Xenllium: Created page with "'''Worcester chords''' are essentially tempered chords tempered by 576/575, the worcester comma. There are 10 triads, 39 tetrads, 65 pentads, 45 hexads, 15 heptads and 2 octads as 2.3.5.23 subgroup 23-odd-limit essentially tempered chords. For triads, there are two palindromic chords and four pairs of chords in inverse relationship: {| class="wikitable center-all" |- ! colspan="2" | Palindromic triads |- | colspan="2" | 1 – 5/4 – 36/23 (s..."

2026-09-12T16:36:09Z

Created page with "'''Worcester chords''' are essentially tempered chords tempered by 576/575, the worcester comma. There are 10 triads, 39 tetrads, 65 pentads, 45 hexads, 15 heptads and 2 octads as 2.3.5.23 subgroup 23-odd-limit essentially tempered chords. For triads, there are two palindromic chords and four pairs of chords in inverse relationship: {| class="wikitable center-all" |- ! colspan="2" | Palindromic triads |- | colspan="2" | 1 – 5/4 – 36/23 (s..."

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'''Worcester chords''' are [[Dyadic chord|essentially tempered chords]] tempered by [[576/575]], the worcester comma.

There are 10 triads, 39 tetrads, 65 pentads, 45 hexads, 15 heptads and 2 octads as 2.3.5.23 subgroup [[23-odd-limit]] essentially tempered chords.

For triads, there are two palindromic chords and four pairs of chords in inverse relationship:

{| class="wikitable center-all"
|-
! colspan="2" | Palindromic triads
|-
| colspan="2" | 1 – 5/4 – 36/23 (steps 5/4, 5/4, 23/18)
|-
| colspan="2" | 1 – 6/5 – 23/16 (steps 6/5, 6/5, 32/23)
|-
! colspan="2" | Inversely related pairs of triads
|-
| 1 – 5/4 – 32/23 (steps 5/4, 10/9, 23/16) || 1 – 10/9 – 32/23 (steps 10/9, 5/4, 23/16)
|-
| 1 – 6/5 – 23/18 (steps 6/5, 16/15, 36/23) || 1 – 16/15 – 23/18 (steps 16/15, 6/5, 36/23)
|-
| 1 – 6/5 – 5/4 (steps 6/5, 24/23, 8/5) || 1 – 24/23 – 5/4 (steps 24/23, 6/5, 8/5)
|-
| 1 – 16/15 – 10/9 (steps 16/15, 24/23, 9/5) || 1 – 24/23 – 10/9 (steps 24/23, 16/15, 9/5)
|}

For tetrads, there are seven palindromic chords and sixteen pairs of chords in inverse relationship:

