Cuthbert chords: Difference between revisions
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Revision as of 11:32, 11 May 2023
Cuthbert chords are essentially tempered dyadic chords 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
- 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:
- 1-11/10-13/11 with steps 11/10-14/13-22/13, and its inverse,
- 1-14/13-13/11 with steps 14/13-11/10-22/13.
They can be extended to the following inversely related tetrads:
- 1-13/11-14/11-7/5 with steps 13/11-14/13-11/10-10/7, and its inverse,
- 1-11/10-13/11-7/5 with steps 11/10-14/13-13/11-10/7;
- 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:
- 1-11/10-13/11-13/10-7/5 with steps 11/10-14/13-11/10-14/13-10/7, and its inverse,
- 1-14/13-13/11-14/11-7/5 with steps 14/13-11/10-14/13-11/10-10/7.
The first cuthbert triad can be extended to the garibert tetrad, which is the {275/273, 847/845} garibert tempering of a tetrad,
Equal temperaments with cuthbert triads include 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.