# Ratwolfsmic chords

**Ratwolfsmic chords** are essentially tempered dyadic chords tempered by the ratwolfsma, 351/350.

Ratwolfsmic chords are of pattern 2 in the 13-odd-limit, meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures.

For triads, there are three pairs of chords in inverse relationship:

- 1-9/7-20/13 with steps of 9/7-6/5-13/10, and its inverse
- 1-6/5-20/13 with steps of 6/5-9/7-13/10; (→ratwolf triad)
- 1-7/6-13/10 with steps of 7/6-10/9-20/13, and its inverse
- 1-10/9-13/10 with steps of 10/9-7/6-20/13;
- 1-10/9-6/5 with steps of 10/9-14/13-5/3, and its inverse
- 1-14/13-6/5 with steps of 14/13-10/9-5/3.

For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are

- 1-6/5-13/10-14/7 with steps of 6/5-13/12-6/5-9/7;
- 1-7/6-13/10-9/5 with steps of 7/6-10/9-18/13-10/9;
- 1-3/2-5/3-9/5 with steps of 3/2-10/9-14/13-10/9.

The inversely related pairs of chords are

- 1-7/6-13/10-5/3 with steps of 7/6-10/9-9/7-6/5, and its inverse
- 1-7/6-7/5-9/5 with steps of 7/6-6/5-9/7-10/9;
- 1-7/6-13/10-7/5 with steps of 7/6-10/9-14/13-10/7, and its inverse
- 1-7/6-5/3-9/5 with steps of 7/6-10/7-14/13-10/9;
- 1-13/10-5/3-13/7 with steps of 13/10-9/7-10/9-14/13, and its inverse
- 1-13/10-7/5-14/9 with steps of 13/10-14/13-10/9-9/7;
- 1-9/7-3/2-5/3 with steps of 9/7-7/6-10/9-6/5, and its inverse
- 1-7/6-3/2-9/5 with steps of 7/6-9/7-6/5-10/9;
- 1-9/7-5/3-13/7 with steps of 9/7-13/10-10/9-14/13, and its inverse
- 1-10/9-13/9-13/7 with steps of 10/9-13/10-9/7-14/13;
- 1-13/12-7/6-13/10 with steps of 13/12-14/13-10/9-20/13, and its inverse
- 1-10/9-6/5-13/10 with steps of 10/9-14/13-13/12-20/13.

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

- 1-10/9-13/10-13/9-13/7 with steps of 10/9-7/6-10/9-9/7-14/13, and its inverse
- 1-9/7-10/7-5/3-13/7 with steps of 9/7-10/9-7/6-10/9-14/13;
- 1-13/12-13/10-5/3-13/7 with steps of 13/12-6/5-9/7-10/9-14/13, and its inverse
- 1-10/9-10/7-12/7-13/7 with steps of 10/9-9/7-6/5-13/12-14/13;
- 1-9/7-3/2-5/3-9/5 with steps of 9/7-7/6-10/9-14/13-10/9, and its inverse
- 1-7/6-3/2-5/3-9/5 with steps of 7/6-9/7-10/9-14/13-10/9.

Equal temperaments with ratwolfsmic chords include 5, 7, 8d, 12f, 19, 22, 26, 27, 31, 34d, 46, 53, 58, 72, 77, 84, 111 and 130.

## Ratwolf triad

The **ratwolf triad** is the 13-limit essentially tempered chord of 1-6/5-20/13 of its inversion 1-9/7-20/13, tempered by the ratwolfsma, 351/350. The name comes from the fact that one each of these triads appears in the 12-note meantone gamut ratwolf.