Catadictmic chords
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Catadictmic chords are essentially tempered dyadic chords tempered by the catadictma, 1287/1280.
Catadictmic 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:
- 1-16/13-11/8 with steps of 16/13-10/9-16/11, and its inverse
- 1-16/11-13/8 with steps of 16/11-10/9-16/13;
- 1-13/10-16/11 with steps of 13/10-9/8-11/8, and its inverse
- 1-11/8-20/13 with steps of 11/8-9/8-13/10;
- 1-11/10-16/13 with steps of 11/10-9/8-13/8, and its inverse
- 1-9/8-16/13 with steps of 9/8-11/10-13/8.
For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are
- 1-16/13-16/11-9/5 with steps of 16/13-13/11-16/13-10/9;
- 1-9/8-11/8-20/13 with steps of 9/8-11/9-9/8-13/10;
- 1-9/8-16/13-18/13 with steps of 9/8-11/10-9/8-13/9.
The inversely related pairs of chords are
- 1-13/10-16/11-9/5 with steps of 13/10-9/8-16/13-10/9, and its inverse
- 1-16/13-18/13-9/5 with steps of 16/13-9/8-13/10-10/9;
- 1-9/8-16/11-9/5 with steps of 9/8-13/10-16/13-10/9, and its inverse
- 1-16/13-8/5-9/5 with steps of 16/13-13/10-9/8-10/9;
- 1-13/11-13/10-16/11 with steps of 13/11-11/10-9/8-11/8, and its inverse
- 1-9/8-16/13-16/11 with steps of 9/8-11/10-13/11-11/8;
- 1-13/10-16/11-8/5 with steps of 13/10-9/8-11/10-5/4, and its inverse
- 1-11/10-16/13-8/5 with steps of 11/10-9/8-13/10-5/4;
- 1-11/10-16/13-11/8 with steps of 11/10-9/8-10/9-16/11, and its inverse
- 1-10/9-5/4-11/8 with steps of 10/9-9/8-11/10-16/11;
- 1-11/10-16/13-9/5 with steps of 11/10-9/8-16/11-10/9, and its inverse
- 1-16/11-18/11-9/5 with steps of 16/11-9/8-11/10-10/9.
For pentads, there are three pairs of chords in inverse relationship:
- 1-16/13-16/11-8/5-9/5 with steps of 16/13-13/11-11/10-9/8-10/9, and its inverse
- 1-9/8-16/13-16/11-9/5 with steps of 9/8-11/10-13/11-16/13-10/9;
- 1-9/8-16/11-18/11-9/5 with steps of 9/8-13/10-9/8-11/10-10/9, and its inverse
- 1-11/10-16/13-8/5-9/5 with steps of 11/10-9/8-13/10-9/8-10/9;
- 1-13/10-16/11-8/5-9/5 with steps of 13/10-9/8-11/10-9/8-10/9, and its inverse
- 1-9/8-16/13-18/13-9/5 with steps of 9/8-11/10-9/8-13/10-10/9.
Equal temperaments with catadictmic chords include 7, 12, 19, 22, 24, 26, 29, 31, 43, 46, 50, 53, 72 and 96.