A Matrix Framework for Detuned-Unison Accordion Musette Tuning: Pitch Center, Beat Structure, and Roughness
DOI:
https://doi.org/10.54536/ajmp.v1i1.7687Keywords:
Accordion Musette, Beat Structure, Detuned Unison, Free-Reed Acoustics, Matrix Formulation, Pitch Center, RoughnessAbstract
Detuned-unison tuning is central to the acoustical behavior of accordion musette, yet its consequences are still described more often qualitatively than through explicit analytical relations. This paper develops a matrix framework for detuned-unison accordion musette tuning that links tuning and balance parameters to three descriptors: beat structure, pitch center, and roughness. Starting from a quasi-harmonic superposition model, the analysis expresses beat-rate sets through pairwise frequency spacings, derives the pitch center as an energy-weighted equivalent frequency, and formulates roughness as a quadratic form that aggregates pairwise interactions across harmonics under auditory weighting. The general relations are then specialized to the two-source and three-source chorus configurations, yielding closed-form expressions that are directly interpretable in terms of detune geometry and reed balance. A deterministic computational pipeline is presented and applied to an accordion case study at 440 Hz with an asymmetric three-reed tuning of −5, 0, and +15 cents. The results show that three-reed musette produces a more complex beat structure than two-reed combinations, that asymmetric detuning can shift the pitch center away from the nominal reference even when one reed is tuned exactly at it, and that roughness depends jointly on the number of interacting pairs, amplitude balance, and harmonic weighting. The proposed framework provides an analytical basis for quantitative comparison, tuning design, and voicing analysis in accordion musette. The study is theoretical and computational, and all reported descriptors are obtained from closed-form relations and a deterministic numerical pipeline.
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Copyright (c) 2026 Giovanni Volpatti (Author)
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