Devichromic chords
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Devichromic chords are essentially tempered chords tempered by 400/399, the devichroma.
Devichromic chords are very numerous, including 18 triads, 83 tetrads, 118 pentads, 68 hexads and 14 heptads as 2.3.5.7.19 subgroup 19-odd-limit essentially tempered chords.
For triads, there are nine pairs of chords in inverse relationship:
| Inversely related pairs of triads | |
|---|---|
| 1 – 10/7 – 3/2 (steps 10/7, 20/19, 4/3) | 1 – 20/19 – 3/2 (steps 20/19, 10/7, 4/3) |
| 1 – 19/15 – 10/7 (steps 19/15, 9/8, 7/5) | 1 – 9/8 – 10/7 (steps 9/8, 19/15, 7/5) |
| 1 – 6/5 – 10/7 (steps 6/5, 19/16, 7/5) | 1 – 19/16 – 10/7 (steps 19/16, 6/5, 7/5) |
| 1 – 24/19 – 7/5 (steps 24/19, 10/9, 10/7) | 1 – 10/9 – 7/5 (steps 10/9, 24/19, 10/7) |
| 1 – 8/7 – 19/15 (steps 8/7, 10/9, 30/19) | 1 – 10/9 – 19/15 (steps 10/9, 8/7, 30/19) |
| 1 – 8/7 – 6/5 (steps 8/7, 20/19, 5/3) | 1 – 20/19 – 6/5 (steps 20/19, 8/7, 5/3) |
| 1 – 10/9 – 19/16 (steps 10/9, 15/14, 32/19) | 1 – 15/14 – 19/16 (steps 15/14, 10/9, 32/19) |
| 1 – 10/9 – 7/6 (steps 10/9, 20/19, 12/7) | 1 – 20/19 – 7/6 (steps 20/19, 10/9, 12/7) |
| 1 – 15/14 – 9/8 (steps 15/14, 20/19, 16/9) | 1 – 20/19 – 9/8 (steps 20/19, 15/14, 16/9) |
For tetrads, there are seven palindromic chords and 38 pairs of chords in inverse relationship:
| Palindromic tetrads | |
|---|---|
| 1 – 10/7 – 3/2 – 19/10 (steps 10/7, 20/19, 19/15, 20/19) | |
| 1 – 15/14 – 10/7 – 3/2 (steps 15/14, 4/3, 20/19, 4/3) | |
| 1 – 20/19 – 10/7 – 3/2 (steps 20/19, 19/14, 20/19, 4/3) | |
| 1 – 19/16 – 10/7 – 5/3 (steps 19/16, 6/5, 7/6, 6/5) | |
| 1 – 10/9 – 10/7 – 19/12 (steps 10/9, 9/7, 10/9, 24/19) | |
| 1 – 20/19 – 6/5 – 24/19 (steps 20/19, 8/7, 20/19, 19/12) | |
| 1 – 20/19 – 10/9 – 7/6 (steps 20/19, 19/18, 20/19, 12/7) | |
| Inversely related pairs of tetrads | |
| 1 – 24/19 – 3/2 – 9/5 (steps 24/19, 19/16, 6/5, 10/9) |
1 – 19/16 – 3/2 – 5/3 (steps 19/16, 24/19, 10/9, 6/5) |
| 1 – 4/3 – 10/7 – 3/2 (steps 4/3, 15/14, 20/19, 4/3) |
1 – 4/3 – 7/5 – 3/2 (steps 4/3, 20/19, 15/14, 4/3) |
| 1 – 9/7 – 10/7 – 3/2 (steps 9/7, 10/9, 20/19, 4/3) |
1 – 20/19 – 7/6 – 3/2 (steps 20/19, 10/9, 9/7, 4/3) |
| 1 – 24/19 – 7/5 – 3/2 (steps 24/19, 10/9, 15/14, 4/3) |
1 – 15/14 – 19/16 – 3/2 (steps 15/14, 10/9, 24/19, 4/3) |
| 1 – 5/4 – 10/7 – 3/2 (steps 5/4, 8/7, 20/19, 4/3) |
1 – 20/19 – 6/5 – 3/2 (steps 20/19, 8/7, 5/4, 4/3) |
| 1 – 6/5 – 10/7 – 3/2 (steps 6/5, 19/16, 20/19, 4/3) |
1 – 20/19 – 5/4 – 3/2 (steps 20/19, 19/16, 6/5, 4/3) |
| 1 – 19/16 – 10/7 – 3/2 (steps 19/16, 6/5, 20/19, 4/3) |
1 – 20/19 – 24/19 – 3/2 (steps 20/19, 6/5, 19/16, 4/3) |
| 1 – 9/8 – 10/7 – 3/2 (steps 9/8, 19/15, 20/19, 4/3) |
1 – 20/19 – 4/3 – 3/2 (steps 20/19, 19/15, 9/8, 4/3) |
