Cuthbert chords: Difference between revisions

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~~The~~ '''~~cuthbert triad~~''' ~~is an~~ [[~~Dyadic_chord|~~essentially tempered dyadic ~~triad~~]] ~~which consists~~ of ~~two~~ [[13/11|13/11]] ~~thirds~~ making up a [[~~7/5|~~7/5]], which implies tempering by [[cuthbert~~|cuthbert]]~~, the [[847/845~~|847/845]]~~ comma. It is, in other words, the 847/845-tempered version of 1-13/11-7/5. ~~The cuthbert triad~~ can be extended to the ~~[[garibert_tetrad|garibert tetrad]]~~, ~~which is the {275~~/~~273~~, ~~847~~/~~845} garibert tempering~~ of ~~a tetrad~~ with steps of ~~size~~ 13/11-13/11-13/11~~-[[6~~/5|6/5]], ~~leading to a garibert tempering of 1-~~13/11-7/5~~-[[~~5/~~3|5~~/~~3]]~~. Equal temperaments with cuthbert triads include ~~[[29edo~~|~~29edo]]~~, ~~[[33edo|33edo]]~~, ~~[[37edo|37edo]]~~, ~~[[41edo|41edo]]~~, ~~[[46edo|46edo]]~~, ~~[[50edo|50edo]]~~, ~~[[53edo|53edo]]~~, ~~[[58edo|58edo]]~~, ~~[[70edo|70edo]]~~, ~~[[87edo|87edo]]~~, ~~[[94edo|94edo]]~~, ~~[[99edo|99edo]]~~, ~~[[103edo|103edo]]~~, [[~~111edo|111edo~~]], ~~[[128edo|128edo]]~~, [[~~140edo|140edo~~]], ~~[[149edo|149edo]]~~, ~~[[177edo|177edo]]~~, [[~~190edo|190edo~~]]~~, 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|~~13-limit]] [[~~Schismatic_family#Garibaldi|~~garibaldi temperament]].

'''Cuthbert chords''' are [[essentially tempered dyadic chord]]s tempered by the cuthbert comma, [[847/845]].

[[Category:13-limit]]

[[Category:~~chord~~]]

Cuthbert chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1a]] in the 2.5.7.11.13 [[subgroup]] [[13-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.

[[Category:~~cuthbert~~]]

[[Category:~~dyadic~~]]

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

[[Category:~~garibaldi~~]]

* 1–13/11–7/5 chord with steps of 13/11, 13/11, 10/7.

[[Category:~~garibert~~]]

[[Category:~~gassorma~~]]

There is an inversely related pair which is more squeezed and fit for a sort of secundal harmony:

[[Category:~~triad~~]]

* 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

* 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

* 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:

* 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 }}.

== 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]].

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 chords]]

[[Category:Essentially tempered chords]]

[[Category:Triads]]

[[Category:Tetrads]]

[[Category:Pentads]]

[[Category:Cuthbert]]

[[Category:Garibaldi]]

[[Category:Garibert]]

[[Category:Gassormic]]

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-The '''cuthbert triad''' is an [[Dyadic_chord|essentially tempered dyadic triad]] which consists of two [[13/11|13/11]] thirds making up a [[7/5|7/5]], which implies tempering by [[cuthbert|cuthbert]], the [[847/845|847/845]] comma. It is, in other words, the 847/845-tempered version of 1-13/11-7/5. The cuthbert triad can be extended to the [[garibert_tetrad|garibert tetrad]], which is the {275/273, 847/845} garibert tempering of a tetrad with steps of size 13/11-13/11-13/11-[[6/5|6/5]], leading to a garibert tempering of 1-13/11-7/5-[[5/3|5/3]]. Equal temperaments with cuthbert triads include [[29edo|29edo]], [[33edo|33edo]], [[37edo|37edo]], [[41edo|41edo]], [[46edo|46edo]], [[50edo|50edo]], [[53edo|53edo]], [[58edo|58edo]], [[70edo|70edo]], [[87edo|87edo]], [[94edo|94edo]], [[99edo|99edo]], [[103edo|103edo]], [[111edo|111edo]], [[128edo|128edo]], [[140edo|140edo]], [[149edo|149edo]], [[177edo|177edo]], [[190edo|190edo]], 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|13-limit]] [[Schismatic_family#Garibaldi|garibaldi temperament]].
+'''Cuthbert chords''' are [[essentially tempered dyadic chord]]s tempered by the cuthbert comma, [[847/845]].
-[[Category:13-limit]]
-[[Category:chord]]
+Cuthbert chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1a]] in the 2.5.7.11.13 [[subgroup]] [[13-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.
-[[Category:cuthbert]]
-[[Category:dyadic]]
+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
-[[Category:garibaldi]]
+* 1–13/11–7/5 chord with steps of 13/11, 13/11, 10/7.
-[[Category:garibert]]
-[[Category:gassorma]]
+There is an inversely related pair which is more squeezed and fit for a sort of secundal harmony:
-[[Category:triad]]
+* 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
+* 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
+* 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:
+* 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 }}.
+== 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]].
+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 chords]]
+[[Category:Essentially tempered chords]]
+[[Category:Triads]]
+[[Category:Tetrads]]
+[[Category:Pentads]]
+[[Category:Cuthbert]]
+[[Category:Garibaldi]]
+[[Category:Garibert]]
+[[Category:Gassormic]]