This article introduces a type of harmonic geometry, Fourier phase space, and uses it to advance the understanding of Schubert’s tonal language and comment upon current topics in Schubert analysis. The space derives from the discrete Fourier transform on pitch-class sets developed by David Lewin and Ian Quinn but uses primarily the phases of Fourier components, unlike Lewin and Quinn, who focus more on the magnitudes. The space defined by phases of the third and fifth components closely resembles the Tonnetz and has a similar common-tone basis to its topology but is continuous and takes a wider domain of harmonic objects. A number of musical examples show how expanding the domain enables us to extend and refine some the conclusions of neo-Riemannian theory about Schubert’s harmony. Through analysis of the Trio and Adagio from Schubert’s String Quintet and other works using the geometry, the article develops a number of concepts for the analysis of chromatic harmony, including a geometric concept of interval as direction (intervallic axis), a novel approach to triadic voice leading (triadic orbits), and theories of tonal regions.
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