# SMIR - Structural Music Information Research

**Moreno Andreatta** (Principal Investigator)

CNRS Director of Research and Vice-President of the SMCM

Music Representation Team

IRCAM - CNRS UMR 9912 (STMS) - UPMC

1, place I. Stravinsky

F-75004 Paris

tel: +33 (0)1 44781649

e-mail : Moreno.Andreatta[at]ircam.fr

Invited Researcher at the University of Strasbourg

CNRS IRMA UMR 7501

7, rue René Descartes

F-67000 Strasbourg

tel: ++33 (0)3 88 22 78 93

e-mail : andreatta[at]math.unistra.fr

**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
- Sonia Cannas (PhD student, codirection with Ludovico Pernazza, University of Pavia and Athanase Papadopoulos, université de Strasbourg, cotutelle-agreement)
- Davide Stefani (PhD student, codirection with Grégogy Ginot, UPMC)
- Matteo Pennesi (Master 2 student, codirection with Massimo Ferri, University of Bologna)
- 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), from November 2017

- Alumni:
- 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

- Institutional collaborations:
- GREAM - Groupe de Recherches Expérimentales sur l'Acte Musical
- Conservatoire de Strasbourg and HEAR (Académie supérieure de musique)
- IRCAM - Institut de Recherche et Coordination Acoustique/Musique
- IHES - Institut des hautes études scientifiques

- 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
- Pierre Guillot (Persistent homology) - 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
- Grégoire Genuys (Homometry theory, PhD student) - UPMC/IRCAM, 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
- Matteo Pennesi (Persistent homology, Master student) - University of Bologna / Univ. of Strasbourg
- 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])

**Some references:**

- [0] Popoff A., C. Agon, 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.

**Visitors:**

- 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)

**Future events:**

- Popular music and recording: mathematical and philosophical reflections, mamuphi Seminar, IRCAM, 18 November 2017 (with the participation of Roger Pouivet, Frédéric Bisson, Agnès Gayraud and Moreno Andreatta) - Programme
- A tour between musical paths on geometric models", talk by Sonia Cannas at the Festival della Scienza (Cagliari, 10 November 2017)
- Oubapo/Oumupo (bande dessinée et musique potentielles). A thematic evening within the cycle "Les jeudis de l'Oulipo" (BNF Paris, Grand Auditorium, 9 November 2017, 7pm-8pm) - Flyer
- When cartoons meet music (and vice-versa). A working session with the Oubapo and the Oumupo at the Vaisseau of Strasbourg (Fête de la Science, 14 October 2017). With the participation of (in a strict retrograde alphabetical order) Valentin Villenave, Etienne Lécroart, Andreas Kürdig, Ivan Gulizia, Martin Granger, Alex Baladi, Moreno Andreatta.

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

**Past events:**

- "Grégoire Genuys' PhD thesis defense" on homometry theory in the non-commutative case and generalized distances in chord spaces" (IRCAM, 23 October, 2017) - Video
- "Working seminar around some active research axes of the SMIR project" (IRMA, 10-11 October 2017). With the participation of Corentin Guichaoua (IRISA, Rennes), Davide Stefani, Pierre Guillot, Sonia Cannas, Pierre Relaño, José-Luis Besada, Nathalie Herold). Coordination : Moreno Andreatta. Programme - Overview
- "Le continuum des gammes classification des structures musicales et théorie des intervalles", a talk by composer Julio Estrada (UNAM, Mexico), with an introduction by Moreno Andreatta (IRCAM, 27 September 2017) - web page
- "Some mathematical and computational models for computer-aided music theory, analysis and composition", talk delivered at IRCAM and addressed to ATIAM Master students and to the composers of the Cursus, Paris, 20 September 2017 Slides in pdf - Video
- "Représentations géométriques en musique savante et dans la chanson", concert-conference by Moreno Andreatta, Lycée Franklin, Paris, 15 September 2017 Présentation en pdf
- The use of constraints in cartoons and in music. A working residence of the Oubapo and the Oumupo at the Château de Bosmelet (3-8 july 2017) - Flyer
- "Formal, Theoretical, and Computational Models in Popular Music Analysis" (a panel within the EuroMac 2017 International Conference (30/6/2017 at 2pm). With the participation of Trevor Declercq (Eastman School of Music), Dmitri Tymoczko (Princeton University), Mattia Giuseppe Bergomi (Fundação Champalimaud, Lisbon), Adriano Baratè (LIM - Milan), Louis Bigo (université Lille 3), Moreno Andreatta (IRCAM-CNRS-UPMC / IRMA-GREAM-USIAS, université de Strasbourg) and John Covach (University of Rochester). Organizer: Moreno Andreatta.
- Mathematics and Computation in Music Conference (MCM 2017). Presentation of the paper "On the group of transformations of classical types of seventh chords" by Sonia Cannas (et al.) and the paper "Homometry in the Dihedral Groups: Lifting Sets from Z_n to D_n" by Grégoire Genuys and Alexandre Popoff (Mexico City, 26-29 June 2017)
- Nastri, orologi e ciambelle musicali nella musica colta e nella canzone, Festival della Scienza, Bergamo, Italy, 24 June 2017 (Slides in pdf, low definition) - (Article in a local Newspaper)
- "Dessine-moi la musique", junior conference by Moreno Andreatta, Le Vaisseau, Strasbourg, 3 June 2017 (Flyer - Slides in pdf)
- "Algebra and Geometry in Music and Musicology", concert-conference by Moreno Andreatta, PMMH Seminar at ESPCI, Paris, 9 June 2017 Présentation en pdf
- "Musical Graphs", talk given by Sonia Cannas within the working group "Graphes et Optimisation (GO)" of the CNRS GDR-RO, Université Paris Dauphine, 15 June 2017

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