Major minthmic chords

Minthmic chords are essentially tempered dyadic chords in the 13-limit rank-5 temperament, and in addition the rank-3 2.3.11.13 subgroup temperament, tempering out the minthma, 352/351.

We have two pairs of inversely related minthmic triads, all involving the perfect fifth:

• 1-11/9-3/2 with steps 11/9-16/13-4/3, and its inverse
• 1-16/13-3/2 with steps 16/13-11/9-4/3;
• 1-3/2-16/9 with steps 3/2-13/11-9/8, and its inverse
• 1-3/2-22/13 with steps 3/2-9/8-13/11.

For tetrads, first there is the palindrome, a sus2sus4 chord with the m3 serving a nice ~13/11:

• 1-9/8-4/3-3/2 with steps 9/8-13/11-9/8-4/3.

Then there are inversely related pairs that are concatenations of the triads:

• 1-11/9-3/2-16/9 with steps 11/9-16/13-13/11-9/8, and its inverse
• 1-16/13-3/2-22/13 with steps 16/13-11/9-9/8-13/11;
• 1-11/9-3/2-22/13 with steps 11/9-16/13-9/8-13/11, and its inverse
• 1-16/13-3/2-16/9 with steps 16/13-11/9-13/11-9/8.

As well as

• 1-3/2-13/8-11/6 with steps 3/2-13/12-9/8-12/11, and its inverse
• 1-3/2-18/11-16/9 with steps 3/2-12/11-13/12-9/8.

If we add prime 7 to the mix, we additionally get

• 1-11/9-3/2-7/4 with steps 11/9-16/13-7/6-8/7, and its inverse
• 1-16/13-3/2-12/7 with steps 16/13-11/9-8/7-7/6;
• 1-11/9-3/2-12/7, withs steps 11/9-16/13-8/7-7/6, and its inverse
• 1-16/13-3/2-7/4 with steps 16/13-11/9-7/6-8/7.

Note that tempering 1-11/9-3/2-7/4 and 1-11/9-3/2-12/7 in jove is also possible, leading to a similar but not identical chord.

Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of, and minthmic tempering has the slightly sharp, minty-fresh fifths some people appreciate (Margo Schulter has expressed great fondness for this comma, for example.) Equal temperaments with minthmic chords include 22, 29, 46, 53, 80, 87, 111, 121, 140, 198 and 205.