Perceptually Motivated Alignment and Interpolation of Pitch-Aligned Time-Frequency Representations
We propose a framework for the alignment and interpolation of pitch-aligned time-frequency representations. Building on the tonal interval vector, we introduce a series of extensions that reformulate it as an invertible operator, culminating in a new feature extractor that embeds perceptual consonance priors within a pitch-aligned representation. Accordingly, we develop methods for aligning and interpolating between musical structures. For alignment, we cast the problem as a permutation search under perceptually weighted distances, enabling robust matching without explicit key detection, which is inherently ambiguous in music information retrieval. For interpolation, we employ optimal transport to generate musically meaningful transitions between pitch distributions, proposing a circular formulation over the Circle of Fourths/Fifths to respect harmonic structure. Finally, we learn a low-dimensional geometric representation of scale structure aimed to factorize scale color and density. Experimental results demonstrate the effectiveness and musicality of the proposed methods. Together, our contributions provide a principled, purely signal processing approach to modeling pitch structure in audio and symbolic music signals.