Daniel Moreira

Harmonic Motion in Post-Tonal Music: Voice-leading, Set-Class Progression and Functional Change

Two recent theoretical paradigms – transformational and modulatory – express a growing interest in the dynamic aspects of music modeling. In the former, harmonic motion is seen as stemming from a ‘characteristic gesture’, defined in group-theoretic terms by Lewin (1987) and subsequently developed in neo-Riemannian and voice-leading theories. In the latter, modulation – defined as the process of functional change for a continuing tonal element in a transformed harmonic context – is the key for understanding (diatonic and chromatic) tonal harmonic motion (Ribeiro-Pereira 2005).

Drawing from aspects of both of these paradigms, this paper proposes a theoretical model for harmonic motion in post-tonal (twelve-tone tempered) music, in which harmonic change (in both the chordal as well as the macroharmonic level) results from the complex interaction between voice-leading, interval progression and pitch centricity. In this model, the conjunction of the mutable and permanent elements in each of these three aspects instantiates functional changes, which are defined in terms of harmonic motion.Reworking recent ideas on voice-leading (Morris 1998, Straus 2003, Tymoczko 2011), this paper organizes the entire collection of available chords (set-classes) under a metric of harmonic proximity based on the perfect fifth (as opposed to the semitonal voice-leading proximity). Such organization partitions the entire harmonic space of all possible set classes into demarcated regions (where the pentatonic and diatonic collections fulfill important structural boundaries), and allows us to uniquely characterize interval and chord progression in post-tonal music. I claim this strategy has both acoustic and historical implications, which can still be articulated with semitone-based voice leading conceptions. The paper closes with analytical considerations on three post-tonal pieces: Schönberg’s Op. 11 No. 1; Ligeti’s Arc-en-Ciel; and the ‘Credo’ from Stravinsky’s Mass.