The Q43 Transform
Q43 on C, voice by voice: the chords it pairs, the voice that steps, the source's own words, and every chord each side spells.
On C, Q43 pairs Cmaj7 (C E G B) with C#m7b5 (C# E G B): 1 voice steps, 3 hold, and the lead costs 1 semitone.
| Voice | Becomes | Step |
|---|---|---|
| C | C# | +1 |
| E | E | holds |
| G | G | holds |
| B | B | holds |
What each side spells
- Cmaj7: Cmaj7
- C#m7b5: C#m7b5, Em6
The paper's printed cycle through all 51 chords takes this step 7 times.
As the source prints it
The most parsimonious transformations exchange two types of sevenths moving just a note by a semitone or a whole-tone.
Q43 : [x, x + 4, x + 7, x + 11] ↔ [x + 1, x + 4, x + 7, x + 11]
— A Generalized Dual of the Tonnetz for Seventh Chords: Mathematical, Computational and Compositional Aspects, pp. 301–308; Sonia Cannas and Moreno Andreatta. The source, read 2026-10-25.
Rank every pairing of Cmaj7 and C#m7b5 in the calculator · Every chord one voice from Cmaj7