SMIR - Structural Music Information Research

smir_scheme_mathsmusic.jpg Moreno Andreatta (Principal Investigator)
CNRS Director of Research and Vice-President of the SMCM
Music Representation Team
1, place I. Stravinsky
F-75004 Paris
tel: +33 (0)1 44781649
e-mail : Moreno.Andreatta[at]

Invited Researcher at the University of Strasbourg
7, rue René Descartes
F-67000 Strasbourg
tel: ++33 (0)3 88 22 78 93
e-mail : andreatta[at]

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Structure of the project:

  • Financial support: USIAS - University of Strasbourg Institute for Advanced Studies
  • Hosting institution: IRMA - Institut de Recherche Mathématique Avancée (UMR 7501), University of Strasbourg
  • Members of the research team:
    • Moreno Andreatta (Principal Investigator), CNRS Research Director at IRCAM, STMS Lab, UPMC
    • Pierre Guillot (Assistant Professor - UMR 7501 IRMA, Strasbourg)
    • Sonia Cannas (PhD student in mathematics, co-supervision with Ludovico Pernazza, University of Pavia and Athanase Papadopoulos, université de Strasbourg, cotutelle-agreement)
    • Alessandro Ratoci (PhD student in music research, co-supervision with Laurent Cugny, Sorbonne University)
    • Pierre M. Relaño, mathematician and composer (composition and computer music classes by Daniel D’Adamo and Tom Mays, Conservatory of Strasbourg)
    • José-Luis Besada (post-doctoral researcher at the GREAM Labex on "Mathematical formalisation and computer-aided modelling of the analytical and compositional act in contemporary and popular music")
    • Corentin Guichaoua (post-doctoral researcher)
  • Alumni:
    • Paul Lascabettes (Master 1 student, ENS-Saclay, co-supervised with Corentin Guichaoua) - 2017-2018
    • Matteo Pennesi (Master 2 student, codirection with Massimo Ferri, University of Bologna) - 2017-2018
    • Corentin Bayette (Master 1 student at the University of Strasbourg, co-supervised with Corentin Guichaoua) - 2017-2018
    • Xavier Dambach (Master 2 student at the University of Strasbourg, supervised by Corentin Guichaoua) - 2017-2018
    • Grégoire Genuys (PhD student, codirection with Jean-Paul Allouche, UPMC) - Dissertation and thesis presentation
    • Killian Herraez (Master 2 student, codirection with Isabelle Bloch, Télécom ParisTech, Jamal Atif, université Paris Dauphine and Carlos Agon, UPMC/Ircam/CNRS) - Dissertation and master thesis presentation
  • Complete list of collaborators and field of interest:
    • Athanase Papadopoulos (Geometry and history of maths/music) - UMR 7501 IRMA, Strasbourg
    • Yann Bugeaud (Algebraic numbers and tilings) - UMR 7501 IRMA, Strasbourg
    • Alessandro Arbo (Musicology, musical aesthetics) - GREAM, Strasbourg
    • Xavier Hascher (Transformational music analysis) - GREAM, Strasbourg
    • Pierre Michel (Contemporary music and improvisation) - GREAM, Strasbourg
    • Nathalie Herold (Complex Systems & music, rhythm and form in XXth Century music) - GREAM, Strasbourg
    • Tom Mays (Composition and computer music) - GREAM/HEAR/Conservatory of Strasbourg
    • Philippe Manoury (Composition and real-time systems) - HEAR/Collège de France
    • Daniel D’Adamo (Composition) - HEAR/Conservatory of Strasbourg
    • Georges Bloch (Computer-aided composition/improvisation) - University of Strasbourg / IRCAM
    • Olivia Caramello (Category and topos theory) - IHES, Bures-sur-Yvette, Paris-Saclay
    • Pierre Cartier (Category theory and music representations) - IHES, Bures-sur-Yvette, Paris-Saclay
    • Alain Connes (Spectral theory and music) - IHES, Bures-sur-Yvette, Paris-Saclay
    • Gérard Assayag (Computational musicology) - IRCAM/CNRS UMR 9912/UPMC, Paris
    • Carlos Agon (Visual programming languages) - IRCAM/CNRS UMR 9912/UPMC, Paris
    • Andrea Agostini (Computer-aided analysis and composition) - IRCAM/CNRS UMR 9912/UPMC, Paris
    • Daniele Ghisi (Computer-aided analysis and composition) - IRCAM/CNRS UMR 9912/UPMC, Paris
    • Jean-Louis Giavitto (Programming languages and topology) - IRCAM/CNRS UMR 9912/UPMC, Paris
    • Jean Bresson (Visual programming languages) - IRCAM/CNRS UMR 9912/UPMC, Paris
    • Davide Stefani (Category theory (PhD student) - UPMC / ENS, Paris
    • Grégory Ginot (Persistent homology and category theory) - UPMC, Paris
    • Jean-Paul Allouche (Combinatorics and number theory) - UPMC/CNRS, Paris
    • Louis Bigo (Topology in computer-aided music analysis) - CRIStAL, University of Lille 3
    • Isabelle Bloch (Mathematical Morphology) - LTCI, Télécom ParisTech
    • Jamal Atif (Formal Concept Analysis / computer science) - LAMSADE / University of Paris-Dauphine
    • Polo (Pierre Lamy) - Song writing and composition
    • Ludovico Pernazza (Algebra and geometry) - University of Pavia
    • Sonia Cannas (Transformational theory, PhD student) - Univ. of Pavia /Univ. of Strasbourg
    • Massimo Ferri (Persistent homology) - University of Bologna
    • Elaine Chew (Mathemusical research and performance) - Queen Mary University of London
    • David Meredith (Symbolic music information retrieval) - Aalborg University
    • Thomas Noll (Mathematical Music Theory) - TU-Berlin / ESMuC Barcelona
    • Thomas Fiore (Category theory and music analysis) - University of Michigan-Dearborn, USA
    • Andrée Ehresmann (Category theory and cognitive sciences) - Université de Picardie
    • Alexandre Popoff (Category theory and Transformational Theory) - Paris
    • Emmanuel Amiot (Mathemusical research with focus on DFT) - Perpignan
    • Gilles Baroin (Mathemusical research and visualisation) - Toulouse

