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

* 1-13/11-7/5 with steps 13/11-13/11-10/7.

* 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:

* 1-11/10-13/11 with steps 11/10-14/13-22/13, and its inverse

* 1-11/10-13/11 with steps of 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 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 11/10-14/13-11/10-20/13;

* 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 14/13-11/10-14/13-11/7.

* 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 13/11-14/13-11/10-10/7, and its inverse

* 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 11/10-14/13-13/11-10/7;

* 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 13/11-11/10-14/13-10/7, and its inverse

* 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 14/13-11/10-13/11-10/7.

* 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 11/10-14/13-11/10-14/13-10/7, and its inverse

* 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 14/13-11/10-14/13-11/10-10/7.

* 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 ==

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* 1-13/11-7/5-[[5/3]] with steps of size 13/11-13/11-13/11-[[6/5]].

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]].

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]]

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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
-* 1-13/11-7/5 with steps 13/11-13/11-10/7.
+* 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:
-* 1-11/10-13/11 with steps 11/10-14/13-22/13, and its inverse
+* 1-11/10-13/11 with steps of 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 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 11/10-14/13-11/10-20/13;
+* 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 14/13-11/10-14/13-11/7.
+* 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 13/11-14/13-11/10-10/7, and its inverse
+* 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 11/10-14/13-13/11-10/7;
+* 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 13/11-11/10-14/13-10/7, and its inverse
+* 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 14/13-11/10-13/11-10/7.
+* 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 11/10-14/13-11/10-14/13-10/7, and its inverse
+* 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 14/13-11/10-14/13-11/10-10/7.
+* 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 ==
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 * 1-13/11-7/5-[[5/3]] with steps of size 13/11-13/11-13/11-[[6/5]].
-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]].
+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]]