Seminaiadmic chords

Seminaiadmic chords are essentially tempered dyadic chords tempered by the seminaiadma, 442/441.

Seminaiadmic chords are of pattern 2 in the 2.3.7.13.17 subgroup 17-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:

• 1–17/14–7/4 with steps of 17/14, 13/9, 8/7, and its inverse
• 1–13/9–7/4 with steps of 13/9, 17/14, 8/7;
• 1–9/8–17/14 with steps of 9/8, 14/13, 28/17, and its inverse
• 1–14/13–17/14 with steps of 14/13, 9/8, 28/17;
• 1–14/13–8/7 with steps of 14/13, 18/17, 7/4, and its inverse
• 1–18/17–8/7 with steps of 18/17, 14/13, 7/4.

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

• 1–17/16–17/14–7/4 with steps of 17/16, 8/7, 13/9, 8/7;
• 1–14/13–17/14–17/13 with steps of 14/13, 9/8, 14/13, 26/17;
• 1–14/13–8/7–16/13 with steps of 14/13, 18/17, 14/13, 13/8.

The inversely related pairs of chords are

• 1–9/8–17/14–7/4 with steps of 9/8, 14/13, 13/9, 8/7, and its inverse
• 1–13/9–14/9–7/4 with steps of 13/9, 14/13, 9/8, 8/7;
• 1–9/8–17/14–18/13 with steps of 9/8, 14/13, 8/7, 13/9, and its inverse
• 1–8/7–16/13–18/13 with steps of 8/7, 14/13, 9/8, 13/9;
• 1–9/8–17/14–9/7 with steps of 9/8, 14/13, 18/17, 14/9, and its inverse
• 1–18/17–8/7–9/7 with steps of 18/17, 14/13, 9/8, 14/9;
• 1–17/16–9/8–17/14 with steps of 17/16, 18/17, 14/13, 28/17, and its inverse
• 1–14/13–8/7–17/14 with steps of 14/13, 18/17, 17/16, 28/17;
• 1–14/13–8/7–18/13 with steps of 14/13, 18/17, 17/14, 13/9, and its inverse
• 1–17/14–9/7–18/13 with steps of 17/14, 18/17, 14/13, 13/9;
• 1–14/13–8/7–28/17 with steps of 14/13, 18/17, 13/9, 17/14, and its inverse
• 1–13/9–26/17–28/17 with steps of 13/9, 18/17, 14/13, 17/14.

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

• 1–17/16–9/8–17/14–7/4 with steps of 17/16, 18/17, 14/13, 13/9, 8/7, and its inverse
• 1–17/16–17/14–7/4–17/9 with steps of 17/16, 8/7, 13/9, 14/13, 18/17;
• 1–14/13–17/14–17/13–17/9 with steps of 14/13, 9/8, 14/13, 13/9, 18/17, and its inverse
• 1–14/13–17/14–17/13–18/13 with steps of 14/13, 9/8, 14/13, 18/17, 13/9;
• 1–9/8–17/14–9/7–18/13 with steps of 9/8, 14/13, 18/17, 14/13, 13/9, and its inverse
• 1–14/13–8/7–16/13–18/13 with steps of 14/13, 18/17, 14/13, 9/8, 13/9.

Equal temperaments with seminaiadmic chords include 10, 17g, 19g, 22f, 26, 36, 46, 53, 58, 94, 104, 130 and 140.