Fidesmic chords

Fidesmic chords are essentially tempered chords tempered by the fidesma, 2025/2023.

Fidesmic chords are of pattern 1a in the 2.3.5.7.17 subgroup 17-odd-limit, meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.

For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is

• 1–17/15–9/7 with steps of 17/15, 17/15, 14/9.

The inversely related pair of chords is

• 1–15/14–17/15 with steps of 15/14, 18/17, 30/17, and its inverse
• 1–18/17–17/15 with steps of 18/17, 15/14, 30/17.

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

• 1–15/14–17/15–17/14 with steps of 15/14, 18/17, 15/14, 28/17;
• 1–18/17–17/15–6/5 with steps of 18/17, 15/14, 18/17, 5/3.

The inversely related pairs of chords are

• 1–17/15–17/14–9/7 with steps of 17/15, 15/14, 18/17, 14/9, and its inverse
• 1–18/17–17/15–9/7 with steps of 18/17, 15/14, 17/15, 14/9;
• 1–17/15–6/5–9/7 with steps of 17/15, 18/17, 15/14, 14/9, and its inverse
• 1–15/14–17/15–9/7 with steps of 15/14, 18/17, 17/15, 14/9.

They can be extended to pentads:

• 1–15/14–17/15–17/14–9/7 with steps of 15/14, 18/17, 15/14, 18/17, 14/9, and its inverse
• 1–18/17–17/15–6/5–9/7 with steps of 18/17, 15/14, 18/17, 15/14, 14/9.

Equal temperaments with fidesmic chords include 10, 12, 22, 50, 60, 72, 77, 84, 94, 99, 111, 171, 183, 193, 243, 270, 282 and 354.