/10-14/13-13/11-10/7;
* 1–14/13–13/11 with steps of 14/13, 11/10, 22/13.  
* 1-13/11-13/10-7/5 with steps 13/11-11/10-14/13-10/7, and its inverse,
* 1-14/13-13/11-7/5 with steps 14/13-11/10-13/11-10/7.  


Then there are two inversely related pentads:
They can be extended to the following tetrads, with two palindromic chords and two pairs of chords in inverse relationship. The palindromic tetrads are  
* 1-11/10-13/11-13/10-7/5 with steps 11/10-14/13-11/10-14/13-10/7, and its inverse,
* 1–11/10–13/11–13/10 chord with steps of 11/10, 14/13, 11/10, 20/13;
* 1-14/13-13/11-14/11-7/5 with steps 14/13-11/10-14/13-11/10-10/7.  
* 1–14/13–13/11–14/11 chord with steps of 14/13, 11/10, 14/13, 11/7.


The first cuthbert triad can be extended to the '''garibert tetrad''', which is the {275/273, 847/845} garibert tempering of a tetrad,  
The inversely related pairs of tetrads are
* 1-13/11-7/5-[[5/3]] with steps of size 13/11-13/11-13/11-[[6/5]].  
* 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.  


Equal temperaments with cuthbert triads include {{EDOs| 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 }}. Equal temperaments with garibert tetrads include 41, 53, and 94; and it is a characteristic chord of [[13-limit]] [[garibaldi temperament]].
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.  


[[Category:13-odd-limit]]
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:Essentially tempered chords]]
[[Category:Triad]]
[[Category:Triads]]
[[Category:Tetrad]]
[[Category:Tetrads]]
[[Category:Pentad]]
[[Category:Pentads]]
[[Category:Cuthbert]]
[[Category:Cuthbert]]
[[Category:Garibaldi]]
[[Category:Garibaldi]]
[[Category:Garibert]]
[[Category:Garibert]]
[[Category:Gassormic]]
[[Category:Gassormic]]
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