Lambeth chords: Difference between revisions
Jump to navigation
Jump to search
m Wording |
m +categories and improve wording |
||
| Line 1: | Line 1: | ||
A '''lambeth chord''' is an [[essentially tempered dyadic chord]] which is tempered by [[1573/1568]] | A '''lambeth chord''' is an [[essentially tempered dyadic chord]] which is tempered by the lambeth comma, [[1573/1568]]. | ||
There are three lambeth triads, including a | There are three lambeth triads in the 2.7.11.13 [[subgroup]] [[13-odd-limit]], including 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]]. | ||
| Line 22: | Line 22: | ||
* 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. | ||
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]] | ||
| Line 28: | Line 28: | ||
[[Category:Triad]] | [[Category:Triad]] | ||
[[Category:Tetrad]] | [[Category:Tetrad]] | ||
[[Category:Pentad]] | |||
[[Category:Lambeth]] | [[Category:Lambeth]] | ||
Revision as of 15:14, 28 April 2023
A lambeth chord is an essentially tempered dyadic chord which is tempered by the lambeth comma, 1573/1568.
There are three lambeth triads in the 2.7.11.13 subgroup 13-odd-limit, including 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 are two inversely related 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.