# Cuthbert chords

Cuthbert chords are essentially tempered dyadic chords tempered by the cuthbert comma, 847/845.

Cuthbert chords are of pattern 1a in the 2.5.7.11.13 subgroup 13-odd-limit, meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.

The most basic cuthbert triad is a palindrome, consisting of two 13/11's making up 7/5, which implies tempering by cuthbert, the 847/845 comma. It is, in other words, the 847/845-tempered version of

• 1-13/11-7/5 with steps 13/11-13/11-10/7.

There is an inversely related pair which is more squeezed and fit for a sort of secundal harmony:

• 1-11/10-13/11 with steps 11/10-14/13-22/13, and its inverse
• 1-14/13-13/11 with steps 14/13-11/10-22/13.

They can be extended to the following tetrads, with two palindromic chords and two pairs of chords in inverse relationship. The palindromic tetrads are

• 1-11/10-13/11-13/10 chord with steps 11/10-14/13-11/10-20/13;
• 1-14/13-13/11-14/11 chord with steps 14/13-11/10-14/13-11/7.

The inversely related pairs of tetrads are

• 1-13/11-14/11-7/5 with steps 13/11-14/13-11/10-10/7, and its inverse
• 1-11/10-13/11-7/5 with steps 11/10-14/13-13/11-10/7;
• 1-13/11-13/10-7/5 with steps 13/11-11/10-14/13-10/7, and its inverse
• 1-14/13-13/11-7/5 with steps 14/13-11/10-13/11-10/7.

Then there is an inversely related pair of pentads:

• 1-11/10-13/11-13/10-7/5 with steps 11/10-14/13-11/10-14/13-10/7, and its inverse
• 1-14/13-13/11-14/11-7/5 with steps 14/13-11/10-14/13-11/10-10/7.