| 1 – 7/5 – 3/2 – 5/3 (steps 7/5, 15/14, 10/9, 6/5) |
1 – 15/14 – 3/2 – 9/5 (steps 15/14, 7/5, 6/5, 10/9) |
| 1 – 7/5 – 3/2 – 30/19 (steps 7/5, 15/14, 20/19, 19/15) |
1 – 15/14 – 3/2 – 19/10 (steps 15/14, 7/5, 19/15, 20/19) |
| 1 – 10/7 – 3/2 – 9/5 (steps 10/7, 20/19, 6/5, 10/9) |
1 – 20/19 – 3/2 – 5/3 (steps 20/19, 10/7, 10/9, 6/5) |
| 1 – 10/7 – 3/2 – 12/7 (steps 10/7, 20/19, 8/7, 7/6) |
1 – 20/19 – 3/2 – 7/4 (steps 20/19, 10/7, 7/6, 8/7) |
| 1 – 10/7 – 3/2 – 5/3 (steps 10/7, 20/19, 10/9, 6/5) |
1 – 20/19 – 3/2 – 9/5 (steps 20/19, 10/7, 6/5, 10/9) |
| 1 – 10/7 – 3/2 – 19/12 (steps 10/7, 20/19, 19/18, 24/19) |
1 – 20/19 – 3/2 – 36/19 (steps 20/19, 10/7, 24/19, 19/18) |
| 1 – 5/4 – 10/7 – 19/12 (steps 5/4, 8/7, 10/9, 24/19) |
1 – 10/9 – 19/15 – 19/12 (steps 10/9, 8/7, 5/4, 24/19) |
| 1 – 24/19 – 7/5 – 30/19 (steps 24/19, 10/9, 9/8, 19/15) |
1 – 9/8 – 5/4 – 30/19 (steps 9/8, 10/9, 24/19, 19/15) |
| 1 – 24/19 – 7/5 – 28/19 (steps 24/19, 10/9, 20/19, 19/14) |
1 – 20/19 – 7/6 – 28/19 (steps 20/19, 10/9, 24/19, 19/14) |
| 1 – 19/15 – 19/14 – 10/7 (steps 19/15, 15/14, 20/19, 7/5) |
1 – 20/19 – 9/8 – 10/7 (steps 20/19, 15/14, 19/15, 7/5) |
| 1 – 6/5 – 9/7 – 10/7 (steps 6/5, 15/14, 10/9, 7/5) |
1 – 10/9 – 19/16 – 10/7 (steps 10/9, 15/14, 6/5, 7/5) |
| 1 – 6/5 – 19/15 – 10/7 (steps 6/5, 19/18, 9/8, 7/5) |
1 – 9/8 – 19/16 – 10/7 (steps 9/8, 19/18, 6/5, 7/5) |
| 1 – 19/16 – 19/14 – 10/7 (steps 19/16, 8/7, 20/19, 7/5) |
1 – 20/19 – 6/5 – 10/7 (steps 20/19, 8/7, 19/16, 7/5) |
| 1 – 19/16 – 19/15 – 10/7 (steps 19/16, 16/15, 9/8, 7/5) |
1 – 9/8 – 6/5 – 10/7 (steps 9/8, 16/15, 19/16, 7/5) |
| 1 – 19/16 – 5/4 – 10/7 (steps 19/16, 20/19, 8/7, 7/5) |
1 – 8/7 – 6/5 – 10/7 (steps 8/7, 20/19, 19/16, 7/5) |
| 1 – 8/7 – 19/15 – 10/7 (steps 8/7, 10/9, 9/8, 7/5) |
1 – 9/8 – 5/4 – 10/7 (steps 9/8, 10/9, 8/7, 7/5) |
| 1 – 9/8 – 9/7 – 10/7 (steps 9/8, 8/7, 10/9, 7/5) |
1 – 10/9 – 19/15 – 10/7 (steps 10/9, 8/7, 9/8, 7/5) |
| 1 – 6/5 – 24/19 – 7/5 (steps 6/5, 20/19, 10/9, 10/7) |
1 – 10/9 – 7/6 – 7/5 (steps 10/9, 20/19, 6/5, 10/7) |
| 1 – 8/7 – 19/15 – 19/14 (steps 8/7, 10/9, 15/14, 28/19) |
1 – 15/14 – 19/16 – 19/14 (steps 15/14, 10/9, 8/7, 28/19) |
| 1 – 8/7 – 19/15 – 4/3 (steps 8/7, 10/9, 20/19, 3/2) |
1 – 20/19 – 7/6 – 4/3 (steps 20/19, 10/9, 8/7, 3/2) |
| 1 – 8/7 – 6/5 – 4/3 (steps 8/7, 20/19, 10/9, 3/2) |
1 – 10/9 – 7/6 – 4/3 (steps 10/9, 20/19, 8/7, 3/2) |
| 1 – 10/9 – 19/15 – 4/3 (steps 10/9, 8/7, 20/19, 3/2) |
1 – 20/19 – 6/5 – 4/3 (steps 20/19, 8/7, 10/9, 3/2) |
| 1 – 8/7 – 6/5 – 9/7 (steps 8/7, 20/19, 15/14, 14/9) |
1 – 15/14 – 9/8 – 9/7 (steps 15/14, 20/19, 8/7, 14/9) |
| 1 – 8/7 – 6/5 – 19/15 (steps 8/7, 20/19, 19/18, 30/19) |
1 – 19/18 – 10/9 – 19/15 (steps 19/18, 20/19, 8/7, 30/19) |
