Lambeth chords: Difference between revisions
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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. | 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: | 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: | 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: | 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: | 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 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]]. | 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]] | [[Category:13-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triads]] | [[Category:Triads]] | ||
Latest revision as of 13:55, 19 March 2025
Lambeth chords are essentially tempered chords tempered by the lambeth comma, 1573/1568.
Lambeth chords are of 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:
- 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 lambeth chords include 26, 29, 31, 43, 46, 68, 72, 80, 94, 103, 111, 118f, 140, 183, 212 and 323, with 323edo giving the optimal patent val.