Entropy, energy, and instability in music


Gündüz G.

Physica A: Statistical Mechanics and its Applications, vol.609, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 609
  • Publication Date: 2023
  • Doi Number: 10.1016/j.physa.2022.128365
  • Journal Name: Physica A: Statistical Mechanics and its Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Artic & Antarctic Regions, INSPEC, Public Affairs Index, zbMATH, Civil Engineering Abstracts
  • Keywords: Directed graph, Fractal dimension, Golden ratio, Instability, Shannon entropy, Topological entropy
  • Middle East Technical University Affiliated: Yes

Abstract

© 2022 Elsevier B.V.The structures of eight BEATLES songs were characterized by using the fundamental concepts of statistical physics, thermodynamics, and viscoelastic theory. The Shannon entropy, negentropy, order, topological entropy, fractal dimension, network properties, and conservative and dissipative energies were found for all songs. The sequential entropy change and the persistence of entropy were also discussed. The lengths of notes have an important influence on the psychological perception of the human brain, and it was found that the lengths of notes produce very highly ordered forms of sequential entropy difference. For further characterization, the scattering diagrams of songs were plotted, and the fractal dimensions, network densities, cohesions, and characteristic path lengths of songs were calculated and compared. The instability issues were elucidated based on the alignment of the vectors on the scattering diagram and the angles of these vectors. It was found out that some angles which could be expressed in terms of golden ratio came out to be in high percentages. They are associated with relatively more unstable states. The corresponding notes are the elements of high instability.