A Physicist’s view on Chopin’s Études

Blasone, Massimo

doi:10.1140/epjst/e2017-70008-6

Cited by 3 publications

(1 citation statement)

References 11 publications

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“…Evidence of these vortices and vortex strings has been observed in condensed matter systems [ 3 – 15 ], and are expected to manifest in the axion field as a network of “cosmic strings” threading throughout the universe [ 16 , 17 ]. Interestingly, the KZM has been considered previously as a qualitative metaphor for structures in musical compositions [ 18 ]. Here, we observe these vortex strings in a simulation of a quenched system of interacting tones, with the expected dependence on quench rate.…”

Section: Introductionmentioning

confidence: 99%

Critical behavior and the Kibble-Zurek mechanism in a musical phase transition

Din

Berezovsky

2023

PLoS ONE

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We investigate the critical phenomena emerging from a statistical mechanics model of musical harmony on a three-dimensional (3D) lattice, and the resulting structure of the ordered phase. In this model, each lattice site represents a tone, with nearest neighbors interacting via the perception of dissonance between them. With dissonance assumed to be an octave-wise periodic function of pitch difference, this model is a 3D XY system with the same symmetry and dimensionality as superfluid helium and models of the cosmological axion field. We use numerical simulation to observe a phase transition from disordered sound to ordered arrangements of musical pitches as a parameter analogous to the temperature is quenched towards zero. We observe the divergence of correlation length and relaxation time at the phase boundary, consistent with the critical exponents in similar systems. Furthermore, the quenched low-temperature phase of these systems displays topological defects in the form of vortex strings that thread throughout the system volume. We observe the formation of these vortex strings in accordance with the Kibble-Zurek mechanism, and discuss the structure of these vortex strings in the context of the theory of musical harmony, finding both similarities to established music theory, and uncovering new avenues to explore.

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Section: Introductionmentioning

confidence: 99%

Critical behavior and the Kibble-Zurek mechanism in a musical phase transition

Din

Berezovsky

2023

PLoS ONE

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On Some Analogies

Abdyssagin

2024

Quantum Mechanics and Avant-Garde Music

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Triad’s consonance and dissonance: a detailed analysis of compactness models

Masina

2023

Eur. Phys. J. Plus

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Theories of consonance and dissonance based on the “compactness” approach include the two sub-categories of periodicity and harmonicity. In a previous work, we discussed the related consonance and dissonance indicators for dyads; as they are given by discontinuous functions of the dyad frequency ratio, we proposed a method to extend them to the continuum, based on the auditory discrimination limen. Here, we generalize the compactness indicators to describe the consonance and dissonance for triads and discuss their extension to the continuum. We compare our model predictions with perceptual data from a recent psychoacoustic test by means of a Chi-square analysis. The result is that compactness indicators provide a quite effective, but not fully satisfactory, description of consonance, and dissonance for triads.

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A Physicist’s view on Chopin’s Études

Cited by 3 publications

References 11 publications

Critical behavior and the Kibble-Zurek mechanism in a musical phase transition

Critical behavior and the Kibble-Zurek mechanism in a musical phase transition

On Some Analogies

Triad’s consonance and dissonance: a detailed analysis of compactness models

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