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.