Kevolismic chords

Kevolismic chords are essentially tempered chords tempered by the kevolisma, 1540/1539.

Kevolismic 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:

• 1–11/9–19/14 with steps of 11/9–10/9–28/19, and its inverse
• 1–10/9–19/14 with steps of 10/9–11/9–28/19;
• 1–22/19–9/7 with steps of 22/19–10/9–14/9, and its inverse
• 1–10/9–9/7 with steps of 10/9–22/19–14/9;
• 1–11/9–9/7 with steps of 11/9–20/19–14/9, and its inverse
• 1–20/19–9/7 with steps of 20/19–11/9–14/9.

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

• 1–11/9–9/7–11/7 with steps of 11/9–20/19–11/9–14/11;
• 1–10/9–9/7–10/7 with steps of 10/9–22/19–10/9–7/5;
• 1–10/9–11/9–19/14 with steps of 10/9–11/10–10/9–28/19.

The inversely related pairs of chords are

• 1–11/9–19/14–11/7 with steps of 11/9–10/9–22/19–14/11, and its inverse
• 1–22/19–9/7–11/7 with steps of 22/19–10/9–11/9–14/11;
• 1–10/9–19/14–10/7 with steps of 10/9–11/9–20/19–7/5, and its inverse
• 1–20/19–9/7–10/7 with steps of 20/19–11/9–10/9–7/5;
• 1–11/9–9/7–19/14 with steps of 11/9–20/19–19/18–28/19, and its inverse
• 1–19/18–10/9–19/14 with steps of 19/18–20/19–11/9–28/19;
• 1–10/9–9/7–19/14 with steps of 10/9–22/19–19/18–28/19, and its inverse
• 1–19/18–11/9–19/14 with steps of 19/18–22/19–10/9–28/19;
• 1–22/19–11/9–9/7 with steps of 22/19–19/18–20/19–14/9, and its inverse
• 1–20/19–10/9–9/7 with steps of 20/19–19/18–22/19–14/9;
• 1–10/9–11/9–9/7 with steps of 10/9–11/10–20/19–14/9, and its inverse
• 1–20/19–22/19–9/7 with steps of 20/19–11/10–10/9–14/9.

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

• 1–11/9–9/7–19/14–11/7 with steps of 11/9–20/19–19/18–22/19–14/11, and its inverse
• 1–22/19–11/9–9/7–11/7 with steps of 22/19–19/18–20/19–11/9–14/11;
• 1–10/9–11/9–9/7–19/14 with steps of 10/9–11/10–20/19–19/18–28/19, and its inverse
• 1–19/18–10/9–11/9–19/14 with steps of 19/18–20/19–11/10–10/9–28/19;
• 1–10/9–9/7–19/14–10/7 with steps of 10/9–22/19–19/18–20/19–7/5, and its inverse
• 1–20/19–10/9–9/7–10/7 with steps of 20/19–19/18–22/19–10/9–7/5.

Equal temperaments with kevolismic chords include 31, 41, 46, 53, 72, 94, 111, 118, 152, 270, 311, 342, 422 and 612.