What it is
Neo-Riemannian theory describes the movements between major and minor triads not as functions (tonic, dominant…) but as transformations that move the fewest possible notes. It is named after Hugo Riemann (1849–1919), who classified the "relations" between chords; it was re-founded by David Lewin (Generalized Musical Intervals and Transformations, 1987; essay on Parsifal, 1984), by Richard Cohn (1990s), and by Brian Hyer (1995). It is especially useful for nineteenth-century chromatic music (Schubert, Liszt, Wagner, Bruckner) and for film music, where chords follow one another without dominant logic.
The three basic transformations
Each changes only one note and changes the quality of the chord (major ↔ minor). Each is its own inverse: applied twice, it returns to the starting chord.
| Transformation | What it does | Example |
|---|---|---|
| P (Parallel) | major: lowers the third by a half step; minor: raises it | C (C E G) ↔ Cm (C Eb G) |
| R (Relative) | major: raises the fifth by a whole step; minor: lowers the root by a whole step | C (C E G) ↔ Am (A C E) |
| L (Leittonwechsel, leading-tone exchange) | major: lowers the root by a half step; minor: raises the fifth by a half step | C (C E G) ↔ Em (B E G) |
The common tones are always two: P keeps root and fifth, R keeps C and E, L keeps E and G.
Compound transformations
- N (Nebenverwandt) = R, then L, then P: C ↔ Fm (major → minor subdominant). It is the relationship of the minor plagal cadence.
- S (Slide) = L, then P, then R: connects two triads that share the third: C (C E G) ↔ C#m (C# E G#).
- H (hexatonic pole) = L P L: C ↔ Abm. All voices move by half step.
- LP = C → Em → E: two steps to reach the major chromatic mediant (C → E).
- PL = C → Cm → Ab: C → Ab, the flat submediant.
Cycles
- PL cycle (hexatonic): C → Cm → Ab → Abm → E → Em → C. Six triads, all contained in the hexatonic scale C D# E G Ab B (obtained from two augmented triads). Each step moves a single note by half step: "maximal economy" (Cohn).
- PR cycle (octatonic): C → Cm → Eb → Ebm → Gb → F#m → A → Am → C. Eight triads that fit within a diminished (octatonic) scale.
- LR chain: C → Am → F → Dm → Bb → Gm… This is a descending-fifths progression alternating major and minor; Cohn finds it in a long passage of the Scherzo of Beethoven's Ninth.
Examples in notes
- C → Cm → Ab (PL): voices G, E → Eb, then G → Ab. Inner melody E–Eb–Eb, upper voice G–G–Ab.
- C → E (LP): C → B, G → G#, E stays.
- Am → F (L on minor: raises the fifth E → F): A C F. Common in pop (vi → IV).
Use in a real song
- Wagner, Parsifal: Lewin analyzes the motif and Amfortas's prayer with these transformations.
- Radiohead, Creep: G → B is LP (G → Bm → B), C → Cm is P. The "strangeness" of the progression is described in two neo-Riemannian moves.
- Film: many "wonder" sequences alternate major chords linked by L or S without dominants (Lehman, Hollywood Harmony).
Exercise for the producer
- Choose a starting chord (for example Am).
- Roll a "die": 1–2 = P, 3–4 = L, 5–6 = R. Apply the transformation and write the new chord in the Piano roll.
- Repeat 8 times; keep the voices as still as possible (only one note moves at each step).
- Listen: you'll get a fluid chromatic progression, great for cinematic pads. Add a bass that follows the root only every two chords.
Related topics
Tonnetz, chromatic mediants, chromatic voice leading, extended tonal functions (Riemann), harmony for film music.