The R23 Transform
R23 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, R23 pairs Cm7 (C Eb G Bb) with Am7b5 (A C Eb G): 1 voice steps, 3 hold, and the lead costs 1 semitone.
| Voice | Becomes | Step |
|---|---|---|
| C | C | holds |
| Eb | Eb | holds |
| G | G | holds |
| Bb | A | -1 |
What each side spells
- Cm7: Eb6, Cm7
- Am7b5: Am7b5, Cm6
The paper's printed cycle through all 51 chords takes this step 2 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.
R23 : [x, x + 3, x + 7, x + 10] ↔ [x, x + 3, x + 7, x + 9]
— 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 Cm7 and Am7b5 in the calculator · Every chord one voice from Cm7