Short description:

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 Music Information Research, the SMIR project stresses the necessity of introducing a structural multidisciplinary approach into computational musicology making use of advanced mathematics. The project 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.

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. It aims to create a unique research environment at the University of Strasbourg where mathematicians will collaborate with computer scientists, musicologists and composers. New structural mathematical methods based on algebra, topology and category theory are proposed in order to reveal musical properties, thus opening strategic research directions in computational musicology via a genuinely multidisciplinary approach. They will be integrated into a unique pedagogical software tool strongly reinforcing the scientific and pedagogical outreach. If mathematics has largely shown its power and generality in music theory and analysis, the SMIR project claims that the opposite also holds. Music can occupy a strategic place in the development of mathematics since music-theoretical constructions can be used to solve open mathematical problems.

The SMIR project will also contribute to the emergence of a new structural approach in the field of Music Information Research based on the interplay between different mathematical disciplines such as algebra, topology and category theory. It proposes to approach the computational aspects of musical processes in a unifying way by removing the boundaries between different genres and by paying equal attention to contemporary art music and popular music. The development of ad-hoc computer-aided environments is a necessary condition to enable the systematic comparison between theoretical constructions and computational models. This will not only open new forms of collaborations between mathematicians, computer scientists, musicologists and composers, but will also provide an important contribution to the emergence of new pedagogical approaches in “mathemusical” research which will help to spread this interdisciplinary research outside of the circle of specialists.