| 1 – 10/9 – 19/16 – 19/15 (steps 10/9, 15/14, 16/15, 30/19) |
1 – 16/15 – 8/7 – 19/15 (steps 16/15, 15/14, 10/9, 30/19) |
| 1 – 10/9 – 19/16 – 5/4 (steps 10/9, 15/14, 20/19, 8/5) |
1 – 20/19 – 9/8 – 5/4 (steps 20/19, 15/14, 10/9, 8/5) |
| 1 – 10/9 – 7/6 – 5/4 (steps 10/9, 20/19, 15/14, 8/5) |
1 – 15/14 – 9/8 – 5/4 (steps 15/14, 20/19, 10/9, 8/5) |
| 1 – 15/14 – 19/16 – 5/4 (steps 15/14, 10/9, 20/19, 8/5) |
1 – 20/19 – 7/6 – 5/4 (steps 20/19, 10/9, 15/14, 8/5) |
| 1 – 16/15 – 8/7 – 6/5 (steps 16/15, 15/14, 20/19, 5/3) |
1 – 20/19 – 9/8 – 6/5 (steps 20/19, 15/14, 16/15, 5/3) |
| 1 – 15/14 – 9/8 – 19/16 (steps 15/14, 20/19, 19/18, 32/19) |
1 – 19/18 – 10/9 – 19/16 (steps 19/18, 20/19, 15/14, 32/19) |
For pentads, there are 59 pairs of chords in inverse relationship:
| Inversely related pairs of pentads | |
|---|---|
| 1 – 6/5 – 10/7 – 3/2 – 9/5 (steps 6/5, 19/16, 20/19, 6/5, 10/9) |
1 – 20/19 – 5/4 – 3/2 – 5/3 (steps 20/19, 19/16, 6/5, 10/9, 6/5) |
| 1 – 6/5 – 10/7 – 3/2 – 12/7 (steps 6/5, 19/16, 20/19, 8/7, 7/6) |
1 – 20/19 – 5/4 – 3/2 – 7/4 (steps 20/19, 19/16, 6/5, 7/6, 8/7) |
| 1 – 19/16 – 10/7 – 3/2 – 5/3 (steps 19/16, 6/5, 20/19, 10/9, 6/5) |
1 – 20/19 – 24/19 – 3/2 – 9/5 (steps 20/19, 6/5, 19/16, 6/5, 10/9) |
| 1 – 7/6 – 7/5 – 3/2 – 5/3 (steps 7/6, 6/5, 15/14, 10/9, 6/5) |
1 – 15/14 – 9/7 – 3/2 – 9/5 (steps 15/14, 6/5, 7/6, 6/5, 10/9) |
| 1 – 5/4 – 3/2 – 5/3 – 7/4 (steps 5/4, 6/5, 10/9, 20/19, 8/7) |
1 – 6/5 – 3/2 – 12/7 – 9/5 (steps 6/5, 5/4, 8/7, 20/19, 10/9) |
| 1 – 5/4 – 3/2 – 30/19 – 7/4 (steps 5/4, 6/5, 20/19, 10/9, 8/7) |
1 – 6/5 – 3/2 – 12/7 – 19/10 (steps 6/5, 5/4, 8/7, 10/9, 20/19) |
| 1 – 24/19 – 3/2 – 9/5 – 36/19 (steps 24/19, 19/16, 6/5, 20/19, 19/18) |
1 – 19/16 – 3/2 – 19/12 – 5/3 (steps 19/16, 24/19, 19/18, 20/19, 6/5) |
| 1 – 24/19 – 3/2 – 12/7 – 9/5 (steps 24/19, 19/16, 8/7, 20/19, 10/9) |
1 – 19/16 – 3/2 – 5/3 – 7/4 (steps 19/16, 24/19, 10/9, 20/19, 8/7) |
| 1 – 24/19 – 3/2 – 8/5 – 9/5 (steps 24/19, 19/16, 16/15, 9/8, 10/9) |
1 – 19/16 – 3/2 – 5/3 – 15/8 (steps 19/16, 24/19, 10/9, 9/8, 16/15) |
| 1 – 24/19 – 3/2 – 30/19 – 9/5 (steps 24/19, 19/16, 20/19, 8/7, 10/9) |
1 – 19/16 – 3/2 – 5/3 – 19/10 (steps 19/16, 24/19, 10/9, 8/7, 20/19) |
| 1 – 24/19 – 7/5 – 3/2 – 9/5 (steps 24/19, 10/9, 15/14, 6/5, 10/9) |
1 – 15/14 – 19/16 – 3/2 – 5/3 (steps 15/14, 10/9, 24/19, 10/9, 6/5) |
| 1 – 24/19 – 7/5 – 3/2 – 8/5 (steps 24/19, 10/9, 15/14, 16/15, 5/4) |
1 – 15/14 – 19/16 – 3/2 – 15/8 (steps 15/14, 10/9, 24/19, 5/4, 16/15) |
| 1 – 5/4 – 10/7 – 3/2 – 19/12 (steps 5/4, 8/7, 20/19, 19/18, 24/19) |
1 – 20/19 – 6/5 – 3/2 – 36/19 (steps 20/19, 8/7, 5/4, 24/19, 19/18) |
| 1 – 6/5 – 4/3 – 3/2 – 19/10 (steps 6/5, 10/9, 9/8, 19/15, 20/19) |
1 – 9/8 – 5/4 – 3/2 – 30/19 (steps 9/8, 10/9, 6/5, 20/19, 19/15) |
