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. | 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- | * 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]], | |||
* 1-14/11-[[13/7]] with steps 14/11-16/11-14/13. | |||
They can be extended to the following palindromic tetrads: | |||
* 1-13/11-14/11-13/7 with steps 13/11-14/13-16/11-14/13, | |||
* 1-14/11-11/8-[[7/4]] with steps 14/11-14/13-14/11-[[8/7]]. | |||
And inversely related tetrads: | |||
* 1-13/11-14/11-13/8 with steps 13/11-14/13-14/11-16/13, | * 1-13/11-14/11-13/8 with steps 13/11-14/13-14/11-16/13, | ||
* 1-13/11-16/11-13/7 with steps 13/11-16/13-14/11-14/13, | |||
* 1-14/11-13/8-7/4 with steps 14/11-14/11-14/13-8/7, | |||
* 1-14/11-13/8-13/7 with steps 14/11-14/11-8/7-14/13. | |||
Then there are two pentads: | |||
* 1- | * 1-14/13-14/11-11/8-7/4 with steps 14/13-13/11-14/13-14/11-8/7, | ||
and its inversion, | and its inversion, | ||
* 1-14/11-13/8- | * 1-14/13-14/11-13/8-11/7 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 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]]. | ||
[[Category:13-odd-limit]] | [[Category:13-odd-limit]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triad]] | [[Category:Triad]] | ||
[[Category:Tetrad]] | [[Category:Tetrad]] | ||
[[Category:Lambeth]] | [[Category:Lambeth]] | ||
Revision as of 13:59, 5 February 2022
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:
They can be extended to the following palindromic tetrads:
- 1-13/11-14/11-13/7 with steps 13/11-14/13-16/11-14/13,
- 1-14/11-11/8-7/4 with steps 14/11-14/13-14/11-8/7.
And inversely related tetrads:
- 1-13/11-14/11-13/8 with steps 13/11-14/13-14/11-16/13,
- 1-13/11-16/11-13/7 with steps 13/11-16/13-14/11-14/13,
- 1-14/11-13/8-7/4 with steps 14/11-14/11-14/13-8/7,
- 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,
- 1-14/13-14/11-13/8-11/7 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.