IDEAS home Printed from https://ideas.repec.org/a/spr/eurphb/v95y2022i7d10.1140_epjb_s10051-022-00368-z.html
   My bibliography  Save this article

Harmonic structures of Beethoven quartets: a complex network approach

Author

Listed:
  • Theo Frottier

    (Université de Toulouse,CNRS, UPS)

  • Bertrand Georgeot

    (Université de Toulouse,CNRS, UPS)

  • Olivier Giraud

    (Université Paris Saclay, CNRS, LPTMS)

Abstract

We propose a complex network approach to the harmonic structure underpinning western tonal music. From a database of Beethoven’s string quartets, we construct a directed network whose nodes are musical chords and edges connect chords following each other. We show that the network is scale-free and has specific properties when ranking algorithms are applied. We explore the community structure and its musical interpretation, and propose statistical measures stemming from network theory allowing to distinguish stylistically between periods of composition. Our work opens the way to a network approach of structural properties of tonal harmony. Graphicabstract

Suggested Citation

  • Theo Frottier & Bertrand Georgeot & Olivier Giraud, 2022. "Harmonic structures of Beethoven quartets: a complex network approach," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(7), pages 1-8, July.
  • Handle: RePEc:spr:eurphb:v:95:y:2022:i:7:d:10.1140_epjb_s10051-022-00368-z
    DOI: 10.1140/epjb/s10051-022-00368-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1140/epjb/s10051-022-00368-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1140/epjb/s10051-022-00368-z?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. Fabian C Moss & Markus Neuwirth & Daniel Harasim & Martin Rohrmeier, 2019. "Statistical characteristics of tonal harmony: A corpus study of Beethoven’s string quartets," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-16, June.
    2. Antiqueira, L. & Nunes, M.G.V. & Oliveira Jr., O.N. & F. Costa, L. da, 2007. "Strong correlations between text quality and complex networks features," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 811-820.
    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. 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).
    2. Jorge A. V. Tohalino & Laura V. C. Quispe & Diego R. Amancio, 2021. "Analyzing the relationship between text features and grants productivity," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(5), pages 4255-4275, May.
    3. Liu, Yanyan & Li, Keping & Yan, Dongyang & Gu, Shuang, 2022. "A network-based CNN model to identify the hidden information in text data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    4. Cui, Xue-Mei & Yoon, Chang No & Youn, Hyejin & Lee, Sang Hoon & Jung, Jean S. & Han, Seung Kee, 2017. "Dynamic burstiness of word-occurrence and network modularity in textbook systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 487(C), pages 103-110.
    5. Sabrina Laneve & Ludovica Schaerf & Gabriele Cecchetti & Johannes Hentschel & Martin Rohrmeier, 2023. "The diachronic development of Debussy’s musical style: a corpus study with Discrete Fourier Transform," Palgrave Communications, Palgrave Macmillan, vol. 10(1), pages 1-13, December.
    6. Ausloos, M., 2012. "Measuring complexity with multifractals in texts. Translation effects," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1349-1357.
    7. Amancio, Diego R. & Nunes, Maria G.V. & Oliveira, Osvaldo N. & Costa, Luciano da F., 2012. "Extractive summarization using complex networks and syntactic dependency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1855-1864.
    8. D. R. Amancio & M. G. V. Nunes & O. N. Oliveira & L. F. Costa, 2012. "Using complex networks concepts to assess approaches for citations in scientific papers," Scientometrics, Springer;Akadémiai Kiadó, vol. 91(3), pages 827-842, June.
    9. Daniel Harasim & Fabian C. Moss & Matthias Ramirez & Martin Rohrmeier, 2021. "Exploring the foundations of tonality: statistical cognitive modeling of modes in the history of Western classical music," Palgrave Communications, Palgrave Macmillan, vol. 8(1), pages 1-11, December.
    10. Amancio, Diego R. & Oliveira Jr., Osvaldo N. & Costa, Luciano da F., 2012. "Structure–semantics interplay in complex networks and its effects on the predictability of similarity in texts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(18), pages 4406-4419.
    11. Fabian C. Moss & Robert Lieck & Martin Rohrmeier, 2024. "Computational modeling of interval distributions in tonal space reveals paradigmatic stylistic changes in Western music history," Palgrave Communications, Palgrave Macmillan, vol. 11(1), pages 1-11, December.
    12. Rosso, Osvaldo A. & Craig, Hugh & Moscato, Pablo, 2009. "Shakespeare and other English Renaissance authors as characterized by Information Theory complexity quantifiers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 916-926.
    13. Ke, Xiaohua & Zeng, Yongqiang & Ma, Qinghua & Zhu, Lin, 2014. "Complex dynamics of text analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 307-314.
    14. Amancio, D.R. & Nunes, M.G.V. & Oliveira, O.N. & Pardo, T.A.S. & Antiqueira, L. & da F. Costa, L., 2011. "Using metrics from complex networks to evaluate machine translation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(1), pages 131-142.

    More about this item

    Statistics

    Access and download statistics

    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:spr:eurphb:v:95:y:2022:i:7:d:10.1140_epjb_s10051-022-00368-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.