Gassormic chords

Gassormic chords are essentially tempered dyadic chords tempered by the gassorma, 275/273.

Gassormic chords are of pattern 2 in the 13-odd-limit, meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures.

For triads, there are three pairs of chords in inverse relationship:

• 1–7/5–5/3 with steps of 7/5, 13/11, 6/5, and its inverse
• 1–6/5–10/7 with steps of 6/5, 13/11, 7/5;
• 1–14/11–5/3 with steps of 14/11, 13/10, 6/5, and its inverse
• 1–6/5–11/7 with steps of 6/5, 13/10, 14/11;
• 1–7/5–11/6 with steps of 7/5, 13/10, 12/11, and its inverse
• 1–12/11–10/7 with steps of 12/11, 13/10, 7/5.

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

• 1–6/5–10/7–12/7 with steps of 6/5, 13/11, 6/5, 7/6;
• 1–6/5–13/10–11/7 with steps of 6/5, 13/12, 6/5, 14/11;
• 1–13/10–10/7–13/7 with steps of 13/10, 12/11, 13/10, 14/13.

The inversely related pairs of chords are

• 1–13/10–11/7–11/6 with steps of 13/10, 6/5, 7/6, 12/11, and its inverse
• 1–7/6–7/5–11/6 with steps of 7/6, 6/5, 13/10, 12/11;
• 1–6/5–10/7–11/7 with steps of 6/5, 13/11, 11/10, 14/11, and its inverse
• 1–14/11–7/5–5/3 with steps of 14/11, 11/10, 13/11, 6/5;
• 1–13/10–11/7–13/7 with steps of 13/10, 6/5, 13/11, 14/13, and its inverse
• 1–13/10–7/5–5/3 with steps of 13/10, 14/13, 13/11, 6/5;
• 1–11/10–6/5–11/7 with steps of 11/10, 12/11, 13/10, 14/11, and its inverse
• 1–11/10–7/5–11/6 with steps of 11/10, 14/11, 13/10, 12/11;
• 1–7/5–20/13–5/3 with steps of 7/5, 12/11, 13/12, 6/5, and its inverse
• 1–6/5–13/10–10/7 with steps of 6/5, 13/12, 12/11, 7/5;
• 1–7/5–5/3–11/6 with steps of 7/5, 13/11, 11/10, 12/11, and its inverse
• 1–12/11–6/5–10/7 with steps of 12/11, 11/10, 13/11, 7/5.

For pentads, there are three pairs of chords in inverse relationship:

• 1–11/10–13/10–7/5–11/6 with steps of 11/10, 13/11, 14/13, 13/10, 12/11, and its inverse
• 1–13/10–7/5–5/3–11/6 with steps of 13/10, 14/13, 13/11, 11/10, 12/11;
• 1–6/5–13/10–10/7–11/7 with steps of 6/5, 13/12, 12/11, 11/10, 14/11, and its inverse
• 1–13/12–13/10–5/3–11/6 with steps of 13/12, 6/5, 14/11, 11/10, 12/11;
• 1–7/6–7/5–5/3–11/6 with steps of 7/6, 6/5, 13/11, 11/10, 12/11, and its inverse
• 1–7/6–14/11–7/5–5/3 with steps of 7/6, 12/11, 11/10, 13/11, 6/5.

Equal temperaments with gassormic chords include 10, 15, 22, 26, 29, 31, 41 and 53.