Huntmic chords

Huntmic chords are essentially tempered chords tempered by the huntma, 640/637.

There are three triads, six tetrads and two pentads as 2.5.7.13 subgroup 13-odd-limit essentially tempered chords.

For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is

• 1-8/7-13/10 chord with steps of 8/7-8/7-20/13.

The inversely related pair of chords is

• 1-16/13-7/5 with steps of 16/13-8/7-10/7, and its inverse
• 1-8/7-7/5 with steps of 8/7-16/13-10/7.

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

• 1-16/13-7/5-7/4 chord with steps of 16/13-8/7-5/4-8/7;
• 1-8/7-16/13-7/5 chord with steps of 8/7-14/13-8/7-10/7.

The inversely related pairs of chords are

• 1-5/4-10/7-13/8 with steps of 5/4-8/7-8/7-16/13, and its inverse
• 1-8/7-13/10-13/8 with steps of 8/7-8/7-5/4-16/13;
• 1-8/7-13/10-13/7 with steps of 8/7-8/7-10/7-14/13, and its inverse
• 1-8/7-13/10-7/5 with steps of 8/7-8/7-14/13-10/7.

They can be extended to pentads:

• 1-8/7-10/7-13/8-7/4 with steps of 8/7-5/4-8/7-14/13-8/7, and its inverse
• 1-8/7-16/13-7/5-7/4 with steps of 8/7-14/13-8/7-5/4-8/7.

Equal temperaments with huntmic chords include 22, 53, 68, 80, 94, 111, 121, 137, 205 and 215. The name huntmic comes from the fact that the optimal patent val for huntmic temperament is 205edo, the basis of the Hunt System of Aaron Andrew Hunt.