Qualia Motion in Fourier Space: Formalizing Linear, Nondirected, and Contrapuntal Ambiguity in Schoenberg’s Op. 19, No. 1

Abstract In this article, we formalize and analyze qualia motion, i.e., the process by which a composition transitions across distinct harmonic qualities through the Fourier qualia space (FQS)—a multidimensional and transposition-independent space based on the discrete Fourier transform (DFT) coefficients’ magnitude. In the FQS, the plot of set classes relies on their harmonic qualities—such as diatonicity and octatonicity—enabling us to (1) identify the pitch-class set in a musical phrase that best represents its qualia—a reference sonority; (2) define a harmonic progression using all sequential reference sonorities in a piece; (3) visualize trajectory in space; and (4) establish a statistical metric for the ambiguity of harmonic qualia. Finally, we discuss Schoenberg's Op. 19, No. 1, analyzing the sense of its harmonic path. The proposed space leverages a bipartite, symmetrical, and consequential structure and unveils ambiguity as an element of nondirected linearity and counterpoint.