| 1 – 19/16 – 10/7 – 3/2 – 19/10 (steps 19/16, 6/5, 20/19, 19/15, 20/19) |
1 – 20/19 – 24/19 – 3/2 – 30/19 (steps 20/19, 6/5, 19/16, 20/19, 19/15) |
| 1 – 15/14 – 19/16 – 3/2 – 19/10 (steps 15/14, 10/9, 24/19, 19/15, 20/19) |
1 – 24/19 – 7/5 – 3/2 – 30/19 (steps 24/19, 10/9, 15/14, 20/19, 19/15) |
| 1 – 9/7 – 10/7 – 3/2 – 9/5 (steps 9/7, 10/9, 20/19, 6/5, 10/9) |
1 – 20/19 – 7/6 – 3/2 – 5/3 (steps 20/19, 10/9, 9/7, 10/9, 6/5) |
| 1 – 9/7 – 10/7 – 3/2 – 12/7 (steps 9/7, 10/9, 20/19, 8/7, 7/6) |
1 – 20/19 – 7/6 – 3/2 – 7/4 (steps 20/19, 10/9, 9/7, 7/6, 8/7) |
| 1 – 24/19 – 4/3 – 7/5 – 3/2 (steps 24/19, 19/18, 20/19, 15/14, 4/3) |
1 – 15/14 – 9/8 – 19/16 – 3/2 (steps 15/14, 20/19, 19/18, 24/19, 4/3) |
| 1 – 5/4 – 4/3 – 10/7 – 3/2 (steps 5/4, 16/15, 15/14, 20/19, 4/3) |
1 – 20/19 – 9/8 – 6/5 – 3/2 (steps 20/19, 15/14, 16/15, 5/4, 4/3) |
| 1 – 6/5 – 4/3 – 10/7 – 3/2 (steps 6/5, 10/9, 15/14, 20/19, 4/3) |
1 – 20/19 – 9/8 – 5/4 – 3/2 (steps 20/19, 15/14, 10/9, 6/5, 4/3) |
| 1 – 6/5 – 4/3 – 7/5 – 3/2 (steps 6/5, 10/9, 20/19, 15/14, 4/3) |
1 – 15/14 – 9/8 – 5/4 – 3/2 (steps 15/14, 20/19, 10/9, 6/5, 4/3) |
| 1 – 6/5 – 9/7 – 10/7 – 3/2 (steps 6/5, 15/14, 10/9, 20/19, 4/3) |
1 – 20/19 – 7/6 – 5/4 – 3/2 (steps 20/19, 10/9, 15/14, 6/5, 4/3) |
| 1 – 6/5 – 24/19 – 7/5 – 3/2 (steps 6/5, 20/19, 10/9, 15/14, 4/3) |
1 – 15/14 – 19/16 – 5/4 – 3/2 (steps 15/14, 10/9, 20/19, 6/5, 4/3) |
| 1 – 19/16 – 5/4 – 10/7 – 3/2 (steps 19/16, 20/19, 8/7, 20/19, 4/3) |
1 – 20/19 – 6/5 – 24/19 – 3/2 (steps 20/19, 8/7, 20/19, 19/16, 4/3) |
| 1 – 7/6 – 4/3 – 7/5 – 3/2 (steps 7/6, 8/7, 20/19, 15/14, 4/3) |
1 – 15/14 – 9/8 – 9/7 – 3/2 (steps 15/14, 20/19, 8/7, 7/6, 4/3) |
| 1 – 9/8 – 9/7 – 10/7 – 3/2 (steps 9/8, 8/7, 10/9, 20/19, 4/3) |
1 – 20/19 – 7/6 – 4/3 – 3/2 (steps 20/19, 10/9, 8/7, 9/8, 4/3) |
| 1 – 9/8 – 5/4 – 10/7 – 3/2 (steps 9/8, 10/9, 8/7, 20/19, 4/3) |
1 – 20/19 – 6/5 – 4/3 – 3/2 (steps 20/19, 8/7, 10/9, 9/8, 4/3) |
| 1 – 9/8 – 6/5 – 10/7 – 3/2 (steps 9/8, 16/15, 19/16, 20/19, 4/3) |
1 – 20/19 – 5/4 – 4/3 – 3/2 (steps 20/19, 19/16, 16/15, 9/8, 4/3) |
| 1 – 9/8 – 19/16 – 10/7 – 3/2 (steps 9/8, 19/18, 6/5, 20/19, 4/3) |
1 – 20/19 – 24/19 – 4/3 – 3/2 (steps 20/19, 6/5, 19/18, 9/8, 4/3) |
| 1 – 15/14 – 9/7 – 10/7 – 3/2 (steps 15/14, 6/5, 10/9, 20/19, 4/3) |
1 – 20/19 – 7/6 – 7/5 – 3/2 (steps 20/19, 10/9, 6/5, 15/14, 4/3) |
| 1 – 15/14 – 5/4 – 10/7 – 3/2 (steps 15/14, 7/6, 8/7, 20/19, 4/3) |
1 – 20/19 – 6/5 – 7/5 – 3/2 (steps 20/19, 8/7, 7/6, 15/14, 4/3) |
| 1 – 15/14 – 19/16 – 10/7 – 3/2 (steps 15/14, 10/9, 6/5, 20/19, 4/3) |
1 – 20/19 – 24/19 – 7/5 – 3/2 (steps 20/19, 6/5, 10/9, 15/14, 4/3) |
| 1 – 15/14 – 9/8 – 10/7 – 3/2 (steps 15/14, 20/19, 19/15, 20/19, 4/3) |
1 – 20/19 – 4/3 – 7/5 – 3/2 (steps 20/19, 19/15, 20/19, 15/14, 4/3) |
