A quantum vocal theory of sound
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A quantum vocal theory of sound Davide Rocchesso1
· Maria Mannone1
Received: 6 January 2020 / Accepted: 17 July 2020 © The Author(s) 2020
Abstract Concepts and formalism from acoustics are often used to exemplify quantum mechanics. Conversely, quantum mechanics could be used to achieve a new perspective on acoustics, as shown by Gabor studies. Here, we focus in particular on the study of human voice, considered as a probe to investigate the world of sounds. We present a theoretical framework that is based on observables of vocal production, and on some measurement apparati that can be used both for analysis and synthesis. In analogy to the description of spin states of a particle, the quantum-mechanical formalism is used to describe the relations between the fundamental states associated with phonetic labels such as phonation, turbulence, and supraglottal myoelastic vibrations. The intermingling of these states, and their temporal evolution, can still be interpreted in the Fourier/Gabor plane, and effective extractors can be implemented. The bases for a quantum vocal theory of sound, with implications in sound analysis and design, are presented. Keywords Quantum-inspired algorithms · Audio processing · Sound representation
1 Introduction What are the fundamental elements of sound? What is the most meaningful framework for analyzing existing sonic realities and for expressing new sound concepts? These are long-standing questions in sound physics, perception, and creation. In his analytical theory of heat [1], Joseph Fourier laid the basis for analyzing functions of one variable in terms of sinusoidal components and explicitly wrote that “…if the order which is established in these phenomena could be grasped by our senses, it would produce in us an impression comparable to the sensation of musical sounds.” Hermann von Helmholtz took Fourier’s suggestion seriously and proceeded to analyze all vibratory phenomena as additions of sinusoidal vibrations [2]. Although he
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Davide Rocchesso [email protected] Department of Mathematics and Computer Science, University of Palermo, Palermo, Italy 0123456789().: V,-vol
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admitted that “we can conceive a whole to be split into parts in very different and arbitrary ways,” it was the observation that the ear somehow reflects Fourier analysis and can be described as a bank of sympathetic resonators that led him to state that “the existence of partial tones […] acquire a meaning in nature.” In the twentieth century, despite the Fourier transform being the key to describe sampling and signal reconstruction from samples [3], skepticism arose among physicists such as Norbert Wiener and Dennis Gabor about considering Fourier analysis as the best representation for music [4]. In 1947, in a famous paper published in Nature [5], Gabor embraced the mathematics of quantum theory to shed light on subjective acoustics, thus laying the basis for sound analysis and synthesis based on acoustical quanta, or grains, or wavelets. The F
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