THOMAS, 31 years old
Head of Musical Acoustics Research
National Centre for Scientific Research (CNRS) and Institute for Research and Coordination in Acoustics and Music (IRCAM).
How he became a mathematician
“After completing preparatory classes, I entered the ENST (École Nationale Supérieure for Telecommunications) in Brittany. At the end of my first two years, I decided to attend the ENST in Paris, which offered an audiovisual option. Since I wanted to work on physical modelling and inverse problems in musical acoustics, I also pursued two concurrent masters’ of advanced study: one in acoustics, signal processing, and computer science as applied to music, and the second in direct dialing and signal processing. Then I worked on a thesis, which I completed here at the IRCAM. After receiving my doctorate, I did a post-doc at the École
Polytechnique Générale in Lausanne, were I studied methods for solving weakly non-linear partial derivative equations. Then I taught for one year as an ATER (Temporary Attaché for Teaching and Research). After my post-doc, I passed the CNRS exam, and was accepted as a research head.”
How mathematics comes into play in his job
While producing physical models of the synthesis of sounds, the musical-acoustics researcher studies the mechanisms of sound production in existing instruments.
“I conduct research on the simulated sound production of musical instruments. In other words, I try to produce a virtual instrument that one can play on a computer that will have the same ring of truth as a real instrument. Technically speaking, I try to take the vibratory phenomena produced inside an instrument, as well as the specific manner in which it is played, and represent these in the form of mathematical equations.
“First, I construct a physical model of the sound production of musical instruments. Using methods that rely on signal processing in discrete and continuous time, on differential equations, and equations with partial derivatives, my approach consists in calculating, at each instant, the direct correlation between the actions of the musician and the sound released by the instrument. For example, a trumpeter playing very loudly produces a bright sound. This phenomenon is due to a non-linearity in the propagation of the sound wave; that is, the sound levels inside the instrument are much higher than those which it emits. When the sound levels are sufficiently high, they produce a localized increase in air temperature, which significantly increases the speed of the sound. As a result, part of the soundwave propagates itself more quickly, such that even a pure signal transforms itself into a sawtooth pattern as it propagates itself.
“Then, I test the model. During this phase, known as model inversion, I attempt to verify whether one obtains expressive signs identical to those of a competent musician, or which correspond to a specific style of playing—you don’t play jazz the same way as classical. In other words, the goal is to ensure that we can reproduce all the uses of the instrument in their full richness, from the beginner’s duck-squawk up to the fine vibrato or accentuation of a virtuoso. And the question of how to resolve these inverse problems is much more complicated to master than constructing the model itself.”
What are the qualifications?
Bac + 8, doctorate after a research master’s in applied mathematics.
Translated by David Kramer