Samuel Filipe Silva

Abstract
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, andWebern's Four Pieces for Violin and Piano, Op. 7, No. 1, unveiling increasingly ambiguous wavescapes.

Abstract
FluidHarmony is an algorithmic method for defining a hierarchical harmonic lexicon in equal temperaments. It utilizes an enharmonic weighted Fourier transform space to represent pitch class set (pcsets) relations. The method ranks pcsets based on user-defined constraints: the importance of interval classes (ICs) and a reference pcset. Evaluation of 5,184 Western musical pieces from the 16th to 20th centuries shows FluidHarmony captures 8% of the corpus's harmony in its top pcsets. This highlights the role of ICs and a reference pcset in regulating harmony in Western tonal music while enabling systematic approaches to define hierarchies and establish metrics beyond 12-TET.