Fourier Qualia Wavescapes: Hierarchical Analyses of Set Class Quality and Ambiguity

We introduce a novel perspective on set-class analysis combining the DFT magnitudes with the music visualisation technique of wavescapes. With such a combination, we create a visual representation of a piece’s multidimensional qualia, where different colours indicate saliency in chromaticity, diadicity, triadicity, octatonicity, diatonicity, and whole-tone quality. At the centre of our methods are: 1) the formal definition of the Fourier Qualia Space (FQS), 2) its particular ordering of DFT coefficients that delineate regions linked to different musical aesthetics, and 3) the mapping of such regions into a coloured wavescape. Furthermore, we demonstrate the intrinsic capability of the FQS to express qualia ambiguity and map it into a synopsis wavescape. Finally, we showcase the application of our methods by presenting a few analytical remarks on Bach’s Three-part Invention BWV 795, Debussy’s Reflets dans l’eau, and Webern’s Four Pieces for Violin and Piano, Op. 7, No. 1, unveiling increasingly ambiguous wavescapes.