Volume IV · Chapter 28
Chromatic Mediants
MUSIC 21B · C-ID MUS 150Chapter quiz →
In the musicianship bookChapter 27: Distant Keys
Introduction: Third Relations
Two triads whose roots are a third apart are mediant-related. In a major key, I and iii or I and vi share two common tones: the relation is smooth and diatonic. But nineteenth-century composers discovered a more colorful family: triads a third apart that keep the same quality, which forces at least one chromatic note. These chromatic mediants sound bright, mysterious, or magical, and they've been a staple of film music ever since.
Click any example to hear it.
Chromatic and Doubly Chromatic Mediants
- Chromatic mediants: two major (or two minor) triads whose roots are a major or minor third apart. They share exactly one common tone. From C major: E major, A♭ major, A major, E♭ major.
- Doubly chromatic mediants: a major and a minor triad whose roots are a third apart with no common tones. From C major: E♭ minor and A♭ minor (G♯ minor).
| Relation to C major | Upper (third above) | Lower (third below) | Common tones |
|---|---|---|---|
| Diatonic mediants | E minor (iii) | A minor (vi) | 2 |
| Chromatic mediants (major third) | E major | A♭ major | 1 |
| Chromatic mediants (minor third) | E♭ major | A major | 1 |
| Doubly chromatic mediants | E♭ minor | A♭ minor | 0 |
Chromatic mediants appear as chord-to-chord successions (often between root-position triads, with a dramatic bass leap of a third) and also as key relations: Beethoven's "Waldstein" Sonata places its second theme in E major instead of G major, and Schubert often moves to the key a third away for a new section.
Neo-Riemannian Transformations: P, L, and R
Music theorists describe these chromatic successions with three basic transformations, named after the nineteenth-century theorist Hugo Riemann. Each one changes a triad to the opposite quality by moving just one note by step, while the other two notes stay put:
| Transformation | What moves | C major becomes | C minor becomes |
|---|---|---|---|
| P (Parallel) | the third, by half step | C minor | C major |
| L (Leading-tone exchange) | root down a half step (major) / fifth up a half step (minor) | E minor (C → B) | A♭ major (G → A♭) |
| R (Relative) | fifth up a whole step (major) / root down a whole step (minor) | A minor (G → A) | E♭ major (C → B♭) |
P, L, and R are their own inverses (P undoes P). Combining them produces every chromatic mediant:
- LP (L, then P): C → e → E, the major-third chromatic mediant above.
- PL: C → c → A♭, the major-third chromatic mediant below.
- RP: C → a → A, the minor-third chromatic mediant below.
- PR: C → c → E♭, the minor-third chromatic mediant above.
- PLP: C → c → A♭ → a♭, the doubly chromatic "hexatonic pole."
Cycles: Hexatonic and Octatonic
Alternate two transformations and you cycle back to where you started:
- P and L alternating: C – c – A♭ – a♭ – E – e – C. Six triads, all drawn from one six-note hexatonic collection (C, D♯/E♭, E, G, G♯/A♭, B). The roots move by major thirds.
- P and R alternating: C – c – E♭ – e♭ – G♭ – f♯ – A – a – C. Eight triads, all from an octatonic collection. The roots move by minor thirds.
Because each step is so smooth, these cycles can sound eerie or weightless: there's no dominant pulling toward a tonic, just gliding voice leading. Film composers use them for wonder, magic, and the uncanny.
The Tonnetz
The Tonnetz ("tone network") maps these relations. Moving right is up a perfect fifth; moving up-right is up a major third; moving up-left is down a minor third. Every small triangle is a triad, and P, L, and R flip a triangle across one of its edges, keeping the two shared notes.
Try It: Neo-Riemannian Explorer
Neo-Riemannian Explorer
Start on a triad and transform it. P, L, and R move one voice by step; the mediant buttons jump to a chromatic mediant. The voice leading always takes the smoothest path. Can you get from C major to A♭ minor in three moves?
Summary
- Chromatic mediants: same-quality triads a third apart, sharing one common tone (C–E, C–A♭, C–A, C–E♭).
- Doubly chromatic mediants: opposite-quality triads a third apart with no common tones (C–e♭, C–a♭).
- P, L, R each keep two notes and move one by step. Combinations (LP, PL, RP, PR) produce the chromatic mediants; PLP gives the hexatonic pole.
- Alternating P and L makes the hexatonic cycle (roots by major thirds); alternating P and R makes the octatonic cycle (roots by minor thirds).
- The Tonnetz maps triads as triangles; P, L, and R flip a triangle across an edge.