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.