IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v609y2023ics0378437122009232.html
   My bibliography  Save this article

Entropy, energy, and instability in music

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437122009232
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2022.128365?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fernandes, Leonardo H.S. & de Araujo, Fernando H.A. & Tabak, Benjamin M., 2021. "Insights from the (in)efficiency of Chinese sectoral indices during COVID-19," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    2. Nag, Sayan & Basu, Medha & Sanyal, Shankha & Banerjee, Archi & Ghosh, Dipak, 2022. "On the application of deep learning and multifractal techniques to classify emotions and instruments using Indian Classical Music," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    3. Zhang, Boyi & Shang, Pengjian & Zhou, Qin, 2021. "The identification of fractional order systems by multiscale multivariate analysis," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. Fernandes, Leonardo H.S. & Araújo, Fernando H.A., 2020. "Taxonomy of commodities assets via complexity-entropy causality plane," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    5. Mastroeni, Loretta & Mazzoccoli, Alessandro & Vellucci, Pierluigi, 2024. "Wavelet entropy and complexity–entropy curves approach for energy commodity price predictability amid the transition to alternative energy sources," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    6. Martins, Adriel M.F. & Fernandes, Leonardo H.S. & Nascimento, Abraão D.C., 2023. "Scientific progress in information theory quantifiers," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    7. Fernandes, Leonardo H.S. & de Araújo, Fernando H.A. & Silva, Igor E.M. & Neto, Jusie S.P., 2021. "Macroeconophysics indicator of economic efficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    8. Leite, Gustavo de Novaes Pires & Araújo, Alex Maurício & Rosas, Pedro André Carvalho & Stosic, Tatijana & Stosic, Borko, 2019. "Entropy measures for early detection of bearing faults," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 458-472.
    9. Schadner, Wolfgang, 2022. "U.S. Politics from a multifractal perspective," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    10. 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).
    11. Yin, Yi & Shang, Pengjian, 2016. "Weighted permutation entropy based on different symbolic approaches for financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 137-148.
    12. 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).
    13. Stosic, Darko & Stosic, Dusan & Ludermir, Teresa B. & Stosic, Tatijana, 2019. "Exploring disorder and complexity in the cryptocurrency space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 548-556.
    14. Shang, Binbin & Shang, Pengjian, 2020. "Binary indices of time series complexity measures and entropy plane," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    15. 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.
    16. McDonough, John & Herczyński, Andrzej, 2023. "Fractal patterns in music," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    17. Lima, David H.S. & Aquino, Andre L.L. & Rosso, Osvaldo A. & Curado, Marilia, 2024. "Characterization of task allocation techniques in data centers based on information theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 634(C).
    18. de Novaes Pires Leite, Gustavo & da Cunha, Guilherme Tenório Maciel & dos Santos Junior, José Guilhermino & Araújo, Alex Maurício & Rosas, Pedro André Carvalho & Stosic, Tatijana & Stosic, Borko & Ros, 2021. "Alternative fault detection and diagnostic using information theory quantifiers based on vibration time-waveforms from condition monitoring systems: Application to operational wind turbines," Renewable Energy, Elsevier, vol. 164(C), pages 1183-1194.
    19. Argyroudis, George S. & Siokis, Fotios M., 2019. "Spillover effects of Great Recession on Hong-Kong’s Real Estate Market: An analysis based on Causality Plane and Tsallis Curves of Complexity–Entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 576-586.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:609:y:2023:i:c:s0378437122009232. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.