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]]. | A '''lambeth chord''' is an [[essentially tempered dyadic chord]] which is 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 includes 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]]. | * 1-14/11-13/8 with steps 14/11-14/11-[[16/13]]. | ||
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* 1-14/11-13/8-13/7 with steps 14/11-14/11-8/7-14/13. | * 1-14/11-13/8-13/7 with steps 14/11-14/11-8/7-14/13. | ||
Then there | 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 | * 1-14/13-14/11-11/8-7/4 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. | * 1-14/13-14/11-11/8-11/7 with steps 14/13-13/11-14/13-8/7-14/11. | ||
Revision as of 03:55, 27 July 2023
A lambeth chord is an essentially tempered dyadic chord which is 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 includes 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 26, 29, 31, 43, 46, 68, 72, 80, 94, 103, 111, 118f, 140, 183, 212, and 323, with 323edo giving the optimal patent val.