Tonality and functional equivalence: A multi-level model for the cognition of triadic progressions in 19th century music

Abstract

The subject of this paper is the cognition of triadic progressions in 19th century tonal music. Music psychological research concerning the cognition of harmonic progressions mainly relies on diatonic music in which triads are easily relatable to a key. Triadic distance is therefore measured in terms of root relationships to the tonal center, the tonic (Krumhansl & Kessler, 1982). This conception is not directly applicable to chromatic music where musical coherence is not only obtained by common a key. Transformational music theory puts strong emphasis on voice-leading parsimony as a measure of distance. The most efficient transformations between major and minor triads are P (parallel), R (relative) and L (leading-tone exchange), which is also in accordance with empirical findings of diatonic triadic relatedness (Krumhansl, 1998). Notably, P and R generate an octatonic scale containing eight major and minor triads which are claimed to be functionally equivalent. Transformational analyses result in sequential patterns of triadic progressions and an overarching key is not required. Based on an extended notion of function and acknowledging that there are compelling arguments for both hierarchical and sequential representations of the cognition of harmonic progressions a multi-level model is proposed that combines both approaches, adopting features of the generative model by Rohrmeier (2011). The two main components of the model are the concept of functional equivalence and the distinction between the hierarchic-syntactic cognition of functional progressions and the schematic cognition of functional values.