Aureusmic chords

Aureusmic chords are essentially tempered dyadic chords tempered by the aureusma, 1445/1444.

Aureusmic chords are of pattern 1a in the 2.5.17.19 subgroup 19-odd-limit, meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.

The most typical aureusmic triad is a palindrome since it identifies 5/4 by a stack of two 19/17's:

• 1-19/17-5/4 chord with steps 19/17-19/17-8/5.

There is an inversely related pair which is even more squeezed:

• 1-17/16-19/17 with steps 17/16-20/19-34/19, and its inverse
• 1-20/19-19/17 with steps 20/19-17/16-34/19.

They can be extended to the following tetrads, with two palindromic chords and two pairs of chords in inverse relationship. The palindromic tetrads are

• 1-17/16-19/17-19/16 chord with steps 17/16-20/19-17/16-32/19;
• 1-20/19-19/17-20/17 chord with steps 20/19-17/16-20/19-17/10.

The inversely related pairs of tetrads are

• 1-19/17-19/16-5/4 with steps 19/17-17/16-20/19-8/5, and its inverse
• 1-20/19-19/17-5/4 with steps 20/19-17/16-19/17-8/5;
• 1-19/17-20/17-5/4 with steps 19/17-20/19-17/16-8/5, and its inverse
• 1-17/16-19/17-5/4 with steps 17/16-20/19-19/17-8/5.

Then there is an inversely related pair of pentads:

• 1-17/16-19/17-19/16-5/4 with steps 17/16-20/19-17/16-20/19-8/5 and its inverse,
• 1-20/19-19/17-20/17-5/4 with steps 20/19-17/16-20/19-17/16-8/5.

Equal temperaments with aureusmic chords include 12, 13, 25, 31, 37, 43, 56, 68, 81, 93, 124, 137, 149, 205, 230 and 286.