Cimbrismic chords

Cimbrismic chords are essentially tempered chords tempered by the cimbrisma, 1275/1274.

Cimbrismic chords are of pattern 2 in the 2.3.5.7.13.17 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:

• 1-17/13-7/5 with steps of 17/13-15/14-10/7, and its inverse
• 1-15/14-7/5 with steps of 15/14-17/13-10/7;
• 1-17/14-7/5 with steps of 17/14-15/13-10/7, and its inverse
• 1-15/13-7/5 with steps of 15/13-17/14-10/7;
• 1-17/14-13/10 with steps of 17/14-15/14-20/13, and its inverse
• 1-15/14-13/10 with steps of 15/14-17/14-20/13.

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

• 1-20/17-10/7-28/17 with steps of 20/17-17/14-15/13-17/14;
• 1-15/14-7/5-3/2 with steps of 15/14-17/13-15/14-4/3;
• 1-15/14-17/14-13/10 with steps of 15/14-17/15-15/14-20/13.

The inversely related pairs of chords are

• 1-20/17-10/7-26/17 with steps of 20/17-17/14-15/14-17/13, and its inverse
• 1-15/14-13/10-26/17 with steps of 15/14-17/14-20/17-17/13;
• 1-15/13-7/5-3/2 with steps of 15/13-17/14-15/14-4/3, and its inverse
• 1-15/14-13/10-3/2 with steps of 15/14-17/14-15/13-4/3;
• 1-17/14-17/13-7/5 with steps of 17/14-14/13-15/14-10/7, and its inverse
• 1-15/14-15/13-7/5 with steps of 15/14-14/13-17/14-10/7;
• 1-17/14-13/10-7/5 with steps of 17/14-15/14-14/13-10/7, and its inverse
• 1-14/13-15/13-7/5 with steps of 14/13-15/14-17/14-10/7;
• 1-15/13-17/13-7/5 with steps of 15/13-17/15-15/14-10/7, and its inverse
• 1-15/14-17/14-7/5 with steps of 15/14-17/15-15/13-10/7;
• 1-14/13-17/13-7/5 with steps of 14/13-17/14-15/14-10/7, and its inverse
• 1-15/14-13/10-7/5 with steps of 15/14-17/14-14/13-10/7.

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

• 1-20/17-10/7-26/17-28/17 with steps of 20/17-17/14-15/14-14/13-17/14, and its inverse
• 1-14/13-15/13-7/5-28/17 with steps of 14/13-15/14-17/14-20/17-17/14;
• 1-15/14-13/10-7/5-3/2 with steps of 15/14-17/14-14/13-15/14-4/3, and its inverse
• 1-15/14-15/13-7/5-3/2 with steps of 15/14-14/13-17/14-15/14-4/3;
• 1-14/13-15/13-17/13-7/5 with steps of 14/13-15/14-17/15-15/14-10/7, and its inverse
• 1-15/14-17/14-13/10-7/5 with steps of 15/14-17/15-15/14-14/13-10/7.

Equal temperaments with cimbrismic chords include 31, 41, 50, 53, 58, 60, 68, 72, 111, 121, 130, 140, 171, 183, 243, 311, 354, 364 and 494.