Music and Maths

Hamiltonian and permutational songs by Moreno Andreatta at the “Gala des artistes du CAES” of the CNRS (Théâtre du Ranelagh, 2 December 2017)

I’m convinced that music can help approaching old and new mathematical problems in an original way. This is at the core of my academic research activities at the CNRS. But music can also benefit a lot from mathematics, not only in contemporary (art) music but also in popular (contemporary) music, including pop, rock, jazz, … In this spirit, I use geometrical and topological structures in song writing and improvisation to explore new melodic patterns and harmonic progressions. I also teach the application of these mathematical approaches to music analysis and composition in the ATIAM Master program at Sorbonne University and the “Popular Music” undergraduate program at the University of Strasbourg. I’m also heavily engaged in a range of outreach activities at the maths-music interface, including concert-conference, workshops, or museum exhibitions (see below for a detailed description of one of these outreach activities, i.e. Math’n Pop).



  • La sera non è più la tua canzone (Mario Luzi / Moreno Andreatta).
    A “redondant” Hamiltonian Song. Arrangement: Mattia Bergomi and Simone Geravini (Perfect Music Production). Mastering: Alberto Cutulo at the Massive Arts Studio in Milan)
  • Aprile (Gabriele D’Annunzio / Moreno Andreatta).
    A “decadent” Hamiltonian Song (without inner symmetries)
  • Una storia d’amore finisce una volta soltanto (text and music by Moreno Andreatta). A one-sentence Song on one note.
  • Prenderò d’anticipo il mattino (Vinicio Capossela / Moreno Andreatta). An Oulipo-inspired combinatorial exercice on a text by the Italian song-writer and author Vinicio Capossela
  • Ode à elle (Henri Pichette / Moreno Andreatta). An entire piece written in 7/8.
  • A part (Andrée Chedid / Moreno Andreatta). The simplest Hamiltonian chord progression you can use to write a song.
  • dOMENEdio (Livio Andreatta / Moreno Andreatta). A “open” song based on strict mathematical constrains (and written in the dialect of the Piné region in Trentino, Italy).
  • Ah ! (Jacques Roubaud / Moreno Andreatta). A semi-Hamiltonian song, relaxing the mathematical constraints and allowing to visit several times a given chord.


The Gunner’s Hamiltonian Dream (a Hamiltonian harmonization by Moreno Andreatta of Roger Waters’ hit “The Gunner’s Dream”, from the album The Final Cut; visualisation: Gilles Baroin)

La sera non è più la tua canzone (Mario Luzi / Moreno Andreatta; visualisation: Gilles Baroin)

La sera non è più la tua canzone (Mario Luzi / Moreno Andreatta. Performance at the “Festival artistes en cour#s”, Conservatoire “Hector Berlioz”, 26th June 2014. Produced by Laurence Honnorat from Innovaxiom).

Aprile (Gabriele D’Annunzio / Moreno Andreatta; visualisation: Gilles Baroin). New version.

Aprile (Gabriele D’Annunzio / Moreno Andreatta; visualisation: Gilles Baroin). First version.

dOMENEdio (Livio Andreatta / Moreno Andreatta; visualisation of the correct solution: Gilles Baroin)

dOMENEdio (Livio Andreatta / Moreno Andreatta; visualisation of the “tricky” solution: Gilles Baroin)

Math’n Pop

Initially submitted as a project within the celebration of the 80th Anniversary of CNRS,  Math’n Pop is a show conceived with Laurent Mandeix and devoted to the mathemusical outreach. In addition to the live performance, Math’n Pop also includes a series of workshops addressed to students at different levels (from Primary to High School and University) in which the main mathematical and musical concepts presented in the show are introduced in an interactive way (using the Tonnetz web environment). The drawings for Math’n Pop have been originally conceived by Wiebke Drenckhan.  

Read more on the dedicated “Math’n Pop” website

Three live recordings of the Math’n Pop Show:

Math’n Pop in Sorbonne (Amphithéâtre Richelieu, Paris, 3 October 2019). With the participation of Philippe Cathé (musicologist) and Jonathan Gasser (musician).

Math’n Pop at the Citadelle (Amphithéâtre Simone Veil, Amiens, 6 March 2020). With the participation of Serge Bouc (mathematician) and Céline Pruvost (musician). The video is available here.

Math’n Pop in Brittany (‘Bonjour Minuit’ Concert Hall, Saint-Brieuc, 18 November 2021). Within a Festival entitled “La preuve par 9” organized by Le temps de Sciences.

Some other concert-conferences

The music of maths, a concert-conference at the Centennial of the International Mathematical Union, Palais Universitaire, Strasbourg, 27 September 2021 (in English). The video is available here.

A concert-conference at Mathematics without Borders: The Centennial of the International Mathematical Union

Coding music with maths, a concert-conference at Musicora, Grande Halle de la Villette, plateau of France Musique, 3 June 2018 (in French)

Matematica, geometria e musica. A concert-conference at the “GiovedìScienza”, Teatro Colosseo, Turin, 15 December 2016. With the participation of Alberto Conte (mathematician) and Paolo Conte (musician). Also available in English and French translations.

Geometry, Algebra in Contemporary Music and Songs. A concert-conference at the Laboratoire de Physique des Solides of Orsay, 14 April 2016. With the participation of Wiebke Drenckhan (accordion). In French.

Mathematics and music: a journey though pop music, classical music and songs. A concert-conference at La Chapelle of Montpellier, 4 February 2014. With the participation of Emmanuel Amiot and Gilles Baroin (in French)

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