Biyatismic chords
Biyatismic chords are essentially tempered dyadic chords tempered by the biyatisma, 121/120.
There are two triads, nine tetrads, seven pentads and one hexad as 2.3.5.11 subgroup 11-odd-limit essentially tempered chords.
The two biyatismic triads are in inverse relationship:
- 1-11/8-5/3 chord with steps of 11/8-11/9-6/5;
- 1-6/5-16/11 chord with steps of 6/5-11/9-11/8.
For tetrads, there are three palindromic chords and three 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;
- 1-3/2-18/11-11/6 chord with steps of 3/2-11/10-10/9-11/10.
The inversely related pairs of chords are
- 1-11/8-5/3-11/6 with steps of 11/8-11/9-11/10-11/10 and 1-11/10-6/5-16/11 with steps of 11/10-11/10-11/9-11/8;
- 1-5/4-3/2-11/6 with steps of 5/4-6/5-11/9-11/10 and 1-11/10-4/3-8/5 with steps of 11/10-11/9-6/5-5/4;
- 1-11/8-18/11-11/6 with steps of 11/8-6/5-10/9-11/10 and 1-11/10-11/9-16/11 with steps of 11/10-10/9-6/5-11/8.
For pentads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is
- 1-9/8-11/8-3/2-18/11 chord with steps of 9/8-11/9-11/10-11/10-11/9.
The inversely related pairs of chords are
- 1-11/8-3/2-5/3-11/6 with steps of 11/8-11/10-10/9-11/10-11/10 and 1-11/10-6/5-4/3-16/11 with steps of 11/10-11/10-10/9-11/10-11/8;
- 1-5/4-3/2-5/3-11/6 with steps of 5/4-6/5-10/9-11/10-11/10 and 1-11/10-6/5-4/3-8/5 with steps of 11/10-11/10-10/9-6/5-5/4;
- 1-5/4-11/8-3/2-11/6 with steps of 5/4-11/10-11/10-11/9-11/10 and 1-11/10-4/3-16/11-8/5 with steps of 11/10-11/9-11/10-11/10-5/4.
Finally there is a palindromic hexad,
- 1-5/4-11/8-3/2-5/3-11/6 with steps of 5/4-11/10-11/10-10/9-11/10-11/10.
Equal temperaments with biyatismic chords include 7, 9, 15, 16, 22, 24, 29, 31, 38, 46 and 53.