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.