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 triads and 33 tetrads in the 2.3.5.11 subgroup.

The biyatismic triads consist of a palindromic chord and two pairs 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.

The biyatismic tetrads consist of three palindromic chords and fifteen pairs of chords in inverse relationship. The palindromic chords are 1-9/8-11/8-18/11 chord with steps of 9/8-11/9-6/5-11/9, 1-5/4-11/8-11/6 chord with steps of 5/4-11/10-4/3-11/10, and 1-11/10-3/2-18/11 chord with steps of 11/10-11/8-11/10-11/9. The inversely related pairs of chords are 1-4/3-5/3-11/6 chord with steps of 4/3-5/4-11/10-11/10 and 1-11/10-6/5-3/2 chord with steps of 11/10-11/10-5/4-4/3; 1-11/9-11/8-18/11 chord with steps of 11/9-9/8-6/5-11/9 and 1-11/9-16/11-18/11 chord with steps of 11/9-6/5-9/8-11/9; 1-11/8-5/3-11/6 chord with steps of 11/8-11/9-11/10-11/10 and 1-11/10-6/5-16/11 chord with steps of 11/10-11/10-11/9-11/8; 1-4/3-3/2-11/6 chord with steps of 4/3-9/8-11/9-11/10 and 1-11/10-4/3-3/2 chord with steps of 11/10-11/9-9/8-4/3; 1-9/8-11/8-11/6 chord with steps of 9/8-11/9-4/3-11/10 and 1-11/10-16/11-16/9 chord with steps of 11/10-4/3-11/9-9/8; 1-4/3-3/2-18/11 chord with steps of 4/3-9/8-11/10-11/9 and 1-11/9-4/3-3/2 chord with steps of 11/9-11/10-9/8-4/3; 1-5/4-3/2-11/6 chord with steps of 5/4-6/5-11/9-11/10 and 1-11/10-4/3-8/5 chord with steps of 11/10-11/9-6/5-5/4; 1-6/5-3/2-11/6 chord with steps of 6/5-5/4-11/9-11/10 and 1-11/10-4/3-5/3 chord with steps of 11/10-11/9-5/4-6/5; 1-6/5-16/11-11/6 chord with steps of 6/5-11/9-5/4-11/10 and 1-11/10-11/8-5/3 chord with steps of 11/10-5/4-11/9-6/5; 1-5/4-11/8-16/11 chord with steps of 5/4-11/10-16/15-11/8 and 1-11/8-16/11-8/5 chord with steps of 11/8-16/15-11/10-5/4; 1-5/4-4/3-16/11 chord with steps of 5/4-16/15-11/10-11/8 and 1-11/8-3/2-8/5 chord with steps of 11/8-11/10-16/15-5/4; 1-5/4-4/3-11/6 chord with steps of 5/4-16/15-11/8-11/10 and 1-11/10-3/2-8/5 chord with steps of 11/10-11/8-16/15-5/4; 1-11/9-11/8-16/11 chord with steps of 11/9-9/8-16/15-11/8 and 1-11/8-16/11-18/11 chord with steps of 11/8-16/15-9/8-11/9; 1-11/8-5/3-16/9 chord with steps of 11/8-11/9-16/15-9/8 and 1-9/8-6/5-16/11 chord with steps of 9/8-16/15-11/9-11/8; and 1-11/8-16/11-16/9 chord with steps of 11/8-16/15-11/9-9/8 and 1-9/8-11/8-16/11 chord with steps of 9/8-11/9-16/15-11/8.

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