Lambeth chords: Difference between revisions
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And an inversely related pair: | And an inversely related pair: | ||
* 1-14/11-[[11/8]] with steps 14/11-[[14/13]]-[[16/11]], | * 1-14/11-[[11/8]] with steps 14/11-[[14/13]]-[[16/11]], and its inversion | ||
* 1-14/11 | * 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: | ||
* 1-13 | * 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]]. | * 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- | * 1-14/11-11/8-13/8 with steps 14/11-14/13-13/11-16/13, and its inversion | ||
* 1-13/11- | * 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, | * 1-14/11-13/8-7/4 with steps 14/11-14/11-14/13-8/7, and its inversion | ||
* 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 are two pentads: | Then there are two pentads: | ||
* 1-14/13-14/11-11/8-7/4 with steps 14/13-13/11-14/13-14/11-8/7, | * 1-14/13-14/11-11/8-7/4 with steps 14/13-13/11-14/13-14/11-8/7, and its inversion | ||
* 1-14/13-14/11-11/8-11/7 with steps 14/13-13/11-14/13-8/7-14/11. | |||
and its inversion | |||
* 1-14/13-14/11- | |||
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 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]]. | ||
Revision as of 13:10, 23 February 2023
A lambeth chord is an essentially tempered dyadic chord which is tempered by 1573/1568, the lambeth comma.
There are three lambeth triads, including a palindromic one 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 inversion
- 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 inversion
- 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 inversion
- 1-14/11-13/8-13/7 with steps 14/11-14/11-8/7-14/13.
Then there are two pentads:
- 1-14/13-14/11-11/8-7/4 with steps 14/13-13/11-14/13-14/11-8/7, and its inversion
- 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.