# Augustmic chords

**Augustmic chords** are essentially tempered chords tempered by the augustma, 154/153.

There are 2 triads, 11 tetrads, 8 pentads and 1 hexad as 2.3.7.11.17 subgroup 17-odd-limit essentially tempered chords.

For triads, there is a pair of chords in inverse relationship:

- 1-12/11-7/6 with steps of 12/11-17/16-12/7, and its inverse
- 1-17/16-7/6 with steps of 17/16-12/11-12/7.

For tetrads, there are one palindromic chord and five pairs of chords in inverse relationship. The palindromic chord is

- 1-12/11-7/6-14/11 with steps of 12/11-17/16-12/11-11/7.

The inversely related pairs of chords are

- 1-17/16-3/2-11/6 with steps of 17/16-24/17-11/9-12/11, and its inverse
- 1-24/17-3/2-18/11 with steps of 24/17-17/16-12/11-11/9;
- 1-9/7-3/2-11/6 with steps of 9/7-7/6-11/9-12/11, and its inverse
- 1-7/6-3/2-18/11 with steps of 7/6-9/7-12/11-11/9;
- 1-9/7-24/17-3/2 with steps of 9/7-12/11-17/16-4/3, and its inverse
- 1-17/16-7/6-3/2 with steps of 17/16-12/11-9/7-4/3;
- 1-9/7-11/8-3/2 with steps of 9/7-17/16-12/11-4/3, and its inverse
- 1-12/11-7/6-3/2 with steps of 12/11-17/16-9/7-4/3.
- 1-3/2-12/7-11/6 with steps of 3/2-8/7-17/16-12/11, and its inverse
- 1-3/2-18/11-7/4 with steps of 3/2-12/11-17/16-8/7;

For pentads, there are four pairs of chords in inverse relationship:

- 1-9/7-11/7-12/7-11/6 with steps of 9/7-11/9-12/11-17/16-12/11, and its inverse
- 1-11/9-11/7-12/7-11/6 with steps of 11/9-9/7-12/11-17/16-12/11;
- 1-9/7-11/8-3/2-11/6 with steps of 9/7-17/16-12/11-11/9-12/11, and its inverse
- 1-12/11-7/6-3/2-18/11 with steps of 12/11-17/16-9/7-12/11-11/9;
- 1-9/7-3/2-12/7-11/6 with steps of 9/7-7/6-8/7-17/16-12/11, and its inverse
- 1-7/6-3/2-18/11-7/4 with steps of 7/6-9/7-12/11-17/16-8/7;
- 1-18/17-9/7-24/17-3/2 with steps of 18/17-11/9-12/11-17/16-4/3, and its inverse
- 1-17/16-7/6-17/12-3/2 with steps of 17/16-12/11-11/9-18/17-4/3.

Finally there is a palindromic hexad,

- 1-11/9-9/7-11/7-12/7-11/6 with steps of 11/9-18/17-11/9-12/11-17/16-12/11.

Equal temperaments with augustmic chords include 10, 14, 17g, 22, 24, 27eg, 31, 32, 41 and 46.

## Augustmic plurichords

The augustmic temperament has two inversely related pairs of triads and one palindromic tetrad as plurichords.

The palindromic tetrad is both otonal and utonal in the 17-odd-limit:

- 14:17:18:22 tetrad which has steps of 11/9-18/17-11/9-14/11 or 17/14-18/17-17/14-14/11.

The inversely related pairs of triads are any three of the components of the tetrad:

- 7:9:11 triad which has steps of 22/17-17/14-14/11 and its inverse 14:17:22 triad which has steps of 11/9-9/7-14/11;
- 14:17:18 triad which has steps of 11/9-18/17-17/11 and its inverse 17:18:22 triad which has steps of 18/17-17/14-14/9.