{| class="wikitable center-all"
|-
! colspan="2" | Palindromic tetrads
|-
| colspan="2" | 1 – 23/20 – 23/16 – 8/5 (steps 23/20, 5/4, 10/9, 5/4)
|-
| colspan="2" | 1 – 6/5 – 23/18 – 23/15 (steps 6/5, 16/15, 6/5, 30/23)
|-
| colspan="2" | 1 – 6/5 – 5/4 – 3/2 (steps 6/5, 24/23, 6/5, 4/3)
|-
| colspan="2" | 1 – 10/9 – 5/4 – 32/23 (steps 10/9, 9/8, 10/9, 23/16)
|-
| colspan="2" | 1 – 24/23 – 5/4 – 30/23 (steps 24/23, 6/5, 24/23, 23/15)
|-
| colspan="2" | 1 – 16/15 – 6/5 – 23/18 (steps 16/15, 9/8, 16/15, 36/23)
|-
| colspan="2" | 1 – 24/23 – 6/5 – 5/4 (steps 24/23, 23/20, 24/23, 8/5)
|-
! colspan="2" | Inversely related pairs of tetrads
|-
| 1 – 5/4 – 3/2 – 9/5 (steps 5/4, 6/5, 6/5, 10/9) || 1 – 6/5 – 3/2 – 5/3 (steps 6/5, 5/4, 10/9, 6/5)
|-
| 1 – 5/4 – 3/2 – 8/5 (steps 5/4, 6/5, 16/15, 5/4) || 1 – 6/5 – 3/2 – 15/8 (steps 6/5, 5/4, 5/4, 16/15)
|-
| 1 – 5/4 – 3/2 – 36/23 (steps 5/4, 6/5, 24/23, 23/18) || 1 – 6/5 – 3/2 – 23/12 (steps 6/5, 5/4, 23/18, 24/23)
|-
| 1 – 23/16 – 3/2 – 8/5 (steps 23/16, 24/23, 16/15, 5/4) || 1 – 24/23 – 3/2 – 15/8 (steps 24/23, 23/16, 5/4, 16/15)
|-
| 1 – 6/5 – 23/16 – 3/2 (steps 6/5, 6/5, 24/23, 4/3) || 1 – 24/23 – 5/4 – 3/2 (steps 24/23, 6/5, 6/5, 4/3)
|-
| 1 – 5/4 – 23/16 – 8/5 (steps 5/4, 23/20, 10/9, 5/4) || 1 – 5/4 – 32/23 – 8/5 (steps 5/4, 10/9, 23/20, 5/4)
|-
| 1 – 5/4 – 32/23 – 36/23 (steps 5/4, 10/9, 9/8, 23/18) || 1 – 9/8 – 5/4 – 36/23 (steps 9/8, 10/9, 5/4, 23/18)
|-
| 1 – 5/4 – 30/23 – 36/23 (steps 5/4, 24/23, 6/5, 23/18) || 1 – 6/5 – 5/4 – 36/23 (steps 6/5, 24/23, 5/4, 23/18)
|-
| 1 – 6/5 – 23/16 – 23/15 (steps 6/5, 6/5, 16/15, 30/23) || 1 – 16/15 – 23/18 – 23/15 (steps 16/15, 6/5, 6/5, 30/23)
|-
| 1 – 6/5 – 23/18 – 23/16 (steps 6/5, 16/15, 9/8, 32/23) || 1 – 9/8 – 6/5 – 23/16 (steps 9/8, 16/15, 6/5, 32/23)
|-
| 1 – 6/5 – 5/4 – 23/16 (steps 6/5, 24/23, 23/20, 32/23) || 1 – 23/20 – 6/5 – 23/16 (steps 23/20, 24/23, 6/5, 32/23)
|-
| 1 – 5/4 – 30/23 – 32/23 (steps 5/4, 24/23, 16/15, 23/16) || 1 – 16/15 – 10/9 – 32/23 (steps 16/15, 24/23, 5/4, 23/16)
|-
| 1 – 6/5 – 23/18 – 4/3 (steps 6/5, 16/15, 24/23, 3/2) || 1 – 24/23 – 10/9 – 4/3 (steps 24/23, 16/15, 6/5, 3/2)
|-
| 1 – 6/5 – 5/4 – 4/3 (steps 6/5, 24/23, 16/15, 3/2) || 1 – 16/15 – 10/9 – 4/3 (steps 16/15, 24/23, 6/5, 3/2)
|-
| 1 – 23/20 – 6/5 – 23/18 (steps 23/20, 24/23, 16/15, 36/23) || 1 – 16/15 – 10/9 – 23/18 (steps 16/15, 24/23, 23/20, 36/23)
|-
| 1 – 9/8 – 6/5 – 5/4 (steps 9/8, 16/15, 24/23, 8/5) || 1 – 24/23 – 10/9 – 5/4 (steps 24/23, 16/15, 9/8, 8/5)
|}

For pentads, there are three palindromic chords and 31 pairs of chords in inverse relationship:

