Papers, notebooks, keynotes, conferences, a.s.o.
Right-click (or control click) to download non readable files, like keynotes or .nb - these last require the free reader Mathematica Player.


NB: some French productions are not mentioned here but can be found on the V.F. page.


Preprint about number, type and period of Anatol Vieru’s sequences. Only works for square-free moduli (not modulo 12 but it’s a start).

Preprint purporting to explain the unreasonable efficiency of Fourier coefficients in analyzing musical structures (not sound). Essentially the topic of a conference given in Pavia in 2011 (for lack of the biannual meeting of SMCM, suppressed because of a pandemic).

Papier about products of Fourier coefficients whose indexes sum up to ambiant dimension, a musically meaningful notion. Launched on Jason Yust’s idea, given at MCM 2022, Atlanta, GE.

Pasted Graphic

concerference in lycée Saint Sernin, Toulouse. Great location and public.

Conference for the European Academy of Arts and Science.



Fun fact: some (generated) scales have flat intervallic relationship — the probability of occurrence of any interval between
randomly chosen notes from the two scales are (almost) equal.

concert celebrating the end of my educational labours (yes, off to pension!). May 27th.
A nice free book online (collaboration) about
the most beautiful maths formulas.

April 8: Astor Piazzolla recital (100th birthday).


Récital given on November 23th, 2020, to raise everyone’s badly damaged spirits by way of music’s magic (the same again in January for a second half of the public!)


Entropy of Fourier coefficients of periodic musical objects: Published in JMM, a research note about yet another measure of entropy (of musical objects). This one is computed from the magnitudes of Fourier coefficients (for periodic rhythms, or pc-sets). The sum (of their squares) being constant, it is natural to normalize them and take the Shannon entropy. Strangely, although the magnitudes of Fourier coefficients yield exactly the same information as the interval content, their entropy allows to better differentiate between, say, arithmetic sequences, a chromatic chunk appearing more `random’ than a whole-tone sequence.

Irrational Tonnetz: A preprint (it was judged too tame for JMM!) about the simple trick of drawing lines in the Tonnetz and picking the resulting chords. It produces simple, parsimonious, harmonic changes. I composed a melody on such a chord line, one can hear a sound file here.



In Theoretical and practical pedagogy of mathematical music theory, World Scientific, pp. 179-199, I authored chapter 8 : «Concerférences»: Addressing Different Publics for Mathemusical Popularization. A preprint here.

A special issue of
JMM devoted to Maximally Balanced Sets harbours two revamped papers: my book’s first chapter about discrete Fourier transform of musical structures, and an augmented English version of an old but seminal paper «Sur les sommes nulles de racines de l’unité».

Workshop at Buenos Aires Univ. (Argentina) from 3 to 10 May, around DFT of musical structures. About it,
short vid on the scientific channel of la Universidad.

Conference at the maths seminar of Buenos-Aires’ univ., about Tilings and rhythmic canons; + a concerférence at Centro Cultural de la Ciencia.

Conference in Pavia (18 April 2018, Università di Pavia, Italia) about
Tilings and rhythmic canons. The evening before, a nice concert where I played La Leucatoise & Noli me Tanguero, two compositions with some maths hidden in there.

Conference in Strasbourg (26 January 2018, Institut de Recherche Mathématique Avancée) on
Some aspects of DFT in Music Theory.


Dancing Tango in
compàs is difficult for beginners… and even for many experienced dancers. The Compass Trainer Software allows to learn how to do it better. This paper describes its elaboration (presented at MCM 2017, Mexico City).

Measuring tonal character (technically speaking: the diatonicity), or more generally, chromaticism, octatonicity, etc… is now easy and clearcut thanks to `saliancy’, a concept due to Ian Quinn (presented at MCM 2017, Mexico City).

Inversions reverse major and minor triads, and are really strange symmetries, liable to depend on context and even cease to be symmetries at all in the sense that S°S is not always Id (presented at MCM 2017, Mexico City).


My book Music through Fourier Space was at last issued by Springer (October 2016). This book states the art about Discrete Fourier Transform of musical structures (not sound).

Generators of a scale: how many? « generated » scales (for instance whole-tone, diatonic, pentatonic…) may have many different generators, but not any number: for instance never 14… this paper clarifies the phenomenon. Ultimately presented at MCM London (2015) and published in the acts.

Old and new isometries between pc-sets in the planet-4d model. In the 4D model of Baroin, disposing the 12 pcs on a polytope, the group of isometries is larger than the customary T/I group. This paper classifies the new isometries which are recognised as a representation of a famous group.


