Xenismic chords

Xenismic chords are essentially tempered chords tempered by the xenisma, 2058/2057.

Xenismic chords are of pattern 1a in the 2.3.7.11.17 subgroup 21-odd-limit, meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures. In this article, voicing with the perfect fifth is prioritized.

There are three xenismic triads, including a palindrome since it identifies 34/21 by a stack of two 14/11s:

• 1-21/17-11/7 with steps of 21/17-14/11-14/11.

And an inversely related pair:

• 1-11/7-21/11 with steps of 11/7-17/14-22/21, and its inverse
• 1-17/14-21/11 with steps of 17/14-11/7-22/21.

They can be extended to the following palindromic tetrads:

• 1-3/2-11/7-21/11 with steps of 3/2-22/21-17/14-22/21;
• 1-17/14-11/7-21/11 with steps of 17/14-22/17-17/14-22/21.

And inversely related tetrads:

• 1-21/17-3/2-11/7 with steps of 21/17-17/14-22/21-14/11, and its inverse
• 1-17/14-3/2-21/11 with steps of 17/14-21/17-14/11-22/21;
• 1-21/17-11/7-21/11 with steps of 21/17-14/11-17/14-22/21, and its inverse
• 1-17/14-17/11-21/11 with steps of 17/14-14/11-21/17-22/21.

Then there is an inversely related pair of pentads:

• 1-21/17-3/2-11/7-21/11 with steps of 21/17-17/14-22/21-17/14-22/21, and its inverse
• 1-17/14-3/2-11/7-21/11 with steps of 17/14-21/17-22/21-17/14-22/21.

Equal temperaments with xenismic chords include 46, 58, 63, 72, 89, 104, 118, 135, 193, 207, 253, 342, 400, 446, 535, 607 and 742.