Author: Martins, José Oliveira
Title: Dasian, Guidonian, and other Affinity Spaces in Twentieth-Century Music
Institution: University of Chicago
Completed: March 2006
The dissertation examines the twentieth-century compositional practice of combining strands that appear to invoke different diatonic scales. In the music of Bartók, Stravinsky, and Milhaud, among others, individual strands often privilege diatonic stepwise motion, suggesting that the material can be arranged into scales or scale segments. But the juxtaposition and superimposition of those materials give rise to complex chromatic relationships.
Departing from Bartók’s notion of modal chromaticism as a model rationalizing the coexistence of diatonic modes, the dissertation proposes two conceptual extended scalar spaces that coordinate all potential scalar segments. The constructs are non-octave repeating, cyclic scales named dasian and Guidonian spaces that dispense with the mediating role of complete diatonic scales and pitch centers. The construction design of these spaces is inspired by and generalizes medieval scale structures and practices that rationalized the emergent chromaticism into a diatonic framework. Central to both the medieval constructs and their modern counterparts is the notion that the semitone uniquely defines placement within the scalar space. Distance between adjacent semitones also signals the spaces’ affinities, that is, the interval at which the intervallic structure of the space recurs. Accordingly, combinations of strata involving different semitones correspond to different locations in the spaces, and are related by operations analogous to scalar stepwise motion and hexachordal mutation. The operations allow for precise measurement of both melodic and harmonic distances between scalar segments and account for aspects of harmonic syntax.
Finally, the dissertation generalizes the structure of both dasian and Guidonian spaces, producing a large array of scalar structures called affinity spaces. The generalization addresses instances of twentieth-century practice involving the combination of scalar structures, other than the diatonic.
Keywords: Dasian, Guidonian, affinity, scale, modality, polymodality, Bartók, Stravinsky, Milhaud, Lutoslawski
José Oliveira Martins
Assistant Professor, Music Theory
University of Iowa
Iowa City, IA 52242