Lambeth chords: Difference between revisions

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

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

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.

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

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

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

And an inversely related pair:

* 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.

They can be extended to the following palindromic tetrads:

* 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 inversely related tetrads:

* 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.

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.

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]].

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:13-odd-limit]]

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-A '''lambeth chord''' is an [[essentially tempered dyadic chord]] which is tempered by the lambeth comma, [[1573/1568]].
+'''Lambeth chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the lambeth comma, [[1573/1568]].
 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.
-The three lambeth triads include a palindrome since it identifies [[13/8]] by a stack of two [[14/11]]'s:
+The three lambeth triads include a palindrome since it identifies [[13/8]] by a stack of two [[14/11]]s:
 * 1-14/11-13/8 with steps 14/11-14/11-[[16/13]].
 And an inversely related pair:
 * 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.
 They can be extended to the following palindromic tetrads:
 * 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 inversely related tetrads:
 * 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.
 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.
-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]].
+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:13-odd-limit]]