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Entropy, energy, and instability in music

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  • Gündüz, Güngör

Abstract

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.

Suggested Citation

  • Gündüz, Güngör, 2023. "Entropy, energy, and instability in music," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    • Handle: RePEc:eee:phsmap:v:609:y:2023:i:c:s0378437122009232
    DOI: 10.1016/j.physa.2022.128365
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    References listed on IDEAS

    as
    1. Banerjee, Archi & Sanyal, Shankha & Roy, Souparno & Nag, Sayan & Sengupta, Ranjan & Ghosh, Dipak, 2021. "A novel study on perception–cognition scenario in music using deterministic and non-deterministic approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    2. Sanyal, Shankha & Banerjee, Archi & Patranabis, Anirban & Banerjee, Kaushik & Sengupta, Ranjan & Ghosh, Dipak, 2016. "A study on Improvisation in a Musical performance using Multifractal Detrended Cross Correlation Analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 67-83.
    3. Gündüz, Güngör & Gündüz, Yalin, 2016. "A thermodynamical view on asset pricing," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 310-327.
    4. Corrêa, Débora C. & Jüngling, Thomas & Small, Michael, 2020. "Quantifying the generalization capacity of Markov models for melody prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    5. Jauregui, M. & Zunino, L. & Lenzi, E.K. & Mendes, R.S. & Ribeiro, H.V., 2018. "Characterization of time series via Rényi complexity–entropy curves," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 498(C), pages 74-85.
    6. Ribeiro, Haroldo V. & Zunino, Luciano & Mendes, Renio S. & Lenzi, Ervin K., 2012. "Complexity–entropy causality plane: A useful approach for distinguishing songs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(7), pages 2421-2428.
    7. Ferreira, Paulo & Quintino, Derick & Wundervald, Bruna & Dionísio, Andreia & Aslam, Faheem & Cantarinha, Ana, 2021. "Is Brazilian music getting more predictable? A statistical physics approach for different music genres," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    8. Dai, Yimei & Zhang, Hesheng & Mao, Xuegeng & Shang, Pengjian, 2018. "Complexity–entropy causality plane based on power spectral entropy for complex time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 501-514.
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