Biyatismic chords

Biyatismic chords are essentially tempered dyadic chords tempered by the biyatisma, 121/120.

Biyatismic temperament contains many possibilities for essentially tempered dyadic chords including five triad in the 2.3.5.11 subgroup.

The biyatismic triads consist of a palindromic chord and two paird of chords in inverse relationship. The palindromic chord is 1-11/8-16/11 chord with steps of 11/8-16/15-11/8. The inversely related pairs of chords are 1-11/8-11/6 chord with steps of 11/8-4/3-11/10 and 1-11/10-16/11 chord with steps of 11/10-4/3-11/8; and 1-11/8-5/3 chord with steps of 11/8-11/9-6/5 and 1-6/5-16/11 chord with steps of 6/5-11/9-11/8.

Equal temperaments with biyatismic chords include 7, 9, 15, 16, 22, 24, 29, 31, 38, 46, and 53 EDOs.

Zeus chords

Zeus chords are essentially tempered dyadic chords of the Zeus temperament. Aside from the biyatismic, valinorsmic, and keenanismic chords, there are 43 further essentially Zeus chords - eighteen pentads, ten hexads, and fifteen heptads.

The Zeus pentads consist of two palindromic chords and eight pairs of chords in inverse relationship.

The two palindromic pentads are: 1-6/5-11/8-16/11-5/3 with steps 6/5-8/7-16/15-8/7-6/5 and 1-8/7-11/8-16/11-7/4 with steps 8/7-6/5-16/15-6/5-8/7.

The eight inversely related pairs of pentads are: 1-8/7-11/8-16/11-5/3 with steps 8/7-6/5-16/15-8/7-6/5 and 1-6/5-11/8-16/11-7/4 with steps 6/5-8/7-16/15-6/5-8/7; 1-8/7-11/9-16/11-7/4 with steps 8/7-16/15-6/5-6/5-8/7 and 1-8/7-11/8-18/11-7/4 with steps 8/7-6/5-6/5-16/15-8/7; 1-8/7-11/8-16/11-8/5 with steps 8/7-6/5-16/15-11/10-5/4 and 1-5/4-11/8-16/11-7/4 with steps 5/4-11/10-16/15-6/5-8/7; 1-8/7-11/8-16/11-11/6 with steps 8/7-6/5-16/15-5/4-11/10 and 1-11/10-11/8-16/11-7/4 with steps 11/10-5/4-16/15-6/5-8/7; 1-5/4-11/8-16/11-5/3 with steps 5/4-11/10-16/15-8/7-6/5 and 1-6/5-11/8-16/11-8/5 with steps 6/5-8/7-16/15-11/10-5/4; 1-11/10-11/8-16/11-5/3 with steps 11/10-5/4-16/15-8/7-6/5 and 1-6/5-11/8-16/11-11/6 with steps 6/5-8/7-16/15-5/4-11/10; 1-5/4-3/2-8/5-11/6 with steps 5/4-6/5-16/15-8/7-11/10 and 1-11/10-5/4-4/3-8/5 with steps 11/10-8/7-16/15-6/5-5/4; and 1-5/4-11/8-18/11-7/4 with steps 5/4-11/10-6/5-16/15-8/7 and 1-8/7-11/9-16/11-8/5 with steps 8/7-16/15-6/5-11/10-5/4.

The Zeus hexads consist of two palindromic chords and four pairs of chords in inverse relationship.

The two palindromic hexads are: 1-11/10-5/4-11/8-11/7-12/7 with steps 11/10-8/7-11/10-8/7-11/10-7/6 and 1-8/7-5/4-11/8-3/2-12/7 with steps 8/7-11/10-11/10-11/10-8/7-7/6.

The four inversely related pairs of hexads are: 1-8/7-5/4-11/8-3/2-7/4 with steps 8/7-11/10-11/10-11/10-7/6-8/7 and 1-8/7-4/3-16/11-8/5-7/4 with steps 8/7-7/6-11/10-11/10-11/10-8/7; 1-8/7-5/4-10/7-11/7-12/7 with steps 8/7-11/10-8/7-11/10-11/10-7/6 and 1-7/6-14/11-7/5-8/5-7/4 with steps 7/6-11/10-11/10-8/7-11/10-8/7; 1-7/6-14/11-16/11-8/5-7/4 with steps 7/6-11/10-8/7-11/10-11/10-8/7 and 1-8/7-5/4-11/8-11/7-12/7 with steps 8/7-11/10-11/10-8/7-11/10-7/6; and 1-8/7-5/4-16/11-8/5-7/4 with steps 8/7-11/10-7/6-11/10-11/10-8/7 and 1-8/7-5/4-11/8-8/5-7/4 with steps 8/7-11/10-11/10-7/6-11/10-8/7.

The Zeus heptads consist of three palindromic chords and six pairs of chords in inverse relationship.

The three palindromic heptads are: 1-11/10-6/5-11/8-16/11-5/3-11/6 with steps 11/10-11/10-8/7-16/15-8/7-11/10-11/10, 1-11/10-5/4-11/8-16/11-8/5-11/6 with steps 11/10-8/7-11/10-16/15-11/10-8/7-11/10, and 1-8/7-5/4-11/8-16/11-8/5-7/4 with steps 8/7-11/10-11/10-16/15-11/10-11/10-8/7.

The six inversely related pairs of heptads are: 1-11/10-6/5-11/8-16/11-8/5-7/4 with steps 11/10-11/10-8/7-16/15-11/10-11/10-8/7 and 1-8/7-5/4-11/8-16/11-5/3-11/6 with steps 8/7-11/10-11/10-16/15-8/7-11/10-11/10; 1-11/10-6/5-11/8-16/11-8/5-11/6 with steps 11/10-11/10-8/7-16/15-11/10-8/7-11/10 and 1-11/10-5/4-11/8-16/11-5/3-11/6 with steps 11/10-8/7-11/10-16/15-8/7-11/10-11/10; 1-11/10-5/4-11/8-16/11-8/5-7/4 with steps 11/10-8/7-11/10-16/15-11/10-11/10-8/7 and 1-8/7-5/4-11/8-16/11-8/5-11/6 with steps 8/7-11/10-11/10-16/15-11/10-8/7-11/10; 1-11/10-6/5-14/11-16/11-5/3-11/6 with steps 11/10-11/10-16/15-8/7-8/7-11/10-11/10 and 1-11/10-6/5-11/8-11/7-5/3-11/6 with steps 11/10-11/10-8/7-8/7-16/15-11/10-11/10; 1-11/10-6/5-14/11-16/11-8/5-11/6 with steps 11/10-11/10-16/15-8/7-11/10-8/7-11/10 and 1-11/10-5/4-11/8-11/7-5/3-11/6 with steps 11/10-8/7-11/10-8/7-16/15-11/10-11/10; and 1-8/7-5/4-4/3-16/11-8/5-7/4 with steps 8/7-11/10-16/15-11/10-11/10-11/10-8/7 and 1-8/7-5/4-11/8-3/2-8/5-7/4 with steps 8/7-11/10-11/10-11/10-16/15-11/10-8/7.