Main research axes:

  • Mathematical Morphology, Formal Concept Analysis and computational musicology (see [6], [8] and [12])
  • Generalized Tonnetze, Persistent Homology and automatic classification of musical styles (see [2], [3], [4], [5], [7])
  • Category theory and transformational (computer-aided) music analysis (see [0], [1], [9], [10], [11])
  • Music-theoretical problems and open conjectures in mathematics ([13], [14], [15], [16])
  • Epistemological and cognitive aspects of mathemusical research ([2], [17], [18], [19], [20], [21])

Some references:

  • [0] Popoff A., M. Andreatta, A. Ehresmann, "Relational PK-Nets for Transformational Music Analysis" (forthcoming in the Journal of Mathematics and Music. Online version posted in arXiv).
  • [1] Popoff A., C. Agon, M. Andreatta, A. Ehresmann (2017), « From K-Nets to PK-Nets: A Categorical Approach », Perspectives of New Music, 54(1) draft version).
  • [2] Andreatta M., G. Baroin (2016), "Formal and Computational Models in Popular Music", Z. Kapoula (eds.), AEsthetics & Neurosciences: Scientific and Artistic Perspectives, Springer, p. 257-269 (pdf)
  • [3] Bergomi M., F. Fabbri et M. Andreatta (2016), "Hey Maths ! Modèles formels et computationnels au service des Beatles", Volume ! La revue des musiques populaires (Grégoire Tosser and Olivier Julien editors), vol. 12, n° 2, p. 161-179 (Slides of the invited presentation by Moreno Andreatta at the Beatles Day, Evry, 6 November 2014)
  • [4] Mattia Bergomi, Dynamical and topological tools for (modern) music analysis (PhD in cotutelle UPMC/LIM Milan, co-supervised with Goffredo Haus, December 2015 (pdf)
  • [5] Bigo L., M. Andreatta (2015), "Topological Structures in Computer-Aided Music Analysis", in D. Meredith (ed.), Computational Music Analysis, Springer, p. 57-80 - (pdf).
  • [6] Freund A., M. Andreatta, J.-L. Giavitto (2015), "Lattice-based and Topological Representations of Binary Relations with an Application to Music", Annals of Mathematics and Artificial Intelligence, vol. 73, n° 3-4, p. 311-334. (pdf).
  • [7] Bigo L., D. Ghisi, A. Spicher, M. Andreatta (2014), "Spatial Transformations in Simplicial Chord Spaces", in A. Georgaki and G. Kouroupetroglou (Eds.), Proceedings ICMC|SMC|2014, 14-20 September 2014, Athens, Greece, p. 1112-1119. Best paper award. (pdf).
  • [8] T. Schlemmer, M. Andreatta (2013), "Using Formal Concept Analysis to Represent Chroma Systems", Proceedings of the Conference MCM 2013, McGill University, Montreal, June 12-14, 2013. Lecture Notes in Computer Science / LNAI, Springer, p. 189-200 (pdf).
  • [9] A. Popoff, "Towards A Categorical Approach of Transformational Music Theory", (unpublished manuscript)
  • [10] T. Fiore, T. Noll (2011), "Commuting Groups and the Topos of Triads", in C. Agon et al. (eds), Proceedings of the Third international conference on Mathematics and computation in music (Paris, 15-17 June 2011), Springer LNCS/LNAI, p. 69-83 (draft version)
  • [11] T. Fiore, T. Noll, "Voicing Transformations and a Linear Representation of Uniform Triadic Transformations" (submitted. Arxiv version)
  • [12] Pierre M. Relaño, Morphologie mathématique, FCA et musicologie computationnelle, Master 2 maths-info, ENS-Lyon / LTCI/Télécom ParisTech / LAMSADE, Université Paris Dauphine / IRCAM-CNRS-UPMC), March-July 2017 - Dissertation and master thesis presentation
  • [13] Mandereau J., D. Ghisi, E. Amiot, M. Andreatta, C. Agon, (2011a), « Z-relation and homometry in musical distributions », Journal of Mathematics and Music, vol. 5, n° 2, p. 83-98. (pdf).
  • [14] Mandereau J, D. Ghisi, E. Amiot, M. Andreatta, C. Agon (2011b), « Discrete phase retrieval in musical structures », Journal of Mathematics and Music, vol. 5, n° 2, p. 99-116 (pdf).
  • [15] Lachaussée, G. (2010) Théorie des ensembles homométriques, Stage de troisième année de l'Ecole Polytechnique, Master 1 de Mathématiques. (pdf)
  • [16] Andreatta, M. (2015), « Tiling Canons as a key to approach open Mathematical Conjectures ? », in E. Chew et al. (eds.), Mathemusical Conversations, Wiley, p. 86-104.
  • [17] Andreatta M. (2012), « Mathématiques, Musique et Philosophie dans la tradition américaine : la filiation Babbitt/Lewin », in Andreatta M., F. Nicolas, Ch. Alunni dir. (2012), A la lumière des mathématiques et à l'ombre de la philosophie. Dix ans de séminaire mamuphi, Collection « Musique/Sciences », Ircam-Delatour France, Sampzon, p. 51-74. Draft.
  • [18] Acotto E., M. Andreatta (2012), « Between Mind and Mathematics. Different Kinds of Computational Representations of Music », Mathematics and Social Sciences (50e année, n° 199, 2012(3), p. 9-26. Special Issue devoted to the Conference of the EMPG 2011 (European Mathematical Psychology Group, Telecom ParisTech, 29-31 août 2011). draft
  • [19] Andreatta, M., A. Ehresmann, R. Guitart, G. Mazzola, (2013), « Towards a categorical theory of creativity », Proceedings of the Conference MCM 2013, McGill University, Montreal, June 12-14, 2013. Lecture Notes in Computer Science / LNAI, Springer, p. 19-37 (pdf)
  • [20] Andreatta M. (2015), « Autour de la Set Theory et de l’analyse de la musique atonale : démarche structurale et approche phénoménologique à partir des écrits de Célestin Deliège », dans Modernité musicale au XXe siècle et musicologie critique. Hommage à Célestin Deliège (sous la direction de Valérie Dufour et Robert Wangermée), collection de l’Académie, Bruxelles, p. 93-110. (Draft).
  • [21] Besada L. (2018), « Sharing and Enacting Cognitive Metaphors in Musical Distributed Contexts: A Case Study from IRCAM », to appear in the Proceedings of the 15th International Conference on Music Perception and Cognition (ICMPC) and 10th Triennial Conference of the European Society for the Cognitive Sciences of Music (ESCOM), Montreal, Sydney, La Plata, and Graz, July 23–28 2018


