Neomirkwaismic chords

Neomirkwaismic chords are essentially tempered chords tempered by the neomirkwaisma, 3136/3135.

Neomirkwaismic chords are of pattern 2 in the 2.3.5.7.11.19 subgroup 19-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:

• 1-19/14-16/11 with steps of 19/14-15/14-11/8, and its inverse
• 1-15/14-16/11 with steps of 15/14-19/14-11/8;
• 1-14/11-19/14 with steps of 14/11-16/15-28/19, and its inverse
• 1-16/15-19/14 with steps of 16/15-14/11-28/19;
• 1-19/16-14/11 with steps of 19/16-15/14-11/7, and its inverse
• 1-15/14-14/11 with steps of 15/14-19/16-11/7.

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

• 1-22/19-28/19-11/7 with steps of 22/19-14/11-16/15-14/11;
• 1-15/14-19/14-16/11 with steps of 15/14-19/15-15/14-11/8;
• 1-15/14-14/11-15/11 with steps of 15/14-19/16-15/14-22/15.

The inversely related pairs of chords are

• 1-22/19-11/8-28/19 with steps of 22/19-19/16-15/14-19/14, and its inverse
• 1-15/14-14/11-28/19 with steps of 15/14-19/16-22/19-19/14;
• 1-14/11-19/14-16/11 with steps of 14/11-16/15-15/14-11/8, and its inverse
• 1-15/14-8/7-16/11 with steps of 15/14-16/15-14/11-11/8;
• 1-8/7-19/14-16/11 with steps of 8/7-19/16-15/14-11/8, and its inverse
• 1-15/14-14/11-16/11 with steps of 15/14-19/16-8/7-11/8;
• 1-15/14-15/11-16/11 with steps of 15/14-14/11-16/15-11/8, and its inverse
• 1-16/15-19/14-16/11 with steps of 16/15-14/11-15/14-11/8;
• 1-19/16-14/11-19/14 with steps of 19/16-15/14-16/15-28/19, and its inverse
• 1-16/15-8/7-19/14 with steps of 16/15-15/14-19/16-28/19;
• 1-15/14-14/11-19/14 with steps of 15/14-19/16-16/15-28/19, and its inverse
• 1-16/15-19/15-19/14 with steps of 16/15-19/16-15/14-28/19.

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

• 1-22/19-11/8-28/19-11/7 with steps of 22/19-19/16-15/14-16/15-14/11, and its inverse
• 1-16/15-8/7-19/14-11/7 with steps of 16/15-15/14-19/16-22/19-14/11;
• 1-15/14-14/11-15/11-16/11 with steps of 15/14-19/16-15/14-16/15-11/8, and its inverse
• 1-16/15-8/7-19/14-16/11 with steps of 16/15-15/14-19/16-15/14-11/8;
• 1-15/14-14/11-19/14-16/11 with steps of 15/14-19/16-16/15-15/14-11/8, and its inverse
• 1-15/14-8/7-19/14-16/11 with steps of 15/14-16/15-19/16-15/14-11/8.

Equal temperaments with neomirkwaismic chords include 31, 41, 72, 80, 118, 130, 152, 159, 190, 202, 270, 311, 342, 422, 472, 612, 742 and 894.