{| class="wikitable center-all"
|-
! colspan="2" | Palindromic pentads
|-
| colspan="2" | 1 – 6/5 – 4/3 – 3/2 – 5/3 (steps 6/5, 10/9, 9/8, 10/9, 6/5)
|-
| colspan="2" | 1 – 5/4 – 4/3 – 3/2 – 8/5 (steps 5/4, 16/15, 9/8, 16/15, 5/4)
|-
| colspan="2" | 1 – 24/23 – 5/4 – 3/2 – 36/23 (steps 24/23, 6/5, 6/5, 24/23, 23/18)
|-
! colspan="2" | Inversely related pairs of pentads
|-
| 1 – 23/16 – 3/2 – 9/5 – 15/8 (steps 23/16, 24/23, 6/5, 24/23, 16/15) || 1 – 24/23 – 3/2 – 8/5 – 5/3 (steps 24/23, 23/16, 16/15, 24/23, 6/5)
|-
| 1 – 23/16 – 3/2 – 8/5 – 23/12 (steps 23/16, 24/23, 16/15, 6/5, 24/23) || 1 – 24/23 – 3/2 – 36/23 – 15/8 (steps 24/23, 23/16, 24/23, 6/5, 16/15)
|-
| 1 – 23/16 – 3/2 – 8/5 – 9/5 (steps 23/16, 24/23, 16/15, 9/8, 10/9) || 1 – 24/23 – 3/2 – 5/3 – 15/8 (steps 24/23, 23/16, 10/9, 9/8, 16/15)
|-
| 1 – 30/23 – 3/2 – 36/23 – 15/8 (steps 30/23, 23/20, 24/23, 6/5, 16/15) || 1 – 23/20 – 3/2 – 8/5 – 23/12 (steps 23/20, 30/23, 16/15, 6/5, 24/23)
|-
| 1 – 30/23 – 3/2 – 36/23 – 5/3 (steps 30/23, 23/20, 24/23, 16/15, 6/5) || 1 – 23/20 – 3/2 – 9/5 – 23/12 (steps 23/20, 30/23, 6/5, 16/15, 24/23)
|-
| 1 – 5/4 – 3/2 – 9/5 – 23/12 (steps 5/4, 6/5, 6/5, 16/15, 24/23) || 1 – 6/5 – 3/2 – 36/23 – 5/3 (steps 6/5, 5/4, 24/23, 16/15, 6/5)
|-
| 1 – 5/4 – 3/2 – 9/5 – 15/8 (steps 5/4, 6/5, 6/5, 24/23, 16/15) || 1 – 6/5 – 3/2 – 8/5 – 5/3 (steps 6/5, 5/4, 16/15, 24/23, 6/5)
|-
| 1 – 5/4 – 3/2 – 8/5 – 23/12 (steps 5/4, 6/5, 16/15, 6/5, 24/23) || 1 – 6/5 – 3/2 – 36/23 – 15/8 (steps 6/5, 5/4, 24/23, 6/5, 16/15)
|-
| 1 – 5/4 – 3/2 – 8/5 – 9/5 (steps 5/4, 6/5, 16/15, 9/8, 10/9) || 1 – 6/5 – 3/2 – 5/3 – 15/8 (steps 6/5, 5/4, 10/9, 9/8, 16/15)
|-
| 1 – 5/4 – 3/2 – 8/5 – 5/3 (steps 5/4, 6/5, 16/15, 24/23, 6/5) || 1 – 5/4 – 3/2 – 36/23 – 5/3 (steps 5/4, 6/5, 24/23, 16/15, 6/5)
|-
| 1 – 5/4 – 3/2 – 36/23 – 15/8 (steps 5/4, 6/5, 24/23, 6/5, 16/15) || 1 – 6/5 – 3/2 – 8/5 – 23/12 (steps 6/5, 5/4, 16/15, 6/5, 24/23)
|-
| 1 – 5/4 – 3/2 – 36/23 – 9/5 (steps 5/4, 6/5, 24/23, 23/20, 10/9) || 1 – 6/5 – 3/2 – 5/3 – 23/12 (steps 6/5, 5/4, 10/9, 23/20, 24/23)
|-
| 1 – 5/4 – 23/16 – 3/2 – 9/5 (steps 5/4, 23/20, 24/23, 6/5, 10/9) || 1 – 24/23 – 6/5 – 3/2 – 5/3 (steps 24/23, 23/20, 5/4, 10/9, 6/5)
|-
| 1 – 5/4 – 23/16 – 3/2 – 8/5 (steps 5/4, 23/20, 24/23, 16/15, 5/4) || 1 – 24/23 – 6/5 – 3/2 – 15/8 (steps 24/23, 23/20, 5/4, 5/4, 16/15)
|-
