Our understanding of 20th-century multi-layered harmony (including music of Debussy, Bartók, Stravinsky, Ravel, Milhaud, Prokofiev, etc.) has been marred by a paradox: while the layering and juxtaposition of traditional sound structures is a most characteristic, vital, and novel constructive trait of this music (loosely referred to by terms such as ‘polytonality’ or ‘polymodality’), the classic theoretical models developed in the second half of the 20th century (prolongational post-Schenkerian and atonal set-theory) have rejected, on perceptual and logical grounds, wholesale attributions of traditional tonal structures as organizing pitch markers of this music, arguing that such notions were (to resort to a famous rant) “too fantastic or illogical”, constituting “real horrors of the musical imagination” (van den Toorn, 1983). Dismissive approaches to multi-layered harmony, however, have important analytical and historical consequences and expose a conceptual gap in the literature: what sort of harmony results from the layering/combination of traditional constructs, in ways that preserve and value the constructional character of music in the 20th-century scalar tradition?
Drawing from scale theory, group- and transformational theories, this paper advances four inter-related models of multi-layered pitch space, which I call: scalar dissonance, affinity spaces, mistuning, and transpositional networks. These pitch models, in turn, act as analytical frameworks that interpret a variety of distinct interactions between scale-inflected materials in the music of Bartók, Stravinsky, Ravel, and Milhaud (among others), which coherently explore various global harmonic spectra. The paper further shows how some of the harmonic practices in the late 1950s of composers such as Lutosławski and Kurtág have expanded the earlier polymodal impulse by creating certain extended chordal spaces, which engage with various sorts of (homogeneous, expanding, or contracting) global harmonic networks. The design of the proposed models is intended to show that multi-layered harmonies are not merely constructive tricks, but are capable of creating coherent musical syntaxes, explored through a variety of analytical applications.