Advertisement

Shall We (Math and) Dance?

  • Maria MannoneEmail author
  • Luca Turchet
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11502)

Abstract

Can we use mathematics, and in particular the abstract branch of category theory, to describe some basics of dance, and to highlight structural similarities between music and dance? We first summarize recent studies between mathematics and dance, and between music and categories. Then, we extend this formalism and diagrammatic thinking style to dance.

Keywords

2-categories Music Dance 

Notes

Acknowledgments

The authors are grateful to the mathematician, musician, and tango dancer Emmanuel Amiot for his helpful suggestions.

References

  1. 1.
    Amiot, E., Lerat, J.-P., Recoules, B., Szabo, V.: Developing software for dancing tango in Compás. In: Agustín-Aquino, O.A., Lluis-Puebla, E., Montiel, M. (eds.) MCM 2017. LNCS (LNAI), vol. 10527, pp. 91–103. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-71827-9_8CrossRefzbMATHGoogle Scholar
  2. 2.
    Amiot, E.: Music Through Fourier Spaces. Discrete Fourier Transform in Music Theory. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-319-45581-5CrossRefzbMATHGoogle Scholar
  3. 3.
    Arias, J.S.: Spaces of gestures are function spaces. J. Math. Music 12(2), 89–105 (2018)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Borkovitz, D., Schaffer, K.: A truncated octahedron in dance, art, music, and beyond. Abstract at Joint Mathematics Meetings in San Diego (2018)Google Scholar
  5. 5.
    Charnavel, I.: Steps towards a Generative Theory of Dance Cognition. Manuscript, Harvard University (2016). https://ling.auf.net/lingbuzz/003137
  6. 6.
    Collins, T., Mannone, M., Hsu, D., Papageorgiou, D.: Psychological validation of the mathematical theory of musical gestures (2018, Submitted)Google Scholar
  7. 7.
    Fiore, T., Noll, T., Satyendra, R.: Morphisms of generalized interval systems and PR-groups. J. Math. Music 7(1), 3–27 (2013)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Jedrzejewski, F.: Structures algébriques et topologiques de l’objet musical. Mathematics and Music. Journée Annuelle de la Société Mathématique de France 21(21), 3–78 (2008)zbMATHGoogle Scholar
  9. 9.
    Karin, J.: Recontextualizing dance skills: overcoming impediments to motor learning and expressivity in ballet dancers. Front. Psychol. 7(431) (2016). https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4805647/
  10. 10.
    Kelkar, T., Jensenius, A.R.: Analyzing free-hand sound-tracings of melodic phrases. Appl. Sci. 8(135), 1–21 (2017)Google Scholar
  11. 11.
    Kubota, A., Hori, H., Naruse, M., Akiba, F.: A new kind of aesthetics – the mathematical structure of the aesthetic. Philosophies 3(14), 1–10 (2017)Google Scholar
  12. 12.
    Lawvere, W., Schanuel, S.: Conceptual Mathematics. A First Introduction to Categories. Cambridge University Press, Cambridge (2009)CrossRefGoogle Scholar
  13. 13.
    Lerdahl, F., Jackendoff, R.: Generative Theory of Tonal Music. MIT Press, Cambridge (1983)Google Scholar
  14. 14.
    Mac Lane, S.: Categories for the Working Mathematician. Springer, New York (1971).  https://doi.org/10.1007/978-1-4757-4721-8CrossRefzbMATHGoogle Scholar
  15. 15.
    Mannone, M.: cARTegory theory: framing aesthetics of mathematics. J. Hum. Math. 9(18), 277–294 (2019)Google Scholar
  16. 16.
    Mannone, M.: Knots, music and DNA. J. Creat. Music. Syst. 2(2), 1–20 (2018). https://www.jcms.org.uk/article/id/523/
  17. 17.
    Mannone, M.: Introduction to gestural similarity in music. An application of category theory to the orchestra. J. Math. Music 18(2), 63–87 (2018)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Mazzola, G., et al.: The Topos of Music: I-IV. Springer, Heidelberg (2018).  https://doi.org/10.1007/978-3-319-64495-0CrossRefzbMATHGoogle Scholar
  19. 19.
    Mazzola, G., Andreatta, M.: Diagrams, gestures and formulae in music. J. Math. Music 1(1), 23–46 (2010)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Patel-Grosz, P., Grosz, P.G., Kelkar, T., Jensenius, A.R.: Coreference and disjoint reference in the semantics of narrative dance. Proceedings of Sinn und Bedeutung 22, 199–216 (2018)Google Scholar
  21. 21.
    Popoff, A.: Using monoidal categories in the transformational study of musical time-spans and rhythms (2013). arXiv:1305.7192v3
  22. 22.
    Prusinkiewicz, P., Lindenmayer, A.: The Algorithmic Beauty of Plants. Springer, New York (2004).  https://doi.org/10.1007/978-1-4613-8476-2CrossRefzbMATHGoogle Scholar
  23. 23.
    Schaffer, K., Thie, J., Williams, K.: Quantifying the Center of Attention (CA) for Describing Dance Choreography. Abstract at the Joint Mathematics Meetings in San Diego (2018)Google Scholar
  24. 24.
    Wasilewska, K.: Mathematics in the world of dance. In: Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsUniversity of PalermoPalermoItaly
  2. 2.Department of Information Engineering and Computer ScienceUniversity of TrentoTrentoItaly

Personalised recommendations