| 1 – 5/4 – 23/16 – 3/2 – 36/23 (steps 5/4, 23/20, 24/23, 24/23, 23/18) || 1 – 24/23 – 6/5 – 3/2 – 23/12 (steps 24/23, 23/20, 5/4, 23/18, 24/23)
|-
| 1 – 6/5 – 23/16 – 3/2 – 15/8 (steps 6/5, 6/5, 24/23, 5/4, 16/15) || 1 – 24/23 – 5/4 – 3/2 – 8/5 (steps 24/23, 6/5, 6/5, 16/15, 5/4)
|-
| 1 – 6/5 – 4/3 – 3/2 – 23/12 (steps 6/5, 10/9, 9/8, 23/18, 24/23) || 1 – 9/8 – 5/4 – 3/2 – 36/23 (steps 9/8, 10/9, 6/5, 24/23, 23/18)
|-
| 1 – 6/5 – 5/4 – 3/2 – 23/12 (steps 6/5, 24/23, 6/5, 23/18, 24/23) || 1 – 6/5 – 5/4 – 3/2 – 36/23 (steps 6/5, 24/23, 6/5, 24/23, 23/18)
|-
| 1 – 6/5 – 5/4 – 3/2 – 9/5 (steps 6/5, 24/23, 6/5, 6/5, 10/9) || 1 – 6/5 – 5/4 – 3/2 – 5/3 (steps 6/5, 24/23, 6/5, 10/9, 6/5)
|-
| 1 – 23/20 – 23/16 – 3/2 – 9/5 (steps 23/20, 5/4, 24/23, 6/5, 10/9) || 1 – 24/23 – 30/23 – 3/2 – 5/3 (steps 24/23, 5/4, 23/20, 10/9, 6/5)
|-
| 1 – 23/20 – 23/16 – 3/2 – 8/5 (steps 23/20, 5/4, 24/23, 16/15, 5/4) || 1 – 24/23 – 30/23 – 3/2 – 15/8 (steps 24/23, 5/4, 23/20, 5/4, 16/15)
|-
| 1 – 6/5 – 5/4 – 23/16 – 3/2 (steps 6/5, 24/23, 23/20, 24/23, 4/3) || 1 – 24/23 – 6/5 – 5/4 – 3/2 (steps 24/23, 23/20, 24/23, 6/5, 4/3)
|-
| 1 – 6/5 – 5/4 – 4/3 – 3/2 (steps 6/5, 24/23, 16/15, 9/8, 4/3) || 1 – 9/8 – 6/5 – 5/4 – 3/2 (steps 9/8, 16/15, 24/23, 6/5, 4/3)
|-
| 1 – 23/20 – 6/5 – 23/16 – 3/2 (steps 23/20, 24/23, 6/5, 24/23, 4/3) || 1 – 24/23 – 5/4 – 30/23 – 3/2 (steps 24/23, 6/5, 24/23, 23/20, 4/3)
|-
| 1 – 9/8 – 6/5 – 23/16 – 3/2 (steps 9/8, 16/15, 6/5, 24/23, 4/3) || 1 – 24/23 – 5/4 – 4/3 – 3/2 (steps 24/23, 6/5, 16/15, 9/8, 4/3)
|-
| 1 – 23/20 – 23/18 – 23/16 – 8/5 (steps 23/20, 10/9, 9/8, 10/9, 5/4) || 1 – 10/9 – 5/4 – 32/23 – 8/5 (steps 10/9, 9/8, 10/9, 23/20, 5/4)
|-
| 1 – 5/4 – 30/23 – 32/23 – 36/23 (steps 5/4, 24/23, 16/15, 9/8, 23/18) || 1 – 9/8 – 6/5 – 5/4 – 36/23 (steps 9/8, 16/15, 24/23, 5/4, 23/18)
|-
| 1 – 6/5 – 23/18 – 23/16 – 23/15 (steps 6/5, 16/15, 9/8, 16/15, 30/23) || 1 – 16/15 – 6/5 – 23/18 – 23/15 (steps 16/15, 9/8, 16/15, 6/5, 30/23)
|-
| 1 – 23/20 – 6/5 – 23/18 – 23/16 (steps 23/20, 24/23, 16/15, 9/8, 32/23) || 1 – 9/8 – 6/5 – 5/4 – 23/16 (steps 9/8, 16/15, 24/23, 23/20, 32/23)
|-
| 1 – 16/15 – 6/5 – 23/18 – 4/3 (steps 16/15, 9/8, 16/15, 24/23, 3/2) || 1 – 24/23 – 10/9 – 5/4 – 4/3 (steps 24/23, 16/15, 9/8, 16/15, 3/2)
|-
| 1 – 16/15 – 10/9 – 23/18 – 4/3 (steps 16/15, 24/23, 23/20, 24/23, 3/2) || 1 – 24/23 – 6/5 – 5/4 – 4/3 (steps 24/23, 23/20, 24/23, 16/15, 3/2)
|}

