Probing questions about keys: tonal distributions through the DFT
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Citation (published version)Jason Yust. 2017. "Probing Questions About Keys: Tonal Distributions Through the DFT." MATHEMATICS AND COMPUTATION IN MUSIC, MCM 2017. 6th Biennial International Conference for Mathematics and Computation in Music (MCM). Univ Nacl Autonoma Mexico, Fac Sci, Mexico, MEXICO, 2017-06-26 - 2017-06-29. https://doi.org/10.1007/978-3-319-71827-9_13
Pitch-class distributions are central to much of the computational and psychological research on musical keys. This paper looks at pitch-class distributions through the DFT on pitch-class sets, drawing upon recent theory that has exploited this technique. Corpus-derived distributions consistently exhibit a prominence of three DFT components, 𝑓5, 𝑓3, and 𝑓2, so that we might simplify tonal relationships by viewing them within two- or three-dimensional phase space utilizing just these components. More generally, this simplification, or filtering, of distributional information may be an essential feature of tonal hearing. The DFTs of probe-tone distributions reveal a subdominant bias imposed by the temporal aspect of the behavioral paradigm (as compared to corpus data). The phases of 𝑓5, 𝑓3, and 𝑓2 also exhibit a special linear dependency in tonal music giving rise to the idea of a tonal index.