Photismic chords

Photismic chords are essentially tempered dyadic chords tempered by the photisma, 324/323.

There are two triads, nine tetrads, seven pentads and one hexad as 2.3.17.19 subgroup 19-odd-limit essentially tempered chords.

The two photismic triads are in inverse relationship:

• 1–24/19–17/12 with steps of 24/19–9/8–24/17;
• 1–9/8–17/12 with steps of 9/8–24/19–24/17.

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

• 1–9/8–17/12–19/12 with steps of 9/8–24/19–19/17–24/19;
• 1–17/12–3/2–17/9 with steps of 17/12–18/17–24/19–18/17;
• 1–18/17–9/8–19/16 with steps of 18/17–17/16–18/17–32/19.

The inversely related pairs of chords are

• 1–9/8–17/12–3/2 with steps of 9/8–24/19–18/17–4/3, and its inverse
• 1–18/17–4/3–3/2 with steps of 18/17–24/19–9/8–4/3;
• 1–24/17–3/2–19/12 with steps of 24/17–17/16–18/17–24/19, and its inverse
• 1–17/16–3/2–17/9 with steps of 17/16–24/17–24/19–18/17;
• 1–24/19–17/12–3/2 with steps of 24/19–9/8–18/17–4/3, and its inverse
• 1–18/17–19/16–3/2 with steps of 18/17–9/8–24/19–4/3.

For pentads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is

• 1–9/8–17/12–3/2–19/12 with steps of 9/8–24/19–18/17–18/17–24/19.

The inversely related pairs of chords are

• 1–17/16–9/8–17/12–3/2 with steps of 17/16–18/17–24/19–18/17–4/3, and its inverse
• 1–18/17–4/3–24/17–3/2 with steps of 18/17–24/19–18/17–17/16–4/3;
• 1–24/19–4/3–17/12–3/2 with steps of 24/19–18/17–17/16–18/17–4/3, and its inverse
• 1–18/17–9/8–19/16–3/2 with steps of 18/17–17/16–18/17–24/19–4/3;
• 1–9/8–19/16–3/2–19/12 with steps of 9/8–18/17–24/19–18/17–24/19, and its inverse
• 1–18/17–19/16–3/2–19/12 with steps of 18/17–9/8–24/19–18/17–24/19.

Finally, there is a palindromic hexad,

• 1–18/17–4/3–24/17–3/2–19/12 with steps of 18/17–24/19–18/17–17/16–18/17–24/19.

Equal temperaments with photismic chords include 12, 14, 26, 29, 38, 65, 77, 89, 101 and 113.