The Torii of phases. Explores the musical relevance of the phase of Fourier coefficients of a pitch-classes collection. For instance the torus made up with 3d and 5th coefficients is equivalent to the Tonnetz. (shorter) Published version in the proceedings of SMCM, Montreal, 2013.


Some aspects of rhythmic canons. All there is to know about rhythmic canons. For a special issue of Perspectives of New Music.

video explaining rhythmic canons for non specialists on

A review:
A geometry of music: harmony and counterpoint in the extended common practice
(about Dmitri Tymoczko’s A geometry of Music, O.U.P)

Homometry: sets or more generally multisets can share their intervalic distributions and are then called homometric (i.e. the probabilities of occurrence of random intervals are the same in both sets). Two comprehensive papers have been published in JMM:
Z-relation and homometry in musical distributions and Discrete phase retrieval in musical structures
by C. Agon, M. Andreatta, D. Ghisi, J. Mandereau and myself, in
JMM 2011 (2).

Double Hexachordal Thm
The hexachordal theorem is twice true for general topologic compact groups… Since there are two kinds of intervals (left and right), there are two versions of the theorem, not one ! But only one way to compare the interval contents of a subset and its complement.

Generators of a scale
The major scale is generated either by ascending fifths or by descending fourths. But some scales may have more than two generators. I explain among other things while the number of generators can never be 14... Other results include infinite generated scales, e.g. {n x mod 1 }. Ultimate version published in Proceedings of MCM, London 2015 (Springer).

Scale Algebra
With Bill Sethares, we established methods (mostly about circulating matrixes) for algebraic decomposition of a scale or chord as a sum of other scales or chords. For instance, (C minor melodic) = C M + B flat M - F M.
As it happens, these methods are linked with Discrete Fourier Transform, tilings, and the intervallic functions first unraveled by David Lewin.
The ultimate version is published in JMM 2011 (1).


Reviewing of La Vérité du Beau dans la Musique in JMM 2010.

My PhD : Modèles algébriques et algorithmes pour la formalisation mathématique de structures musicales.
Ircam/Paris VI, dir. C. Agon, defended 5/5/10.

Sommes nulles de racines de l'unité. This short paper (published in Bulletin de l'UPS, april 2010) shows examples of configurations of roots of unity with nil sum, which are not trivial in the sense that they are not unions of regular polygons.


Finite groups of rational spectral units.
These esoteric beings, spectral units, are bridges between homometric sets (like the famous (0 1 4 6) and (0 1 3 7) pc-sets). A little part of the mystery is unveiled as the finite groups of rational spectral units are hereby described and classified.


DFT vs JSB - pdf version
On Music Theory Online, june 2009. How Discrete Fourier Transform enables to compare transpositional qualities of temperaments among major scales, thus perhaps settling the dispute over which was the "good temperament" favored by JS Bach.

Yale panel continuous gestures in Fourier space.
I was privileged to chair the last panel in the 2009 SMCM colloquium in Yale, on the 25th of June. From resurrecting the notion of DFT by the man who did it, Ian Quinn to a  ballet and musical creation,
Dancing the Violent Body of Sound, following an idea of Guerino Mazzola in  Minneapolis University, through implementations in Open Music and `Fourier Scratching' by Thomas Noll and Martin Carlé.


Frame and Flow in Words and Music by Samuel Beckett and Morton Feldman, with Pascale AMIOT-JOUENNE. Proceedings of Colloque «Réflexions autour de la musique en Irlande : esthétique et enjeux», Caen, 10-12 September 2008, Alexandra Slaby (ed.), Presses Universitaires de Caen, 2009.

Fourier again
A round up of applications of the DFT in musical analysis. Conference for the SMT meeting, Nashville 2008.

More Vuza canons
Following recent ideas by Matolcsi, all Vuza canons for n=120 and n=144 have been found. Given in Pisa in 2008, published since in JMM's special issue on Tiling Problems.

Berlin 2007
A talk on Discrete Fourier Transform and how it encapsulates most of the musically relevant information about subsets of Z/cZ; developing an idea of Ian Quinn, pursuing David Lewin's work.

Fourier Oracles for Computer-Aided Improvisation
About Fourier transform and real-time grooving of scales or rhythms. ICMC 2006, New Orleans. A real-time implementation was shown by Thomas Noll at the 2009 SMCM congress in Yale.

Vulgarisation talk about rhythmic canons. Close to

Autosimilar melodies
A fascinating notion discovered by Tom Johnson: autosimilar melodies, as shown during the colloque
Mélodie organized by the SFAM (October 2006). In French.
Autosimilar melodies
Same thing in more detail (MaMuX, october 2006).

