Twosquare chords

Twosquare chords are essentially tempered chords tempered by the twosquare comma, 1089/1088.

Twosquare chords are of pattern 1b in the 2.3.11.17 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

• 1-11/8-17/9 with steps of 11/8-11/8-18/17.

The inversely related pair of chords is

• 1-11/8-17/11 with steps of 11/8-9/8-22/17, and its inverse
• 1-9/8-17/11 with steps of 9/8-11/8-22/17.

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

• 1-9/8-11/8-17/11 with steps of 9/8-11/9-9/8-22/17;
• 1-9/8-16/11-17/11 with steps of 9/8-22/17-17/16-22/17.

The inversely related pairs of chords are

• 1-11/8-17/11-17/9 with steps of 11/8-9/8-11/9-18/17, and its inverse
• 1-11/9-11/8-17/9 with steps of 11/9-9/8-11/8-18/17;
• 1-11/8-16/9-17/9 with steps of 11/8-22/17-17/16-18/17, and its inverse
• 1-17/16-11/8-17/9 with steps of 17/16-22/17-11/8-18/17.

Then there is an inversely related pair of pentads:

• 1-11/9-11/8-16/9-17/9 with steps of 11/9-9/8-22/17-17/16-18/17, and its inverse
• 1-17/16-11/8-17/11-17/9 with steps of 17/16-22/17-9/8-11/9-18/17.

Equal temperaments with twosquare chords include 22, 24, 41, 46, 65, 70, 89, 94, 111, 135, 159, 183, 207 and 231.