A quantum mechanical approach to the psychoacoustic effect of Shepard tones has been explored. Melodic intervals are represented by qubits. The phenomenon of bistable perception of intervals and their acoustic collapse has been considered and described in the language of quantum mechanics. It is shown that the perception of intervals can be understood as a result of measuring the standard basis vector in different bases rotated in a plane of the chroma circle. For comparison, the Stern-Gerlach and photon polarization experiments have been cited to show an analogy. A quantum analog of the Shepard interval source, with a photonic random number generator, has been proposed. The topic of quantum entanglement transferred to the field of sound and psychoacoustics is also discussed. Based on quantum-like calculations, it has been shown how disturbances in time coherence between the playing of different music band members could affect the modification of the melody.
A quantum mechanical approach to the psychoacoustic effect of Shepard tones has been explored. Melodic intervals are represented by qubits. The phenomenon of bistable perception of intervals and their acoustic collapse has been considered and described in the language of quantum mechanics. It is shown that the perception of intervals can be understood as a result of measuring the standard basis vector in different bases rotated in a plane of the chroma circle. For comparison, the Stern-Gerlach and photon polarization experiments have been cited to show an analogy. A quantum analog of the Shepard interval source, with a photonic random number generator, has been proposed. The topic of quantum entanglement transferred to the field of sound and psychoacoustics is also discussed. Based on quantum-like calculations, it has been shown how disturbances in time coherence between the playing of different music band members could affect the modification of the melody.
I propose a quantum-like approach to the description of melody perception where classic intervals that constitute a melody are replaced by acoustical qubits, i.e. two-level acoustic systems, using Shepard tones for this purpose. Each of such qubits is considered to be a superposition of two intervals, ascending and descending, that form an octave when put together. Any melody perception can thus be treated analogously to a sequence of quantum measurements. Because of an acoustical collapse, analogous to the wave function reduction in quantum mechanics, just a single interval, ascending or descending, can be heard each time. Different melodies generated by the same sequence of acoustical qubits can be then perceived.
The theory of measurement with white and colored noise operators is discussed, utilizing the Collision Model representation of weak continuous measurement. While the former embodies an ideal measurement, the latter admits correlations between pointer states at different times, as it embodies a quantum delay line. The response of this apparatus is shown to be equivalent to a sort of comb filter. We apply these measurements to a simplified scheme for the process of musical sensing. While the measurement with white noise leads to a monotone rise in the certainty of a specific sound, measuring with colored noise introduces several patterns in the output, which we term as the quantum color of the sound and propose several sonifications of the outcome. Much like how feedback delay networks in digital acoustic models create the richness of simulated spaces, our quantum sensor introduces temporal correlations to sound perception through coherent feedback mechanism. Under the speculation that the human ear is sensitive to such temporal correlations, measurement with colored noise could be used to charge a sound signal with rhythmic meaning.
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.
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 slow 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. This would constitute the basis for a Quantum Vocal Theory of sound, with implications in sound analysis and design.
In this paper we describe methods for mapping the information contained in a spline model of one cycle of an audio signal to the quantum information setting. We use this mapping to describe methods of sonification of quantum algorithms which use spline models to describe and generate timbre, melody, and rhythm. We show how a musical state vector given by n B-spline coefficients, which represent one cycle of a waveform, can produce these three musical elements simultaneously. We present two modes of correspondence between quantum and musical states. The first mode is derived from proposed signal processing of quantum audio, such as QPAM (Quantum Probability Amplitude Modulation), and the second mode is more abstract, modeling the evolution of musical states through unitary evolution of intermediate states in quantum algorithms. Musical states are initialized using approximate timbres derived from instrument sam- ples or synthesized timbres. Melodic contours are derived from spline models of these timbres, using continuous pitch and duration spaces. Musical examples are discussed, and larger compositional works are currently under development.
Quantum mechanics is a notoriously difficult subject to learn, due to a lack of real-world analogies that might help provide an intuitive grasp of the underlying ideas. Discrete energy levels and absorption and emission wavelengths in atoms are sometimes described as uniquely quantum phenomena, but are actually general to spatially confined waves of any sort. Here, we provide an experiment demonstrating the acoustic spectroscopy of a drum. We show that a struck drum emits sounds of discrete frequencies (tones), and that the lifetime of each emitted tone is directly related by Heisenberg’s uncertainty principle to its line width in the drum’s frequency spectrum. We also show that a still drum absorbs only those same frequencies when exposed to monochromatic sound from an audio speaker. The resonant motion of the drum membrane is too fast to see by eye (>60 Hz), but can be observed with the aid of a strobe light. The observed resonant modes of the drum are the eigenfunctions of a particle trapped in an infinite circular well, and analogous to the shapes of atomic orbitals (1s, 2p, 3d, 2s, etc.). This experiment can be built for under $50, and is an excellent demo or lab exercise for general and physical chemistry courses to provide a visual example of abstract quantum mechanical ideas.