| 1 – 20/19 – 4/3 – 10/7 – 3/2 (steps 20/19, 19/15, 15/14, 20/19, 4/3) |
1 – 20/19 – 9/8 – 10/7 – 3/2 (steps 20/19, 15/14, 19/15, 20/19, 4/3) |
| 1 – 20/19 – 5/4 – 10/7 – 3/2 (steps 20/19, 19/16, 8/7, 20/19, 4/3) |
1 – 20/19 – 6/5 – 10/7 – 3/2 (steps 20/19, 8/7, 19/16, 20/19, 4/3) |
| 1 – 20/19 – 10/7 – 3/2 – 9/5 (steps 20/19, 19/14, 20/19, 6/5, 10/9) |
1 – 20/19 – 10/7 – 3/2 – 5/3 (steps 20/19, 19/14, 20/19, 10/9, 6/5) |
| 1 – 7/5 – 3/2 – 5/3 – 19/10 (steps 7/5, 15/14, 10/9, 8/7, 20/19) |
1 – 15/14 – 3/2 – 30/19 – 9/5 (steps 15/14, 7/5, 20/19, 8/7, 10/9) |
| 1 – 7/5 – 3/2 – 5/3 – 7/4 (steps 7/5, 15/14, 10/9, 20/19, 8/7) |
1 – 15/14 – 3/2 – 12/7 – 9/5 (steps 15/14, 7/5, 8/7, 20/19, 10/9) |
| 1 – 7/5 – 3/2 – 30/19 – 9/5 (steps 7/5, 15/14, 20/19, 8/7, 10/9) |
1 – 15/14 – 3/2 – 5/3 – 19/10 (steps 15/14, 7/5, 10/9, 8/7, 20/19) |
| 1 – 7/5 – 3/2 – 30/19 – 7/4 (steps 7/5, 15/14, 20/19, 10/9, 8/7) |
1 – 15/14 – 3/2 – 12/7 – 19/10 (steps 15/14, 7/5, 8/7, 10/9, 20/19) |
| 1 – 7/5 – 3/2 – 30/19 – 5/3 (steps 7/5, 15/14, 20/19, 19/18, 6/5) |
1 – 15/14 – 3/2 – 9/5 – 19/10 (steps 15/14, 7/5, 6/5, 19/18, 20/19) |
| 1 – 10/7 – 3/2 – 9/5 – 19/10 (steps 10/7, 20/19, 6/5, 19/18, 20/19) |
1 – 10/7 – 3/2 – 19/12 – 19/10 (steps 10/7, 20/19, 19/18, 6/5, 20/19) |
| 1 – 10/7 – 3/2 – 12/7 – 19/10 (steps 10/7, 20/19, 8/7, 10/9, 20/19) |
1 – 10/7 – 3/2 – 5/3 – 19/10 (steps 10/7, 20/19, 10/9, 8/7, 20/19) |
| 1 – 10/7 – 3/2 – 12/7 – 9/5 (steps 10/7, 20/19, 8/7, 20/19, 10/9) |
1 – 20/19 – 3/2 – 5/3 – 7/4 (steps 20/19, 10/7, 10/9, 20/19, 8/7) |
| 1 – 10/7 – 3/2 – 19/12 – 5/3 (steps 10/7, 20/19, 19/18, 20/19, 6/5) |
1 – 20/19 – 3/2 – 9/5 – 36/19 (steps 20/19, 10/7, 6/5, 20/19, 19/18) |
| 1 – 10/9 – 19/15 – 10/7 – 19/12 (steps 10/9, 8/7, 9/8, 10/9, 24/19) |
1 – 10/9 – 5/4 – 10/7 – 19/12 (steps 10/9, 9/8, 8/7, 10/9, 24/19) |
| 1 – 24/19 – 7/5 – 28/19 – 30/19 (steps 24/19, 10/9, 20/19, 15/14, 19/15) |
1 – 15/14 – 9/8 – 5/4 – 30/19 (steps 15/14, 20/19, 10/9, 24/19, 19/15) |
| 1 – 19/16 – 19/15 – 19/14 – 10/7 (steps 19/16, 16/15, 15/14, 20/19, 7/5) |
1 – 20/19 – 9/8 – 6/5 – 10/7 (steps 20/19, 15/14, 16/15, 19/16, 7/5) |
| 1 – 8/7 – 19/15 – 19/14 – 10/7 (steps 8/7, 10/9, 15/14, 20/19, 7/5) |
1 – 20/19 – 9/8 – 5/4 – 10/7 (steps 20/19, 15/14, 10/9, 8/7, 7/5) |
| 1 – 8/7 – 6/5 – 9/7 – 10/7 (steps 8/7, 20/19, 15/14, 10/9, 7/5) |
1 – 10/9 – 19/16 – 5/4 – 10/7 (steps 10/9, 15/14, 20/19, 8/7, 7/5) |
| 1 – 8/7 – 6/5 – 19/15 – 10/7 (steps 8/7, 20/19, 19/18, 9/8, 7/5) |
1 – 9/8 – 19/16 – 5/4 – 10/7 (steps 9/8, 19/18, 20/19, 8/7, 7/5) |
| 1 – 9/8 – 6/5 – 9/7 – 10/7 (steps 9/8, 16/15, 15/14, 10/9, 7/5) |
1 – 10/9 – 19/16 – 19/15 – 10/7 (steps 10/9, 15/14, 16/15, 9/8, 7/5) |
| 1 – 8/7 – 6/5 – 19/15 – 4/3 (steps 8/7, 20/19, 19/18, 20/19, 3/2) |
