The P35 Transform
P35 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, P35 pairs Cm7b5 (C Eb Gb Bb) with Cdim7 (C Eb Gb Bbb): 1 voice steps, 3 hold, and the lead costs 1 semitone. The paper also names this step R35, R53, RR35.
| Voice | Becomes | Step |
|---|---|---|
| C | C | holds |
| Eb | Eb | holds |
| Gb | Gb | holds |
| Bb | Bbb | -1 |
What each side spells
- Cm7b5: Cm7b5, Ebm6
- Cdim7: Cdim7, Ebdim7, F#dim7, Adim7
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.
P35 : [x, x + 3, x + 6, x + 10] ↔ [x, x + 3, x + 6, x + 9]
R35 : [x, x + 3, x + 6, x + 10] ↔ [x, x + 3, x + 6, x + 9]
R53 : [x, x + 3, x + 6, x + 9] ↔ [x, x + 3, x + 7, x + 9]
RR35 : [x, x + 3, x + 6, x + 10] ↔ [x, x + 3, x + 6, x + 9]The paper groups these names as one step:
P35 ∼ R35 ∼ R53 ∼ RR35 and L15 ∼ Q15 ∼ QQ51 ∼ N51.
— 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 Cm7b5 and Cdim7 in the calculator · Every chord one voice from Cm7b5