Cuthbert chords: Difference between revisions
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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 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 | ||
* | * 1–13/11–7/5 chord with steps of 13/11, 13/11, 10/7. | ||
There is an inversely related pair which is more squeezed and fit for a sort of secundal harmony: | 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 of 11/10, 14/13, 22/13, and its inverse | ||
* | * 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 | 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 | 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: | 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 }}. | 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 }}. | ||
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== Garibert 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, | 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]]. | 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]] | [[Category:13-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triads]] | [[Category:Triads]] | ||