For hexads, there are three palindromic chords and 21 pairs of chords in inverse relationship:

{| class="wikitable center-all"
|-
! colspan="2" | Palindromic hexads
|-
| colspan="2" | 1 – 23/16 – 3/2 – 8/5 – 9/5 – 23/12 (steps 23/16, 24/23, 16/15, 9/8, 16/15, 24/23)
|-
| colspan="2" | 1 – 6/5 – 5/4 – 3/2 – 36/23 – 15/8 (steps 6/5, 24/23, 6/5, 24/23, 6/5, 16/15)
|-
| colspan="2" | 1 – 6/5 – 5/4 – 23/16 – 3/2 – 9/5 (steps 6/5, 24/23, 23/20, 24/23, 6/5, 10/9)
|-
! colspan="2" | Inversely related pairs of hexads
|-
| 1 – 5/4 – 3/2 – 8/5 – 9/5 – 23/12 (steps 5/4, 6/5, 16/15, 9/8, 16/15, 24/23) || 1 – 6/5 – 3/2 – 36/23 – 5/3 – 15/8 (steps 6/5, 5/4, 24/23, 16/15, 9/8, 16/15)
|-
| 1 – 30/23 – 3/2 – 36/23 – 5/3 – 15/8 (steps 30/23, 23/20, 24/23, 16/15, 9/8, 16/15) || 1 – 23/20 – 3/2 – 8/5 – 9/5 – 23/12 (steps 23/20, 30/23, 16/15, 9/8, 16/15, 24/23)
|-
| 1 – 5/4 – 23/16 – 3/2 – 9/5 – 23/12 (steps 5/4, 23/20, 24/23, 6/5, 16/15, 24/23) || 1 – 23/20 – 23/16 – 3/2 – 8/5 – 23/12 (steps 23/20, 5/4, 24/23, 16/15, 6/5, 24/23)
|-
| 1 – 5/4 – 23/16 – 3/2 – 8/5 – 23/12 (steps 5/4, 23/20, 24/23, 16/15, 6/5, 24/23) || 1 – 23/20 – 23/16 – 3/2 – 9/5 – 23/12 (steps 23/20, 5/4, 24/23, 6/5, 16/15, 24/23)
|-
| 1 – 5/4 – 23/16 – 3/2 – 8/5 – 9/5 (steps 5/4, 23/20, 24/23, 16/15, 9/8, 10/9) || 1 – 24/23 – 6/5 – 3/2 – 5/3 – 15/8 (steps 24/23, 23/20, 5/4, 10/9, 9/8, 16/15)
|-
| 1 – 5/4 – 30/23 – 3/2 – 36/23 – 5/3 (steps 5/4, 24/23, 23/20, 24/23, 16/15, 6/5) || 1 – 23/20 – 6/5 – 3/2 – 9/5 – 23/12 (steps 23/20, 24/23, 5/4, 6/5, 16/15, 24/23)
|-
| 1 – 6/5 – 23/16 – 3/2 – 9/5 – 23/12 (steps 6/5, 6/5, 24/23, 6/5, 16/15, 24/23) || 1 – 6/5 – 23/16 – 3/2 – 8/5 – 23/12 (steps 6/5, 6/5, 24/23, 16/15, 6/5, 24/23)
|-
| 1 – 6/5 – 23/16 – 3/2 – 9/5 – 15/8 (steps 6/5, 6/5, 24/23, 6/5, 24/23, 16/15) || 1 – 6/5 – 5/4 – 3/2 – 9/5 – 23/12 (steps 6/5, 24/23, 6/5, 6/5, 16/15, 24/23)
|-
| 1 – 23/20 – 23/16 – 3/2 – 8/5 – 9/5 (steps 23/20, 5/4, 24/23, 16/15, 9/8, 10/9) || 1 – 24/23 – 30/23 – 3/2 – 5/3 – 15/8 (steps 24/23, 5/4, 23/20, 10/9, 9/8, 16/15)