1 – 20/19 – 10/9 – 7/6 – 4/3 (steps 20/19, 19/18, 20/19, 8/7, 3/2) |
| 1 – 10/9 – 7/6 – 5/4 – 4/3 (steps 10/9, 20/19, 15/14, 16/15, 3/2) |
1 – 16/15 – 8/7 – 6/5 – 4/3 (steps 16/15, 15/14, 20/19, 10/9, 3/2) |
| 1 – 16/15 – 8/7 – 19/15 – 4/3 (steps 16/15, 15/14, 10/9, 20/19, 3/2) |
1 – 20/19 – 7/6 – 5/4 – 4/3 (steps 20/19, 10/9, 15/14, 16/15, 3/2) |
| 1 – 19/18 – 10/9 – 19/15 – 4/3 (steps 19/18, 20/19, 8/7, 20/19, 3/2) |
1 – 20/19 – 6/5 – 24/19 – 4/3 (steps 20/19, 8/7, 20/19, 19/18, 3/2) |
| 1 – 16/15 – 8/7 – 6/5 – 19/15 (steps 16/15, 15/14, 20/19, 19/18, 30/19) |
1 – 19/18 – 10/9 – 19/16 – 19/15 (steps 19/18, 20/19, 15/14, 16/15, 30/19) |
| 1 – 15/14 – 9/8 – 19/16 – 5/4 (steps 15/14, 20/19, 19/18, 20/19, 8/5) |
1 – 20/19 – 10/9 – 7/6 – 5/4 (steps 20/19, 19/18, 20/19, 15/14, 8/5) |
For hexads, there are two palindromic chords and 33 pairs of chords in inverse relationship:
| Palindromic hexads | |
|---|---|
| 1 – 9/7 – 10/7 – 3/2 – 12/7 – 9/5 (steps 9/7, 10/9, 20/19, 8/7, 20/19, 10/9) | |
| 1 – 19/16 – 10/7 – 3/2 – 19/12 – 5/3 (steps 19/16, 6/5, 20/19, 19/18, 20/19, 6/5) | |
| Inversely related pairs of hexads | |
| 1 – 6/5 – 10/7 – 3/2 – 9/5 – 19/10 (steps 6/5, 19/16, 20/19, 6/5, 19/18, 20/19) |
1 – 6/5 – 24/19 – 3/2 – 9/5 – 36/19 (steps 6/5, 20/19, 19/16, 6/5, 20/19, 19/18) |
| 1 – 6/5 – 10/7 – 3/2 – 12/7 – 19/10 (steps 6/5, 19/16, 20/19, 8/7, 10/9, 20/19) |
1 – 19/16 – 10/7 – 3/2 – 5/3 – 19/10 (steps 19/16, 6/5, 20/19, 10/9, 8/7, 20/19) |
| 1 – 6/5 – 10/7 – 3/2 – 12/7 – 9/5 (steps 6/5, 19/16, 20/19, 8/7, 20/19, 10/9) |
1 – 20/19 – 5/4 – 3/2 – 5/3 – 7/4 (steps 20/19, 19/16, 6/5, 10/9, 20/19, 8/7) |
| 1 – 6/5 – 4/3 – 10/7 – 3/2 – 12/7 (steps 6/5, 10/9, 15/14, 20/19, 8/7, 7/6) |
1 – 20/19 – 9/8 – 5/4 – 3/2 – 7/4 (steps 20/19, 15/14, 10/9, 6/5, 7/6, 8/7) |
| 1 – 6/5 – 9/7 – 10/7 – 3/2 – 12/7 (steps 6/5, 15/14, 10/9, 20/19, 8/7, 7/6) |
1 – 20/19 – 7/6 – 5/4 – 3/2 – 7/4 (steps 20/19, 10/9, 15/14, 6/5, 7/6, 8/7) |
| 1 – 6/5 – 9/7 – 10/7 – 3/2 – 9/5 (steps 6/5, 15/14, 10/9, 20/19, 6/5, 10/9) |
1 – 6/5 – 24/19 – 7/5 – 3/2 – 9/5 (steps 6/5, 20/19, 10/9, 15/14, 6/5, 10/9) |
| 1 – 6/5 – 4/3 – 3/2 – 12/7 – 19/10 (steps 6/5, 10/9, 9/8, 8/7, 10/9, 20/19) |
1 – 9/8 – 5/4 – 3/2 – 30/19 – 7/4 (steps 9/8, 10/9, 6/5, 20/19, 10/9, 8/7) |
| 1 – 6/5 – 4/3 – 3/2 – 8/5 – 19/10 (steps 6/5, 10/9, 9/8, 16/15, 19/16, 20/19) |
1 – 9/8 – 5/4 – 3/2 – 30/19 – 15/8 (steps 9/8, 10/9, 6/5, 20/19, 19/16, 16/15) |
| 1 – 6/5 – 24/19 – 3/2 – 12/7 – 9/5 (steps 6/5, 20/19, 19/16, 8/7, 20/19, 10/9) |
1 – 19/16 – 5/4 – 3/2 – 5/3 – 7/4 (steps 19/16, 20/19, 6/5, 10/9, 20/19, 8/7) |
| 1 – 6/5 – 9/7 – 3/2 – 12/7 – 9/5 (steps 6/5, 15/14, 7/6, 8/7, 20/19, 10/9) |
1 – 7/6 – 5/4 – 3/2 – 5/3 – 7/4 (steps 7/6, 15/14, 6/5, 10/9, 20/19, 8/7) |
