Pinkanberry chords

Pinkanberry chords are essentially tempered chords tempered by the pinkanberry comma, 1521/1520.

Pinkanberry chords are of pattern 2 in the 2.3.5.13.19 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:

• 1–13/10–19/13 with steps of 13/10–9/8–26/19, and its inverse
• 1–9/8–19/13 with steps of 9/8–13/10–26/19;
• 1–16/13–26/19 with steps of 16/13–10/9–19/13, and its inverse
• 1–10/9–26/19 with steps of 10/9–16/13–19/13;
• 1–16/13–13/10 with steps of 16/13–19/18–20/13, and its inverse
• 1–19/18–13/10 with steps of 19/18–16/13–20/13.

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

• 1–19/16–19/13–13/8 with steps of 19/16–16/13–10/9–16/13;
• 1–16/13–13/10–8/5 with steps of 16/13–19/18–16/13–5/4;
• 1–9/8–19/13–20/13 with steps of 9/8–13/10–20/19–13/10.

The inversely related pairs of chords are

• 1–9/8–18/13–20/13 with steps of 9/8–16/13–10/9–13/10, and its inverse
• 1–10/9–26/19–20/13 with steps of 10/9–16/13–9/8–13/10;
• 1–9/8–5/4–20/13 with steps of 9/8–10/9–16/13–13/10, and its inverse
• 1–16/13–26/19–20/13 with steps of 16/13–10/9–9/8–13/10;
• 1–16/13–13/10–19/13 with steps of 16/13–19/18–9/8–26/19, and its inverse
• 1–9/8–19/16–19/13 with steps of 9/8–19/18–16/13–26/19;
• 1–9/8–18/13–19/13 with steps of 9/8–16/13–19/18–26/19, and its inverse
• 1–19/18–13/10–19/13 with steps of 19/18–16/13–9/8–26/19;
• 1–10/9–26/19–13/9 with steps of 10/9–16/13–19/18–18/13, and its inverse
• 1–19/18–13/10–13/9 with steps of 19/18–16/13–10/9–18/13;
• 1–16/13–13/10–26/19 with steps of 16/13–19/18–20/19–19/13, and its inverse
• 1–20/19–10/9–26/19 with steps of 20/19–19/18–16/13–19/13.

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

• 1–9/8–5/4–20/13–13/8 with steps of 9/8–10/9–16/13–19/18–16/13, and its inverse
• 1–10/9–5/4–20/13–13/8 with steps of 10/9–9/8–16/13–19/18–16/13;
• 1–9/8–19/16–19/13–13/8 with steps of 9/8–19/18–16/13–10/9–16/13, and its inverse
• 1–10/9–26/19–13/9–13/8 with steps of 10/9–16/13–19/18–9/8–16/13;
• 1–9/8–18/13–19/13–20/13 with steps of 9/8–16/13–19/18–20/19–13/10, and its inverse
• 1–20/19–10/9–26/19–20/13 with steps of 20/19–19/18–16/13–9/8–13/10.

Equal temperaments with pinkanberry chords include 24, 27, 53, 77, 80, 84, 111, 130, 137, 140, 164, 190, 217, 243, 270, 323, 407, 460 and 513.