Quantum Theory and Harmonic Analysis of Sound: Foundations, Models, and Implications

Resumo

This study introduces an innovative theoretical and analytical framework called Quantum Vocal Theory of Sound (QVTS), which applies the concepts of quantum mechanics to the modeling, analysis, and synthesis of sound, especially vocal and acoustic events. In contrast to traditional acoustics rooted in classical wave theory, QVTS views sound as a quantum phenomenon, defined by superposition, coherence, and entanglement among essential phonatory states like phonation, turbulence, and myoelastic vibrations. The research presents Quantum Harmonic Analysis (QHA) as a fundamental mathematical instrument, extending Fourier and wavelet transforms into Hilbert-space frameworks directed by quantum operators. In this process, sound is broken down into quantized spectral elements, enabling accurate analysis of phonon interactions, harmonic structures, and random fluctuations. The study additionally develops quantum-analog correspondences between human vocal apparatus and quantum entities, like spin states and qubits, to introduce a novel framework for voice-based sound modeling and auditory scene interpretation. This theoretical development connects auditory perception, speech acoustics, and quantum-inspired signal processing, creating new avenues in quantum acoustic synthesis, quantum-based sonification, and voice-controlled quantum computing systems. The results illustrate the capability of QVTS to integrate physical acoustics with the principles of quantum computation, thus providing a fundamental advancement toward a quantum structure for sonic intelligence and sound-oriented information processing.