Quantum Memory and Mathematical Gestures: Two Perspectives on Verdi and Wagner | SpringerLink
Skip to main content
Springer Nature Link
Log in

Quantum Memory and Mathematical Gestures: Two Perspectives on Verdi and Wagner

  • Conference paper
  • First Online:
Mathematics and Computation in Music (MCM 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14639))

Included in the following conference series:

  • 229 Accesses

Abstract

Concepts and methods from theoretical physics and abstract mathematics can inspire new techniques to analyze the structure of musical compositions, seen as the unfolding of phenomena over time. Here, we consider an adaptation to music of a criterion to measure memory in quantum states (degree of non-Markovianity) and elements from the mathematical theory of musical gestures. We analyze salient features of two opera pieces, from Verdi’s La forza del destino and Wagner’s Tristan und Isolde, commenting the obtained results and the limits of these techniques.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 12583
Price includes VAT (Japan)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 10581
Price includes VAT (Japan)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    Original code in C by MM; version for MAX/MSP by OCH. The original idea of a musical non-Markovianity degree is due to the physicist Giuseppe Compagno.

  2. 2.

    Traditionally referred to as hypergestures, or 2-gestures.

References

  1. Amiot, E.: Music Through Fourier Space. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45581-5

    Book  Google Scholar 

  2. Arias-Valero, J.S., Lluis-Puebla, E.: Explicit presentations of topological categories of gestures. J. Math. Music 17(2), 213–243 (2023). https://doi.org/10.1080/17459737.2022.2111612

    Article  MathSciNet  Google Scholar 

  3. beim Graben, P.: Gauge symmetries of musical and visual forces. J. Math. Arts 17(3–4), 347–382 (2023). https://doi.org/10.1080/17513472.2023.2281895

    Article  MathSciNet  Google Scholar 

  4. beim Graben, P., Blutner, R.: Quantum approaches to music cognition. J. Math. Psychol. 91, 38–50 (2019). https://doi.org/10.1016/j.jmp.2019.03.002

    Article  MathSciNet  Google Scholar 

  5. Breuer, H.P., Petruccione, F.: Theory of Open Quantum Systems. Oxford University Press, New York (2002)

    Google Scholar 

  6. Fugiel, B.: Quantum-like melody perception. J. Math. Music 17(2), 319–331 (2022)

    Article  MathSciNet  Google Scholar 

  7. Hamido, O.C., Mannone, M.: Musical_non-Markovianity (v1.0.0). Zenodo (2023). https://doi.org/10.5281/zenodo.8152691

  8. Larson, S.: Musical Forces: Motion, Metaphor, and Meaning in Music. Indiana University Press (2012)

    Google Scholar 

  9. Lerdahl, F., Jackendoff, R.: Generative Theory of Tonal Music. MIT Press, Cambridge (1983)

    Google Scholar 

  10. Mannone, M., Hamido, O.C.: Quantum memory of musical compositions. In: Miranda, E., Jansen, K. (eds.) 2nd International Symposium on Quantum Computing and Musical Creativity (ISQCMC), Berlin (2023). https://doi.org/10.5281/zenodo.10206714

  11. Mannone, M., Turchet, L.: Shall we (math and) dance? In: Montiel, M., Gomez-Martin, F., Agustín-Aquino, O.A. (eds.) MCM 2019. LNCS, vol. 11502, pp. 84–97. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-21392-3_7

    Chapter  Google Scholar 

  12. Mannone, M.: Introduction to gestural similarity in music. J. Math. Music 12(2), 63–87 (2018)

    Article  MathSciNet  Google Scholar 

  13. Mannone, M., Compagno, G.: Characterisation of the degree of musical non-Markovianity. J. Creative Musical Syst. 6(1), 1–21 (2022)

    Google Scholar 

  14. Mazzola, G., Andreatta, M.: Diagrams, gestures and formulae in music. J. Math. Music 1(1), 23–46 (2007)

    Article  MathSciNet  Google Scholar 

  15. Miranda, E.R. (ed.): Quantum Computer Music. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-13909-3

    Book  Google Scholar 

  16. Putz, V., Svozil, K.: Quantum music. Soft. Comput. 21, 1467–1471 (2017)

    Article  Google Scholar 

  17. Rocchesso, D., Mannone, M.: A quantum vocal theory of sound. Quantum Inf. Process. 19(292), 1–28 (2020). https://doi.org/10.1007/s11128-020-02772-9

    Article  MathSciNet  Google Scholar 

  18. Preskill, J.: Lecture notes for physics 219: quantum computation. California Institute of Technology (2004)

    Google Scholar 

  19. Rivas, Á., Huelga, S.F., Plenio, M.B.: Quantum non-Markovianity. Rep. Prog. Phys. 77(9), 094001 (2014)

    Article  Google Scholar 

  20. Tempereley, D.: A probabilistic model of melody perception. Cogn. Sci. 32, 418–444 (2008)

    Article  Google Scholar 

Download references

Acknowledgments

The authors thank Prof. Domenico Fiorenza, supervisor (jointly with MM) of the MSc thesis in Mathematics by AA, for his suggestions on algebraic geometry. The work by OCH is supported by the European Project IIMPAQCT, under grant agreement Nr. 101109258 (DOI 10.3030/101109258).

figure a

Author information

Authors and Affiliations

  1. Department of Mathematics, La Sapienza University, Rome, Italy

    Alberto Avitabile

  2. Centre for Interdisciplinary Studies (CEIS20), University of Coimbra, Coimbra, Portugal

    Omar Costa Hamido

  3. Institute of Physics and Astronomy, Universität Potsdam, Potsdam, Germany

    Maria Mannone

  4. MIRMI, Technische Universität München, Munich, Germany

    Maria Mannone

  5. DSMN and ECLT, Ca’ Foscari University of Venice, Venice, Italy

    Maria Mannone

Authors
  1. Alberto Avitabile
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Omar Costa Hamido
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maria Mannone
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Conceptualization and writing: AA, OCH, and MM; gestures: AA; non-Markovianity: MM and OCH; revision: MM.

Corresponding author

Correspondence to Maria Mannone .

Editor information

Editors and Affiliations

  1. Escola Superior de Música de Catalunya, Barcelona, Spain

    Thomas Noll

  2. Georgia State University, Atlanta, Georgia

    Mariana Montiel

  3. Universidad Politécnica de Madrid, Madrid, Spain

    Francisco Gómez

  4. University of Coimbra, Coimbra, Portugal

    Omar Costa Hamido

  5. Complutense University of Madrid, Madrid, Spain

    José Luis Besada

  6. University of Coimbra, Coimbra, Portugal

    José Oliveira Martins

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Avitabile, A., Hamido, O.C., Mannone, M. (2024). Quantum Memory and Mathematical Gestures: Two Perspectives on Verdi and Wagner. In: Noll, T., Montiel, M., Gómez, F., Hamido, O.C., Besada, J.L., Martins, J.O. (eds) Mathematics and Computation in Music. MCM 2024. Lecture Notes in Computer Science, vol 14639. Springer, Cham. https://doi.org/10.1007/978-3-031-60638-0_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-60638-0_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-60637-3

  • Online ISBN: 978-3-031-60638-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation