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

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

• 1–9/8–9/7–3/2–7/4 with steps 9/8, 8/7, 7/6, 7/6, 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

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

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