Charismic chords

Diasemismic chords are essentially tempered dyadic chords tempered by the diasemisma, 256/255.

The diasemismic temperament contains many possibilities for essentially tempered dyadic chords including two triads and twelve tetrads in the 17-odd-limit of the 2.3.5.17 subgroup.

The two diasemismic triads are in inverse relationship:

• 1-5/4-24/17 with steps of 5/4-9/8-17/12;
• 1-9/8-24/17 with steps of 9/8-5/4-17/12.

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

• 1-5/4-24/17-30/17 with steps of 5/4-9/8-5/4-17/15;
• 1-9/8-5/4-24/17 with steps of 9/8-10/9-9/8-17/12;
• 1-16/15-4/3-17/12 with steps of 16/15-5/4-16/15-24/17;
• 1-16/15-9/8-6/5 with steps of 16/15-18/17-16/15-5/3.

The inversely related pairs of chords are

• 1-5/4-24/17-15/8 with steps of 5/4-9/8-4/3-16/15 and its inverse 1-4/3-3/2-15/8 with steps of 4/3-9/8-5/4-16/15;
• 1-5/4-24/17-3/2 with steps of 5/4-9/8-16/15-4/3 and its inverse 1-16/15-6/5-3/2 with steps of 16/15-9/8-5/4-4/3;
• 1-5/4-4/3-24/17 with steps of 5/4-16/15-18/17-17/12 and its inverse 1-18/17-9/8-24/17 with steps of 18/17-16/15-5/4-17/12;
• 1-20/17-5/4-24/17 with steps 20/17-16/15-9/8-17/12 and its inverse 1-9/8-6/5-24/17 with steps of 9/8-16/15-20/17-17/12.

Remarkable hexads include a palindromic chord:

• 1-9/8-5/4-24/17-3/2-15/8 with steps of 9/8-10/9-9/8-16/15-5/4-16/15.

Equal temperaments with diasemismic chords include 7, 9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111.