The L13 Transform
L13 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, L13 pairs C7 (C E G Bb) with Em7b5 (E G Bb D): 1 voice steps, 3 hold, and the lead costs 2 semitones.
| Voice | Becomes | Step |
|---|---|---|
| C | D | +2 |
| E | E | holds |
| G | G | holds |
| Bb | Bb | holds |
What each side spells
- C7: C7
- Em7b5: Em7b5, Gm6
The paper's printed cycle through all 51 chords takes this step 6 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.
L13 : [x, x + 4, x + 7, x + 10] ↔ [x + 2, x + 4, x + 7, x + 10]
— 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 C7 and Em7b5 in the calculator · Every chord one voice from C7