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.