| 1 – 15/14 – 9/7 – 10/7 – 3/2 – 9/5 (steps 15/14, 6/5, 10/9, 20/19, 6/5, 10/9) |
1 – 15/14 – 19/16 – 10/7 – 3/2 – 5/3 (steps 15/14, 10/9, 6/5, 20/19, 10/9, 6/5) |
| 1 – 5/4 – 3/2 – 5/3 – 7/4 – 15/8 (steps 5/4, 6/5, 10/9, 20/19, 15/14, 16/15) |
1 – 6/5 – 3/2 – 8/5 – 12/7 – 9/5 (steps 6/5, 5/4, 16/15, 15/14, 20/19, 10/9) |
| 1 – 5/4 – 3/2 – 30/19 – 7/4 – 15/8 (steps 5/4, 6/5, 20/19, 10/9, 15/14, 16/15) |
1 – 6/5 – 3/2 – 8/5 – 12/7 – 19/10 (steps 6/5, 5/4, 16/15, 15/14, 10/9, 20/19) |
| 1 – 5/4 – 3/2 – 30/19 – 5/3 – 7/4 (steps 5/4, 6/5, 20/19, 19/18, 20/19, 8/7) |
1 – 6/5 – 3/2 – 12/7 – 9/5 – 19/10 (steps 6/5, 5/4, 8/7, 20/19, 19/18, 20/19) |
| 1 – 24/19 – 4/3 – 7/5 – 3/2 – 8/5 (steps 24/19, 19/18, 20/19, 15/14, 16/15, 5/4) |
1 – 5/4 – 4/3 – 10/7 – 3/2 – 19/12 (steps 5/4, 16/15, 15/14, 20/19, 19/18, 24/19) |
| 1 – 24/19 – 3/2 – 8/5 – 12/7 – 9/5 (steps 24/19, 19/16, 16/15, 15/14, 20/19, 10/9) |
1 – 19/16 – 3/2 – 5/3 – 7/4 – 15/8 (steps 19/16, 24/19, 10/9, 20/19, 15/14, 16/15) |
| 1 – 24/19 – 3/2 – 30/19 – 9/5 – 36/19 (steps 24/19, 19/16, 20/19, 8/7, 20/19, 19/18) |
1 – 19/16 – 3/2 – 19/12 – 5/3 – 19/10 (steps 19/16, 24/19, 19/18, 20/19, 8/7, 20/19) |
| 1 – 24/19 – 7/5 – 3/2 – 30/19 – 9/5 (steps 24/19, 10/9, 15/14, 20/19, 8/7, 10/9) |
1 – 15/14 – 19/16 – 3/2 – 5/3 – 19/10 (steps 15/14, 10/9, 24/19, 10/9, 8/7, 20/19) |
| 1 – 24/19 – 7/5 – 3/2 – 8/5 – 9/5 (steps 24/19, 10/9, 15/14, 16/15, 9/8, 10/9) |
1 – 15/14 – 19/16 – 3/2 – 5/3 – 15/8 (steps 15/14, 10/9, 24/19, 10/9, 9/8, 16/15) |
| 1 – 6/5 – 4/3 – 7/5 – 3/2 – 19/10 (steps 6/5, 10/9, 20/19, 15/14, 19/15, 20/19) |
1 – 15/14 – 9/8 – 5/4 – 3/2 – 30/19 (steps 15/14, 20/19, 10/9, 6/5, 20/19, 19/15) |
| 1 – 6/5 – 4/3 – 10/7 – 3/2 – 19/10 (steps 6/5, 10/9, 15/14, 20/19, 19/15, 20/19) |
1 – 15/14 – 19/16 – 10/7 – 3/2 – 19/10 (steps 15/14, 10/9, 6/5, 20/19, 19/15, 20/19) |
| 1 – 6/5 – 24/19 – 4/3 – 7/5 – 3/2 (steps 6/5, 20/19, 19/18, 20/19, 15/14, 4/3) |
1 – 15/14 – 9/8 – 19/16 – 5/4 – 3/2 (steps 15/14, 20/19, 19/18, 20/19, 6/5, 4/3) |
| 1 – 9/8 – 6/5 – 9/7 – 10/7 – 3/2 (steps 9/8, 16/15, 15/14, 10/9, 20/19, 4/3) |
1 – 20/19 – 7/6 – 5/4 – 4/3 – 3/2 (steps 20/19, 10/9, 15/14, 16/15, 9/8, 4/3) |
| 1 – 9/8 – 19/16 – 5/4 – 10/7 – 3/2 (steps 9/8, 19/18, 20/19, 8/7, 20/19, 4/3) |
1 – 20/19 – 6/5 – 24/19 – 4/3 – 3/2 (steps 20/19, 8/7, 20/19, 19/18, 9/8, 4/3) |
| 1 – 15/14 – 19/16 – 5/4 – 10/7 – 3/2 (steps 15/14, 10/9, 20/19, 8/7, 20/19, 4/3) |
1 – 20/19 – 6/5 – 24/19 – 7/5 – 3/2 (steps 20/19, 8/7, 20/19, 10/9, 15/14, 4/3) |
| 1 – 15/14 – 9/8 – 9/7 – 10/7 – 3/2 (steps 15/14, 20/19, 8/7, 10/9, 20/19, 4/3) |
1 – 20/19 – 7/6 – 4/3 – 7/5 – 3/2 (steps 20/19, 10/9, 8/7, 20/19, 15/14, 4/3) |
| 1 – 15/14 – 9/8 – 5/4 – 10/7 – 3/2 (steps 15/14, 20/19, 10/9, 8/7, 20/19, 4/3) |
