Abstract
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.

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.