"Spectral Harmony" Towards the Unification of Timbre and Speech: Resolution of the Young Mahler Schoenberg Dream

This paper deals with the introduction of "geometric harmony", a discipline that explicitly addresses the spectral characteristics of musical gamut. The framework of Western music, from Renaissance to the present, represents sound in terms of "pitch"-as is evident from its five-line staff notation system-and employs the fundamental frequency as its representative value, 440 Hz, etc. In this paper, by taking the timbres of specific individual instruments as elements and examining the Wasserstein distance between two voices, and Wasserstein deviations between three or more voices, we demonstrate that it is possible to expand the system whilst retaining the entire framework of conventional music theory. At the same time, as an example of practical utility in ensemble playing, we provide a detailed account of the two-voices affinity of the "Throat G" on clarinet, a note known for its fragility in ensemble contexts.

Timbre transfer aims to modify the timbral identity of a musical recording while preserving its original melody and rhythm. While single-instrument timbre transfer has made substantial progress, existing approaches to multi-instrument settings commonly rely on separate-then-transfer pipelines that propagate source-separation artifacts and process the resulting stems independently. This paper proposes MixtureTT, to the best of our knowledge the first system for flexible per-stem timbre transfer directly from a polyphonic mixture. Given a mixture and a separate timbre reference for each target voice, MixtureTT jointly transfers all stems to the specified instruments. Its Joint Stem Diffusion Transformer first models cross-stem harmonic context and then refines each output under its own content and timbre conditions. All stems are generated within a single joint diffusion process rather than through separate per-stem diffusion runs. This design avoids propagating waveform-level separation errors through a cascade and produces more coherent multi-stem outputs. Despite operating under a harder input condition, MixtureTT outperforms practical separate-then-transfer pipelines on objective and subjective evaluations, while remaining competitive with single-instrument methods given ground-truth isolated stems. Results on both synthesized and real-audio SATB benchmarks further demonstrate its generalization. Controlled ablations show that jointly modeling cross-stem dependencies improves over an equivalent independent-stem variant, while the structure and timing of this coordination are also critical for effective mixture-level timbre transfer.

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.