Lambeth chords

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.