Cuthbert chords: Difference between revisions
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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 | 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. | * 1-13/11-7/5 with steps 13/11-13/11-10/7. | ||
There is an inversely related pair which | There is an inversely related pair which is 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 | * 1-11/10-13/11 with steps 11/10-14/13-22/13, and its inverse | ||
* 1-14/13-13/11 with steps 14/13-11/10-22/13. | * 1-14/13-13/11 with steps 14/13-11/10-22/13. | ||
They can be extended to the following inversely related tetrads: | 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 | * 1-13/11-14/11-7/5 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; | * 1-11/10-13/11-7/5 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 | * 1-13/11-13/10-7/5 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. | * 1-14/13-13/11-7/5 with steps 14/13-11/10-13/11-10/7. | ||
Then there are two inversely related pentads: | 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 | * 1-11/10-13/11-13/10-7/5 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. | * 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, | == 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]]. | * 1-13/11-7/5-[[5/3]] with steps of size 13/11-13/11-13/11-[[6/5]]. | ||