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From Music to Mathematics and Backwards: Introducing Algebra, Topology and Category Theory into Computational Musicology

In: Imagine Math 6

Author

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  • Moreno Andreatta

    (Sorbonne University, IRCAM, CNRS UMR 9912 STMS
    USIAS, CNRS IRMA UMR 7501, GREAM)

Abstract

Despite a long historical relationship between mathematics and music, the interest of mathematicians is a recent phenomenon. In contrast to statistical methods and signal-based approaches currently employed in MIR (Music Information Research), the research project described in this paper stresses the necessity of introducing a structural multidisciplinary approach into computational musicology making use of advanced mathematics. It is based on the interplay between three main mathematical disciplines: algebra, topology and category theory. It therefore opens promising perspectives on important prevailing challenges, such as the automatic classification of musical styles or the solution of open mathematical conjectures, asking for new collaborations between mathematicians, computer scientists, musicologists, and composers. Music can in fact occupy a strategic place in the development of mathematics since music-theoretical constructions can be used to solve open mathematical problems. The SMIR project also differs from traditional applications of mathematics to music in aiming to build bridges between different musical genres, ranging from contemporary art music to popular music, including rock, pop, jazz and chanson. Beyond its academic ambition, the project carries an important societal dimension stressing the cultural component of ‘mathemusical’ research, that naturally resonates with the underlying philosophy of the “Imagine Maths” conference series. The article describes for a general public some of the most promising interdisciplinary research lines of this project.

Suggested Citation

  • Moreno Andreatta, 2018. "From Music to Mathematics and Backwards: Introducing Algebra, Topology and Category Theory into Computational Musicology," Springer Books, in: Michele Emmer & Marco Abate (ed.), Imagine Math 6, pages 77-88, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-93949-0_7
    DOI: 10.1007/978-3-319-93949-0_7
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