Type III ME sets
Solution of a conjecture by Norman Carey about type III ME sets (some kind of generated scales). With a pretty movie alongside the notebook.

DFT Clough
A simple talk clarifying what is DFT at the John Clough meeting in Chicago, 2005. Had I known where it would lead…:)

Cyclotomic canons
Given inICMC 2005, Barcelona: applications of cyclotomic polynomials to music via OpenMusic.


AMS Chicago 2004
A conference for the 'Fall session 2004' of AMS, in Evanston (Illinois) with previously unknown correlations between Vuza canons and Fuglede's conjecture. No article, on request slideShow (Keynote™ format, zipped, for MacOS only) available. There is a Powerpoint version too.

Salomé sur le Pont des Arts, Passerelles et Impasses / Barriers and Bridges, avec P. Amiot-Jouenne; Actes du Colloque de la SOFEIR, Rennes, mars 2004, Le Faouet, Liv’ Editions, 2007 (also DVD version).

Cyclotomic canons
Talk for ICMC, Barcelona 2005: applications of cyclotomic polynomials for musicians, in software OpenMusic.

Implementation of a recent and simple algorithm by Frank Jedrzejewsky, building acyclic canons (aka RCMC, or Vuza canons). Included in canonCrawler.

Another (glutton) algorithm, very simple, yet effective, from canadian Jonathan Wild, for tiling with a 3 note motif and its retrograde version.

Canons July 2005
Conference for musicians: DIY rhythmic canons. Little or no maths.

Canons For Geeks
The other side of the coin: all out on mathematical properties (Galoisian theory of finite fields, spectral conjecture)

A large file (1608 ko) of a talk (slideShow) in Graz colloquium, may 2004. MathPlayer required.

Paper from the same conference in Graz. Mostly mathematic stuff.

IrcamDiapo.nb (in french)
Slideshow of a recent conference (january 2004) in Ircam, about computing new canons and especially Vuza canons not obtainable by Vuza's algorithm. MathReader required.

Nouveaux Vuza canons (in french)
An abstract of above item, but in html (about new Vuza canons).

Same in english. Mathematica Player Required.

idem, in .pdf


Midi files for diverse canons.

Les canons rythmiques
A paper for la Gazette des Mathématiciens, a good specialized revue. Summarizing all the connections I have found between canons and mathematics of tiling the line.

Mathematica 5.X package for exporting Midi files. Required for some of my routines, for instance canonToMidi. Rather obsolete with newer versions of Mathematica (though importation of Midi is still in the blue print stage).

A file explaining the above package Musica.m.

An elementary (I hope ;) ) slideShow about rhythmic canons. MathReader.

Perhaps an unusual file format for this slideShow (AppleWorks…) of a conference in Zürich. Right-click (or control-click sous MacOS) for download. I promise I'll translate to another format should anyone ask nicely ;-)

Paper after MaMuTh colloquium in Zürich (november 2003). Published by Epos in a valuable reference book.

Tiling problems in Music Composition
Presented in ICMC 2002, Göteborg.

Vuza Algo Produced.nb
All acyclic canons produced by Vuza's algorithm with period less than 216.

This precious notebook includes most of the routines I have developed for computing with and about rhythmic canons.
NB: obsolete for Mathematica 6.x and upward. Replaced by a newer version.

Johnson Conjecture
Proof of Johnson's conjecture about tilings (canons) with augmentation. Where Galois theory over finite fields unexpectedly arises about rhythmic canons.

exposé Ircam (in french)
Web page retracing my first steps in the wonderful world of rhythmic canons. Better stuff since.

Procedures for turning some canons into Midi files. Not necessary in Mathematica 6.0

Ircam 01/2003.nb
(in french) A conference (Ircam 2003) with some simple ideas about rhythmic canons.

Ircam 2003
Same thing, as a .html file.


Pour en finir avec le Désir
How the initial stance in
Tristan is overdetermined by alimited transposition mode. Published in Revue d’Analyse Musicale.

Les groupes de frise et Chopin
Much more mathematics in Chopin than Horatio ever dreamed of. Virtuosity involves repetition which leads to frieze groups.

2001 and before

Les symétries des séries dodécaphoniques
All possible symmetries of twelve-tone series (in Schönberg’s group of transformations) and how many of each. This paper (and the last one) were published in
Quadrature. The subject received a more modern treatment in the AMM.

Mathématiques et analyse musicale: une fécondation réciproque.
Three examples given at the colloque de Chantilly (Logique et Musique) in 1992. Published in Revue d’Analyse Musicale, 28, June 1992.