  • Thomas M. Fiore, University of Michigan–Dearborn, USA (17-28 July 2017)
  • Thomas Noll, ESMuC, Barcelona (17-28 July 2017)
  • Andrée Ehresmann, Université de Picardie (26-27 July 2017)
  • Alexandre Popoff, mathematical music theorist (26 July 2017)
  • Davide Stefani, PhD student working on infinite categories and persistent homology, UPMC (2017-2018)
  • Paul Lanthier, PhD student working on cellular automata and music, university of Rouan-Normandie (27 August - 8 September)

Future events:

  • International Conference "Chanter les poètes - Poésique 18", Université de Grenoble Alpes, 16-18 October 2018 (org. Caroline Bertonèche and Anne Cayuela) - Flyer with the schedule
  • Next season (2018-2019) of the IRMA/USIAS Mathemusical Research Seminar (IRMA, salle des conférences). The schedule of the seminar is in progress.
  • Next season (2018-2019) of the mamuphi (mathematics, music & philosophy) seminar at IRCAM (with a special session on "Mathematics, Philosophy and Popular Music", January 12, 2019)

Past events:

(click to see Etienne Lécroart's animation done with bouboucle by Andréas Kündig and Ivan Gulizia)


(back to the main homepage at IRCAM and to the Maths & Popular Music Course)


moreno/smir.txt · Dernière modification: 2018/10/08 18:48 par Moreno Andreatta