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    The fundamental principle of IRCAM is to encourage productive interaction among scientific research, technological developments, and contemporary music production. Since its establishment in 1977, this initiative has provided the foundation for the institute’s activities. One of the major issues is the importance of contributing to the renewal of musical expression through science and technology. Conversely, sp…

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  • Research

    The fundamental principle of IRCAM is to encourage productive interaction among scientific research, technological developments, and contemporary music production. Since its establishment in 1977, this initiative has provided the foundation for the institute’s activities. One of the major issues is the importance of contributing to the renewal of musical expression through science and technology. Conversely, sp…

    • Research Topics
    • The STMS Lab
    • Research Teams
    • Sound Systems and Signals: Audio/Acoustics, InstruMents
    • Acoustic and Cognitive Spaces
    • Perception and Sound Design
    • Sound Analysis-Synthesis
    • Sound Music Movement Interaction
    • Musical Representations
    • Analysis of Musical Practices
    • Projects
    • Sound Workshop
    • The Musical Body
    • Creative Dynamics
    • Musique/Sciences Collection
  • Creation

    IRCAM is an internationally recognized research center dedicated to creating new technologies for music. The institute offers a unique experimental environment where composers strive to enlarge their musical experience through the concepts expressed in new technologies.

    • Composers & Artists in Studio
    • In Ex Machina
    • Jazz Ex Machina
    • Improvise cum machina 1/2
    • Improvise cum machina 2/2
    • Like Sound, Like Flesh
    • Silent Talks
    • Music-Fictions
    • Tablado
    • Musical creation around Outer Space
    • Campo Abierto
    • Musical creation around Dream Work
    • Biotope
    • EROR
    • IDEA
    • Artistic Research Residency
    • Artistic Residencies: The Blog
    • Rendez Vous 20.21
    • Season 2021.22
    • Seasons from 1996 to present
    • ManiFeste-2022
    • ManiFeste festival from 2012 to 2022
    • L’Étincelle, IRCAM’s journal of creation
  • Transmission

    In parallel to its fundamental missions of research and creation, IRCAM is committed to sharing its knowledge and know-how, its technologies with the general public. Cutting-edge research and diffusion of innovations, an international reference for education and the democratization of artistic practices are the driving forces behind the institute’s educational activities.

    • 2022.23 Training Courses
    • Max, Max for Live
    • OpenMusic
    • Modalys
    • TS2 and Partiels
    • Sound spatialization
    • From PureData to audio plugins
    • Sensors, Interfaces, and Interactive Machine Learning
    • Other training programs
    • Practical Information
    • Advanced Programs
    • Cursus Program on Composition and Computer Music
    • Supersonic Chair
    • Master ATIAM
    • Sound Design Master's Program
    • Music Doctorate
    • AIMove Master
    • School Programs
    • Studios of Creation
    • Mixed-Music
    • Artistic and Cultural Education
    • Career Discovery Visit
    • Art School Reserach and Creation Workshop
    • Images of a Work Collection
    • ManiFeste-2022, the Academy
  • Innovations

    At the center of societal and economic concerns combining culture and information technologies, the current research at IRCAM is seen by the international research community as a reference for interdisciplinary projects on the sciences and technologies for sound and music, constantly exposed to society’s new needs and uses.

    • The IRCAM Forum
    • Subscribe to the Forum
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Mathematics and Music

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Algebraic Models, Topologies, and Categories in Computational Musicology
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The project "Modèles algébriques, topologiques et catégoriels en musicologie  computationnelle  (Algebraic Models, Topologies, and Categories in Computational Musicology)" was selected by the CNRS upon the creation of a director’s position in the Musical Representations team. This project follows the MISA project (Computer Modeling of Algebraic Structures in Music and Musicology), broadening the spectrum of mathematical tools for computational musicology (tools from algebra and also from topology and category theory). At the same time, this project attacks the theoretical and practical articulations between classical and popular music (rock, pop, jazz, song). Four institutions support the project: the Society for Mathematics and Computation in Music (an international society for which the MISA project was a federating force), the GDR ESARS (Esthétique, Art et Science), a collaboration with Sorbonne Universités’ IReMus (during international encounters held at the Centre de Recherche on popular music), and a partnership with université de Strasbourg (in particular with IRMA and Labex GREAM). This project also supports the Mamuphi seminar on mathematics, music, and philosophy organized in collaboration with the école normale supérieure and the book collections: Musique/Sciences (Delatour France) and Computational Music Sciences (Springer).

The spatial program aims to model problems such as movements in a specific space or the transformation of spatial structures. It provides computer tools that enable the development of analyses in line with Set Theory. This work has already made it possible to explore the pertinence of topological tools for the representation and classification of musical objects such as calculating all-interval series, Neo-Reimannian harmonic theory, and the geometric representation of chord progressions.

The result is an experimental environment to assist analysis of musical sequences called HexaChord.                                    
 HexaChord is an environment that makes it possible to build spatial representations associated with a group of chords and analyzes them via several topological notions. The spatial representations proposed include divers Tonnetz and simplical complexes corresponding to groups of chords’ pitches. The software offers 2D and 3D visualizations of the representations produced.

IRCAM's Teams: Music Representations team.

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  • The tonnetz / One key - many representations  None
    The tonnetz / One key - many representations
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