On nonlinear oscillations in audio and musical acoustics: modelling, simulation, visualisation
Résumé
This introductory presentation to the ENOC conference focuses on non-linear oscillations in audio systems and music acoustics. It addresses the issues of modelling, simulation and visualisation for the accurate analysis of sounds. A brief presentation of IRCAM and the laboratory (foundations and current themes) describes the context and motivates this work.
First, we introduce the physical modelling of musical instruments, emphasising the relevance of non-linearities and damping. Then, we present how Volterra series provide an appropriate tool to capture the evolution of timbre with nuance (a sound example reproducing the brassy effect from nonlinear acoustic equations is given).
Then, Port Hamiltonian Systems (PHS) are presented as a general formalism to represent nonlinear physical systems (i.e. satisfying a power balance). Sound examples are given in audio electronics, vibration mechanics, acoustics and for multi-physics systems. A robotic experimental platform to study brass playing and numerical results based on PHS are presented.
Finally, a precise spectral process with visual rendering adapted to a musical scale is presented: the patented method is explained and its interest is illustrated on a variety of sound examples, addressing questions on pitch, temperament, inharmonicity and manifestations of nonlinearities such as oscillation regimes and bifurcations.