Lambeth chords: Difference between revisions

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A '''~~lambeth chord~~''' ~~is an~~ [[essentially tempered ~~dyadic chord~~]] ~~which is~~ tempered by [[1573/1568]]~~, the lambeth comma~~.

'''Lambeth chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the lambeth comma, [[1573/1568]].

~~The lambeth triad consists~~ of ~~a stack of two~~ [[14/11]]~~'s followed by~~ [[~~16/13~~]]:

Lambeth chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1b]] in the 2.7.11.13 [[subgroup]] [[13-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.

* 1-14/11-[[13/8]] ~~with steps 14/11-14/~~11~~-16/13~~.

~~This can be extended to tetrads as~~

The three lambeth triads include a palindrome since it identifies [[13/8]] by a stack of two [[14/11]]'s:

* 1-13/~~11-~~14/11~~-13~~/8 with steps 13/11~~-14/13-~~14/11-16/13,

* 1–14/11–13/8 with steps 14/11, 14/11, [[16/13]].

~~and its inversion,~~

And an inversely related pair:

* ~~1-13~~/~~11-16/11-~~[[13/7]] with steps ~~13/11-16/13-~~14/11-[[14/13]],

* 1–14/11–[[11/8]] with steps 14/11, [[14/13]], [[16/11]], and its inverse

* 1–14/13–11/8 with steps 14/13, 14/11, 16/11.

~~as well as~~

They can be extended to the following palindromic tetrads:

* 1-14/11-13/8-[[7/4]] with steps 14/11-14/~~11-~~14/~~13-~~[[8/7]],

* 1–14/13–14/11–11/8 with steps 14/13, 13/11, 14/13, 16/11;

* 1–14/11–11/8–[[7/4]] with steps 14/11, 14/13, 14/11, [[8/7]].

and its ~~inversion~~,

And inversely related tetrads:

* 1-14/11-13/~~8-13~~/7 with steps 14/11-14/11-8/7-14/13.

* 1–14/11–11/8–13/8 with steps 14/11, 14/13, 13/11, 16/13, and its inverse

* 1–13/11–14/11–13/8 with steps 13/11, 14/13, 14/11, 16/13;

* 1–14/11–13/8–7/4 with steps 14/11, 14/11, 14/13, 8/7, and its inverse

* 1–14/11–13/8–13/7 with steps 14/11, 14/11, 8/7, 14/13.

~~Equal temperaments~~ with ~~these chords include {{EDOs| 26~~, 29, 31, 43, 46, ~~68, 72, 80~~, 94, ~~103~~, ~~111~~, ~~118f, 140, 183, 212, and 323}}, with 323edo giving the [[optimal patent val]]~~.

Then there is an inversely related pair of pentads:

* 1–14/13–14/11–11/8–7/4 with steps 14/13, 13/11, 14/13, 14/11, 8/7, and its inverse

* 1–14/13–14/11–11/8–11/7 with steps 14/13, 13/11, 14/13, 8/7, 14/11.

[[Category:13-odd-limit]]

Equal temperaments with lambeth chords include {{Optimal ET sequence| 26, 29, 31, 43, 46, 68, 72, 80, 94, 103, 111, 118f, 140, 183, 212 and 323 }}, with 323edo giving the [[optimal patent val]].

~~[[Category:Chords~~]]

[[Category:13-odd-limit chords]]

[[Category:Essentially tempered chords]]

[[Category:~~Triad~~]]

[[Category:Triads]]

[[Category:~~Tetrad~~]]

[[Category:Tetrads]]

[[Category:Pentads]]

[[Category:Lambeth]]

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-A '''lambeth chord''' is an [[essentially tempered dyadic chord]] which is tempered by [[1573/1568]], the lambeth comma.
+'''Lambeth chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the lambeth comma, [[1573/1568]].
-The lambeth triad consists of a stack of two [[14/11]]'s followed by [[16/13]]:
+Lambeth chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1b]] in the 2.7.11.13 [[subgroup]] [[13-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.
-* 1-14/11-[[13/8]] with steps 14/11-14/11-16/13.
-This can be extended to tetrads as
+The three lambeth triads include a palindrome since it identifies [[13/8]] by a stack of two [[14/11]]'s:
-* 1-13/11-14/11-13/8 with steps 13/11-14/13-14/11-16/13,
+* 1–14/11–13/8 with steps 14/11, 14/11, [[16/13]].
-and its inversion,
+And an inversely related pair:
-* 1-13/11-16/11-[[13/7]] with steps 13/11-16/13-14/11-[[14/13]],
+* 1–14/11–[[11/8]] with steps 14/11, [[14/13]], [[16/11]], and its inverse
+* 1–14/13–11/8 with steps 14/13, 14/11, 16/11.
-as well as
+They can be extended to the following palindromic tetrads:
-* 1-14/11-13/8-[[7/4]] with steps 14/11-14/11-14/13-[[8/7]],
+* 1–14/13–14/11–11/8 with steps 14/13, 13/11, 14/13, 16/11;
+* 1–14/11–11/8–[[7/4]] with steps 14/11, 14/13, 14/11, [[8/7]].
-and its inversion,
+And inversely related tetrads:
-* 1-14/11-13/8-13/7 with steps 14/11-14/11-8/7-14/13.
+* 1–14/11–11/8–13/8 with steps 14/11, 14/13, 13/11, 16/13, and its inverse
+* 1–13/11–14/11–13/8 with steps 13/11, 14/13, 14/11, 16/13;
+* 1–14/11–13/8–7/4 with steps 14/11, 14/11, 14/13, 8/7, and its inverse
+* 1–14/11–13/8–13/7 with steps 14/11, 14/11, 8/7, 14/13.
-Equal temperaments with these chords include {{EDOs| 26, 29, 31, 43, 46, 68, 72, 80, 94, 103, 111, 118f, 140, 183, 212, and 323}}, with 323edo giving the [[optimal patent val]].
+Then there is an inversely related pair of pentads:
+* 1–14/13–14/11–11/8–7/4 with steps 14/13, 13/11, 14/13, 14/11, 8/7, and its inverse
+* 1–14/13–14/11–11/8–11/7 with steps 14/13, 13/11, 14/13, 8/7, 14/11.
-[[Category:13-odd-limit]]
+Equal temperaments with lambeth chords include {{Optimal ET sequence| 26, 29, 31, 43, 46, 68, 72, 80, 94, 103, 111, 118f, 140, 183, 212 and 323 }}, with 323edo giving the [[optimal patent val]].
-[[Category:Chords]]
+[[Category:13-odd-limit chords]]
 [[Category:Essentially tempered chords]]
-[[Category:Triad]]
+[[Category:Triads]]
-[[Category:Tetrad]]
+[[Category:Tetrads]]
+[[Category:Pentads]]
 [[Category:Lambeth]]