Sextantonismic chords

Sextantonismic chords are essentially tempered chords tempered by the sextantonisma, 2601/2600.

Sextantonismic chords are of pattern 1b in the 2.3.5.13.17 subgroup 17-odd-limit, meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.

The three sextantonismic triads include a palindrome since it identifies 18/13 by a stack of two 20/17's:

• 1–20/17–18/13 with steps of 20/17, 20/17, 13/9.

And an inversely related pair:

• 1–20/17–17/13 with steps of 20/17, 10/9, 26/17, and its inverse
• 1–10/9–17/13 with steps of 10/9, 20/17, 26/17.

They can be extended to the following palindromic tetrads:

• 1–10/9–20/17–17/13 with steps of 10/9, 18/17, 10/9, 26/17;
• 1–20/17–17/13–20/13 with steps of 20/17, 10/9, 20/17, 13/10.

And inversely related tetrads:

• 1–20/17–17/13–18/13 with steps of 20/17, 10/9, 18/17, 13/9, and its inverse
• 1–18/17–20/17–18/13 with steps of 18/17, 10/9, 20/17, 13/9;
• 1–20/17–18/13–20/13 with steps of 20/17, 20/17, 10/9, 13/10, and its inverse
• 1–20/17–18/13–9/5 with steps of 20/17, 20/17, 13/10, 10/9.

Then there is an inversely related pair of pentads:

• 1–10/9–20/17–17/13–20/13 with steps of 10/9, 18/17, 10/9, 20/17, 13/10, and its inverse
• 1–10/9–20/17–17/13–17/10 with steps of 10/9, 18/17, 10/9, 13/10, 20/17.

Equal temperaments with sextantonismic chords include 34, 46, 60, 72, 77, 106, 111, 137, 140, 171, 183, 217, 243, 277, 354, 388, 460, 494 and 848.