Cuthbert chords: Difference between revisions

Line 1:

~~The~~ '''~~cuthbert triad~~''' ~~is an~~ [[~~Dyadic chord|~~essentially tempered dyadic ~~triad~~]] ~~which consists of two [[13/11]] thirds making up a [[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 [[essentially tempered dyadic chord]]s tempered by the cuthbert comma, [[847/845]].

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

The cuthbert triad can be extended to the '''garibert tetrad''', which is the {275/273, 847/845} garibert tempering of a tetrad,

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,

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

Line 10:

Line 26:

[[Category:Essentially tempered chords]]

[[Category:Triad]]

[[Category:Tetrad]]

[[Category:Pentad]]

[[Category:Cuthbert]]

[[Category:Garibaldi]]

[[Category:Garibert]]

[[Category:Gassormic]]

@@ Line 1: / Line 1: @@
-The '''cuthbert triad''' is an [[Dyadic chord|essentially tempered dyadic triad]] which consists of two [[13/11]] thirds making up a [[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 [[essentially tempered dyadic chord]]s tempered by the cuthbert comma, [[847/845]].
-* 1-13/11-7/5, with steps 13/11-13/11-7/5.
-The cuthbert triad can be extended to the '''garibert tetrad''', which is the {275/273, 847/845} garibert tempering of a tetrad,
+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,
 * 1-13/11-7/5-[[5/3]] with steps of size 13/11-13/11-13/11-[[6/5]].
@@ Line 10: / Line 26: @@
 [[Category:Essentially tempered chords]]
 [[Category:Triad]]
+[[Category:Tetrad]]
+[[Category:Pentad]]
 [[Category:Cuthbert]]
 [[Category:Garibaldi]]
 [[Category:Garibert]]
 [[Category:Gassormic]]