Mothwellsmic chords

Mothwellsmic chords are essentially tempered chords tempered by the mothwellsma, 99/98.

There are one triad, six tetrads and four pentads as 2.3.7.11 subgroup 11-odd-limit essentially tempered chords.

The mothwellsmic triad consists of a stack of two 7/6's and 16/11 closing at the octave:

• 1-7/6-11/8 with steps 7/6-7/6-16/11.

For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are

• 1-11/8-11/7-7/4 with steps 11/8-8/7-9/8-8/7;
• 1-7/6-9/7-3/2 with steps 7/6-12/11-7/6-4/3.

The inversely related pairs of chords are

• 1-7/6-11/8-3/2 with steps 7/6-7/6-12/11-4/3, and its inverse
• 1-7/6-11/8-11/6 with steps 7/6-7/6-4/3-12/11;
• 1-7/6-11/8-7/4 with steps 7/6-7/6-9/7-8/7, and its inverse
• 1-7/6-11/8-11/7 with steps 7/6-7/6-8/7-9/7.

For pentads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are

• 1-7/6-11/8-11/7-7/4 with steps 7/6-7/6-8/7-9/8-8/7;
• 1-7/6-11/8-3/2-11/6 with steps 7/6-7/6-12/11-11/9-12/11.

The inversely related pair of chords is

• 1-7/6-11/8-3/2-7/4 with steps 7/6-7/6-12/11-7/6-8/7, and its inverse
• 1-7/6-11/8-11/7-11/6 with steps 7/6-7/6-8/7-7/6-12/11.

Equal divisions with mothwellsmic chords include 22edo, 31edo, 53edo, 96edo and 127edo.