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.