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 14/11s:

• 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.