Buzurgismic chords

Buzurgismic chords are essentially tempered dyadic chords tempered by the buzurgisma, 169/168.

The buzurgismic temperament is very comparable to the biyatismic temperament. It has two triads, nine tetrads, seven pentads and one hexad in the 2.3.7.13 subgroup 13-odd-limit.

The two buzurgismic triads are in inverse relationship:

• 1-7/6-13/8 with steps 7/6-18/13-16/13;
• 1-18/13-13/8 with steps 18/13-7/6-16/13.

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

• 1-9/8-18/13-13/8 with steps 9/8-16/13-7/6-16/13;
• 1-3/2-13/8-13/7 with steps 3/2-13/12-8/7-13/12;
• 1-13/12-18/13-3/2 with steps 13/12-9/7-13/12-4/3.

The inversely related pairs of chords are

• 1-18/13-3/2-13/8 with steps 18/13-13/12-13/12-16/13, and its inverse
• 1-13/12-3/2-13/7 with steps 13/12-18/13-16/13-13/12;
• 1-13/12-3/2-7/4 with steps 13/12-18/13-7/6-8/7, and its inverse
• 1-18/13-3/2-12/7 with steps 18/13-13/12-8/7-7/6;
• 1-7/6-3/2-13/8 with steps 7/6-9/7-13/12-16/13, and its inverse
• 1-9/7-3/2-13/7 with steps 9/7-7/6-16/13-13/12.

For pentads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is

• 1-9/8-18/13-3/2-13/8 with steps 9/8-16/13-13/12-13/12-16/13.

The inversely related pairs of chords are

• 1-13/12-7/6-3/2-13/8 with steps 13/12-13/12-9/7-13/12-16/13, and its inverse
• 1-9/7-18/13-3/2-13/7 with steps 9/7-13/12-13/12-16/13-13/12;
• 1-13/12-7/6-3/2-7/4 with steps 13/12-13/12-9/7-7/6-8/7, and its inverse
• 1-9/7-18/13-3/2-12/7 with steps 9/7-13/12-13/12-8/7-7/6;
• 1-13/12-3/2-13/8-7/4 with steps 13/12-18/13-13/12-13/12-8/7, and its inverse
• 1-18/13-3/2-12/7-13/7 with steps 18/13-13/12-8/7-13/12-13/12;

Finally, there is a palindromic hexad,

• 1-13/12-7/6-3/2-13/8-7/4 with steps 13/12-13/12-9/7-13/12-13/12-8/7.

Equal temperaments with buzurgismic chords include 7, 9, 10, 17, 19, 26, 27, 36, 46, 53, 63 and 72.