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2025-03-19T10:25:08Z

Created page with "'''Devichromic chords''' are essentially tempered chords tempered by 400/399, the devichroma. Devichromic chords are very numerous, including 18 triads,..."

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'''Devichromic chords''' are [[Dyadic chord|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:

{| class="wikitable center-all"
|-
! colspan="2" | 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:

{| class="wikitable center-all"
|-
! colspan="2" | Palindromic tetrads
|-
| colspan="2" | 1 – 10/7 – 3/2 – 19/10 (steps 10/7, 20/19, 19/15, 20/19)
|-
| colspan="2" | 1 – 15/14 – 10/7 – 3/2 (steps 15/14, 4/3, 20/19, 4/3)
|-
| colspan="2" | 1 – 20/19 – 10/7 – 3/2 (steps 20/19, 19/14, 20/19, 4/3)
|-
| colspan="2" | 1 – 19/16 – 10/7 – 5/3 (steps 19/16, 6/5, 7/6, 6/5)
|-
| colspan="2" | 1 – 10/9 – 10/7 – 19/12 (steps 10/9, 9/7, 10/9, 24/19)
|-
| colspan="2" | 1 – 20/19 – 6/5 – 24/19 (steps 20/19, 8/7, 20/19, 19/12)
|-
| colspan="2" | 1 – 20/19 – 10/9 – 7/6 (steps 20/19, 19/18, 20/19, 12/7)
|-
! colspan="2" | 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:

{| class="wikitable center-all"
|-
! colspan="2" | 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:

{| class="wikitable center-all"
|-
! colspan="2" | Palindromic hexads
|-
| colspan="2" | 1 – 9/7 – 10/7 – 3/2 – 12/7 – 9/5 (steps 9/7, 10/9, 20/19, 8/7, 20/19, 10/9)
|-
| colspan="2" | 1 – 19/16 – 10/7 – 3/2 – 19/12 – 5/3 (steps 19/16, 6/5, 20/19, 19/18, 20/19, 6/5)
|-
! colspan="2" | 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:

{| class="wikitable center-all"
|-
! colspan="2" | 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 {{Optimal ET sequence|12, 19, 22, 26, 27, 31, 41, 53, 68, 72, 94, 99, 140, 152 and 345}}, with [[345edo]] giving the optimal patent val.

[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]
[[Category:Heptads]]
[[Category:Devichromic]]

Devichromic chords - Revision history

Xenllium at 08:21, 11 September 2026

Xenllium: Created page with "'''Devichromic chords''' are essentially tempered chords tempered by 400/399, the devichroma. Devichromic chords are very numerous, including 18 triads,..."

← Older revision		Revision as of 08:21, 11 September 2026
Line 354:		Line 354:
	Equal temperaments with devichromic chords include {{Optimal ET sequence\|12, 19, 22, 26, 27, 31, 41, 53, 68, 72, 94, 99, 140, 152 and 345}}, with [[345edo]] giving the optimal patent val.		Equal temperaments with devichromic chords include {{Optimal ET sequence\|12, 19, 22, 26, 27, 31, 41, 53, 68, 72, 94, 99, 140, 152 and 345}}, with [[345edo]] giving the optimal patent val.

			[[Category:19-odd-limit]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Triads]]		[[Category:Triads]]