|-
| 1 – 6/5 – 5/4 – 23/16 – 3/2 – 8/5 (steps 6/5, 24/23, 23/20, 24/23, 16/15, 5/4) || 1 – 24/23 – 6/5 – 5/4 – 3/2 – 15/8 (steps 24/23, 23/20, 24/23, 6/5, 5/4, 16/15)
|-
| 1 – 6/5 – 5/4 – 23/16 – 3/2 – 15/8 (steps 6/5, 24/23, 23/20, 24/23, 5/4, 16/15) || 1 – 24/23 – 6/5 – 5/4 – 3/2 – 8/5 (steps 24/23, 23/20, 24/23, 6/5, 16/15, 5/4)
|-
| 1 – 6/5 – 5/4 – 23/16 – 3/2 – 23/12 (steps 6/5, 24/23, 23/20, 24/23, 23/18, 24/23) || 1 – 23/20 – 6/5 – 23/16 – 3/2 – 23/12 (steps 23/20, 24/23, 6/5, 24/23, 23/18, 24/23)
|-
| 1 – 6/5 – 5/4 – 4/3 – 3/2 – 23/12 (steps 6/5, 24/23, 16/15, 9/8, 23/18, 24/23) || 1 – 9/8 – 6/5 – 5/4 – 3/2 – 36/23 (steps 9/8, 16/15, 24/23, 6/5, 24/23, 23/18)
|-
| 1 – 6/5 – 5/4 – 4/3 – 3/2 – 5/3 (steps 6/5, 24/23, 16/15, 9/8, 10/9, 6/5) || 1 – 9/8 – 6/5 – 5/4 – 3/2 – 9/5 (steps 9/8, 16/15, 24/23, 6/5, 6/5, 10/9)
|-
| 1 – 6/5 – 5/4 – 4/3 – 3/2 – 8/5 (steps 6/5, 24/23, 16/15, 9/8, 16/15, 5/4) || 1 – 9/8 – 6/5 – 5/4 – 3/2 – 15/8 (steps 9/8, 16/15, 24/23, 6/5, 5/4, 16/15)
|-
| 1 – 23/20 – 6/5 – 23/16 – 3/2 – 9/5 (steps 23/20, 24/23, 6/5, 24/23, 6/5, 10/9) || 1 – 24/23 – 5/4 – 30/23 – 3/2 – 5/3 (steps 24/23, 6/5, 24/23, 23/20, 10/9, 6/5)
|-
| 1 – 23/20 – 6/5 – 23/16 – 3/2 – 8/5 (steps 23/20, 24/23, 6/5, 24/23, 16/15, 5/4) || 1 – 24/23 – 5/4 – 30/23 – 3/2 – 15/8 (steps 24/23, 6/5, 24/23, 23/20, 5/4, 16/15)
|-
| 1 – 9/8 – 5/4 – 23/16 – 3/2 – 9/5 (steps 9/8, 10/9, 23/20, 24/23, 6/5, 10/9) || 1 – 24/23 – 6/5 – 4/3 – 3/2 – 5/3 (steps 24/23, 23/20, 10/9, 9/8, 10/9, 6/5)
|-
| 1 – 9/8 – 6/5 – 23/16 – 3/2 – 9/5 (steps 9/8, 16/15, 6/5, 24/23, 6/5, 10/9) || 1 – 24/23 – 5/4 – 4/3 – 3/2 – 5/3 (steps 24/23, 6/5, 16/15, 9/8, 10/9, 6/5)
|-
| 1 – 9/8 – 6/5 – 23/16 – 3/2 – 15/8 (steps 9/8, 16/15, 6/5, 24/23, 5/4, 16/15) || 1 – 24/23 – 5/4 – 4/3 – 3/2 – 8/5 (steps 24/23, 6/5, 16/15, 9/8, 16/15, 5/4)
|-
| 1 – 9/8 – 6/5 – 5/4 – 23/16 – 3/2 (steps 9/8, 16/15, 24/23, 23/20, 24/23, 4/3) || 1 – 24/23 – 6/5 – 5/4 – 4/3 – 3/2 (steps 24/23, 23/20, 24/23, 16/15, 9/8, 4/3)
|}

