V. Chromaticism
Neo-Riemannian Triadic Progressions
Bryn Hughes
Key Takeaways
- Neo-Riemannian theory, named after music theorist Hugo Riemann, provides a means of rationalizing triadic progressions that involve sharing common tones, more so than staying within one key.
- Every Neo-Riemannian transformation toggles between one major and one minor triad.
- The most basic Neo-Riemannian transformations shift one note and keep two common tones.
- Relative relates a major triad and the minor triad a minor third lower, such as C and Ami.
- Parallel relates a major triad and the minor triad sharing the same root, such as C and Cmi.
- Leading-tone exchange relates a major triad and the minor triad a major third higher, such as C and Emi.
- Other important Neo-Riemannian transformations keep one common tone and shift two notes.
- Slide relates a major triad and the minor triad one semitone higher, such as C and C♯mi.
- Nebenverwandt relates a major triad and the minor triad a fifth below, such as C and Fmi.
- Hexpole relates a major triad and the minor triad a major third below, such as C and A♭mi. This transformation is unique because it does not keep any common tones; instead, each note is shifted by a half step to get to the new chord.
- Neo-Riemannian transformations are abbreviated to one letter each: R, P, L, S, N, and H.
- Theorists have come up with several networks of transformations that help visualize these relationships, such as the Tonnetz, the Weitzmann regions, and the Cube Dance.
A one-page summary of transformations is available as an interactive score and as a PDF.
In the late 19th century, composers often used triadic progressions that confound conventional Roman numeral analysis. Consider the following excerpt from Brahms’s concerto for violin and cello (
):A reduction of the chord progression in the excerpt above can be found in
The passage connects two A♭ major triads; however, the chords in between those triads do not belong to A♭ major in any useful way, nor do they follow any of the conventions of functional harmony.One might dismiss the passage altogether as “non-functional harmony,” but when you listen to it, it follows a certain kind of logic. As Richard Cohn writes, “if this music [music that is triadic but functionally indeterminate] is not fully coherent according to the principles of diatonic tonality, by what other principles might it cohere?” (1998, 169).
Neo-Riemannian Transformations
Neo-Riemannian theory describes a way of connecting major and minor triads without a tonal context.
shows the three basic Neo-Riemannian operations. Notice that each operation preserves two common tones in a triad and changes its mode.- The Relative transformation (R) preserves the major third in the triad and moves the remaining note by whole tone.
- The Parallel transformation (P) preserves the perfect fifth in the triad and moves the remaining note by semitone.
- The Leading-Tone Exchange transformation (L) preserves the minor third in