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Moreno Andreatta Et Paul Lascabettes
Mathematical morphology applied to pattern discovery and the algebraic combinatorics of perfectly balanced rhythms
19 juin 2025 - 09:00Salle de séminaires IRMA
After providing a short overview of the interdisciplinary research we are carrying on in the field of Structural Music Information Research (SMIR), we focus on two very active axes: the application of mathematical morphology to music analysis and the algebraic combinatorics of a special family of rhythmic structures. Although mathematical morphology was originally developed for image processing, it has been successfully applied to pattern discovery in the case of symbolic music representations (i.e. representations such as MIDI that are not based on the audio signal). We will present some recent approaches aiming to extend the classical morphological operators (erosion, dilation and opening) to the case of pattern discovery up to variations. These constructions can also be applied to the study of musical meters and rhythms, together with some other approaches that are more algebraically oriented. We will focus in particular to the family of so-called "perfectly balanced rhythms", i.e. rhythms that are obtained as sums or differences of regular rhythms seen as regular polygons within a cyclic group of a given order. Surprisingly, the classification of these algebraic structures remains an open problem in mathematics.
Moreno Andreatta holds diplomas in mathematics from the University of Pavia, piano performance from the Novara Conservatory and computational musicology from the EHESS in Paris. Senior researcher in maths & music at CNRS/IRMA he is also associate researcher at IRCAM. He is at the present the coordinator of the SMIR (Structural Music Information Research) and LaMaMu (LaboMathéMusique) projects at IRMA.
Paul Lascabettes is a postdoctoral researcher at IRMA at the University of Strasbourg, working on the discovery of musical patterns and the generation of musical rhythms. He holds a PhD in mathematics applied to music, obtained at IRCAM and Sorbonne University under the supervision of Isabelle Bloch and Elaine Chew.