For heptads, there are one palindromic chord and seven pairs of chords in inverse relationship:

{| class="wikitable center-all"
|-
! colspan="2" | Palindromic heptad
|-
| colspan="2" | 1 – 6/5 – 5/4 – 4/3 – 3/2 – 8/5 – 5/3 (steps 6/5, 24/23, 16/15, 9/8, 16/15, 24/23, 6/5)
|-
! colspan="2" | Inversely related pairs of heptads
|-
| 1 – 5/4 – 23/16 – 3/2 – 8/5 – 9/5 – 23/12 (steps 5/4, 23/20, 24/23, 16/15, 9/8, 16/15, 24/23) || 1 – 23/20 – 23/16 – 3/2 – 8/5 – 9/5 – 23/12 (steps 23/20, 5/4, 24/23, 16/15, 9/8, 16/15, 24/23)
|-
| 1 – 6/5 – 5/4 – 4/3 – 3/2 – 5/3 – 23/12 (steps 6/5, 24/23, 16/15, 9/8, 10/9, 23/20, 24/23) || 1 – 9/8 – 6/5 – 5/4 – 3/2 – 36/23 – 9/5 (steps 9/8, 16/15, 24/23, 6/5, 24/23, 23/20, 10/9)
|-
| 1 – 6/5 – 5/4 – 4/3 – 3/2 – 8/5 – 23/12 (steps 6/5, 24/23, 16/15, 9/8, 16/15, 6/5, 24/23) || 1 – 9/8 – 6/5 – 5/4 – 3/2 – 36/23 – 15/8 (steps 9/8, 16/15, 24/23, 6/5, 24/23, 6/5, 16/15)
|-
| 1 – 6/5 – 5/4 – 23/16 – 3/2 – 9/5 – 23/12 (steps 6/5, 24/23, 23/20, 24/23, 6/5, 16/15, 24/23) || 1 – 6/5 – 5/4 – 23/16 – 3/2 – 9/5 – 15/8 (steps 6/5, 24/23, 23/20, 24/23, 6/5, 24/23, 16/15)
|-
| 1 – 6/5 – 5/4 – 23/16 – 3/2 – 8/5 – 23/12 (steps 6/5, 24/23, 23/20, 24/23, 16/15, 6/5, 24/23) || 1 – 23/20 – 6/5 – 23/16 – 3/2 – 9/5 – 23/12 (steps 23/20, 24/23, 6/5, 24/23, 6/5, 16/15, 24/23)
|-
| 1 – 9/8 – 6/5 – 5/4 – 23/16 – 3/2 – 15/8 (steps 9/8, 16/15, 24/23, 23/20, 24/23, 5/4, 16/15) || 1 – 24/23 – 6/5 – 5/4 – 4/3 – 3/2 – 8/5 (steps 24/23, 23/20, 24/23, 16/15, 9/8, 16/15, 5/4)
|-
| 1 – 9/8 – 6/5 – 5/4 – 23/16 – 3/2 – 9/5 (steps 9/8, 16/15, 24/23, 23/20, 24/23, 6/5, 10/9) || 1 – 24/23 – 6/5 – 5/4 – 4/3 – 3/2 – 5/3 (steps 24/23, 23/20, 24/23, 16/15, 9/8, 10/9, 6/5)
|}

Finally, there is a pair of octads in inverse relationship:

{| class="wikitable center-all"
|-
! colspan="2" | Inversely related pair of octads
|-
| 1 – 9/8 – 6/5 – 5/4 – 23/16 – 3/2 – 9/5 – 15/8 (steps 9/8, 16/15, 24/23, 23/20, 24/23, 6/5, 24/23, 16/15) || 1 – 24/23 – 6/5 – 5/4 – 4/3 – 3/2 – 8/5 – 5/3 (steps 24/23, 23/20, 24/23, 16/15, 9/8, 16/15, 24/23, 6/5)
|}

Equal temperaments with worcester chords include {{Optimal ET sequence|12, 15, 19, 22, 31, 34, 46, 53, 65, 84, 99, 118, 164 and 183}}.

[[Category:23-odd-limit]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]
[[Category:Heptads]]
[[Category:Octads]]
[[Category:Worcester]]

Worcester chords - Revision history