1 – 20/19 – 6/5 – 4/3 – 7/5 – 3/2 (steps 20/19, 8/7, 10/9, 20/19, 15/14, 4/3) |
| 1 – 15/14 – 9/8 – 19/16 – 10/7 – 3/2 (steps 15/14, 20/19, 19/18, 6/5, 20/19, 4/3) |
1 – 20/19 – 24/19 – 4/3 – 7/5 – 3/2 (steps 20/19, 6/5, 19/18, 20/19, 15/14, 4/3) |
| 1 – 20/19 – 5/4 – 4/3 – 10/7 – 3/2 (steps 20/19, 19/16, 16/15, 15/14, 20/19, 4/3) |
1 – 20/19 – 9/8 – 6/5 – 10/7 – 3/2 (steps 20/19, 15/14, 16/15, 19/16, 20/19, 4/3) |
| 1 – 20/19 – 6/5 – 4/3 – 10/7 – 3/2 (steps 20/19, 8/7, 10/9, 15/14, 20/19, 4/3) |
1 – 20/19 – 9/8 – 5/4 – 10/7 – 3/2 (steps 20/19, 15/14, 10/9, 8/7, 20/19, 4/3) |
| 1 – 7/5 – 3/2 – 30/19 – 5/3 – 7/4 (steps 7/5, 15/14, 20/19, 19/18, 20/19, 8/7) |
1 – 15/14 – 3/2 – 12/7 – 9/5 – 19/10 (steps 15/14, 7/5, 8/7, 20/19, 19/18, 20/19) |
| 1 – 10/7 – 3/2 – 12/7 – 9/5 – 19/10 (steps 10/7, 20/19, 8/7, 20/19, 19/18, 20/19) |
1 – 10/7 – 3/2 – 19/12 – 5/3 – 19/10 (steps 10/7, 20/19, 19/18, 20/19, 8/7, 20/19) |
| 1 – 16/15 – 8/7 – 6/5 – 19/15 – 4/3 (steps 16/15, 15/14, 20/19, 19/18, 20/19, 3/2) |
1 – 20/19 – 10/9 – 7/6 – 5/4 – 4/3 (steps 20/19, 19/18, 20/19, 15/14, 16/15, 3/2) |
For heptads, there are seven pairs of chords in inverse relationship:
| Inversely related pairs of heptads | |
|---|---|
| 1 – 6/5 – 10/7 – 3/2 – 12/7 – 9/5 – 19/10 (steps 6/5, 19/16, 20/19, 8/7, 20/19, 19/18, 20/19) |
1 – 20/19 – 5/4 – 3/2 – 30/19 – 5/3 – 7/4 (steps 20/19, 19/16, 6/5, 20/19, 19/18, 20/19, 8/7) |
| 1 – 6/5 – 4/3 – 3/2 – 8/5 – 12/7 – 19/10 (steps 6/5, 10/9, 9/8, 16/15, 15/14, 10/9, 20/19) |
1 – 9/8 – 5/4 – 3/2 – 30/19 – 7/4 – 15/8 (steps 9/8, 10/9, 6/5, 20/19, 10/9, 15/14, 16/15) |
| 1 – 6/5 – 4/3 – 10/7 – 3/2 – 12/7 – 19/10 (steps 6/5, 10/9, 15/14, 20/19, 8/7, 10/9, 20/19) |
1 – 15/14 – 19/16 – 10/7 – 3/2 – 5/3 – 19/10 (steps 15/14, 10/9, 6/5, 20/19, 10/9, 8/7, 20/19) |
| 1 – 6/5 – 9/7 – 10/7 – 3/2 – 12/7 – 9/5 (steps 6/5, 15/14, 10/9, 20/19, 8/7, 20/19, 10/9) |
1 – 15/14 – 9/7 – 10/7 – 3/2 – 12/7 – 9/5 (steps 15/14, 6/5, 10/9, 20/19, 8/7, 20/19, 10/9) |
| 1 – 6/5 – 24/19 – 3/2 – 8/5 – 12/7 – 9/5 (steps 6/5, 20/19, 19/16, 16/15, 15/14, 20/19, 10/9) |
1 – 19/16 – 5/4 – 3/2 – 5/3 – 7/4 – 15/8 (steps 19/16, 20/19, 6/5, 10/9, 20/19, 15/14, 16/15) |
| 1 – 5/4 – 3/2 – 30/19 – 5/3 – 7/4 – 15/8 (steps 5/4, 6/5, 20/19, 19/18, 20/19, 15/14, 16/15) |
1 – 6/5 – 3/2 – 8/5 – 12/7 – 9/5 – 19/10 (steps 6/5, 5/4, 16/15, 15/14, 20/19, 19/18, 20/19) |
| 1 – 15/14 – 9/8 – 19/16 – 5/4 – 10/7 – 3/2 (steps 15/14, 20/19, 19/18, 20/19, 8/7, 20/19, 4/3) |
1 – 20/19 – 6/5 – 24/19 – 4/3 – 7/5 – 3/2 (steps 20/19, 8/7, 20/19, 19/18, 20/19, 15/14, 4/3) |
Equal temperaments with devichromic chords include 12, 19, 22, 26, 27, 31, 41, 53, 68, 72, 94, 99, 140, 152 and 345, with 345edo giving the optimal patent val.