CONTINUATION OF A PHYSICAL MODEL OF BRASS INSTRUMENT FOR TRUMPET COMPARISONS

The system formed by a trumpet player and his/her instrument can be seen as a non-linear dynamical system, and modeled by a biomechanical model of the lips, a non-linear flow equation, and an acoustic impedance of the instrument represented by a superposition of complex modes. Different numerical tools can then be used to study these models in order to understand the effects of the parameters on the behavior of the system. In particular, the modal parameters that describe the impedance are strongly dependent on the geometry and design of the instrument, and the understanding of their influence is therefore of primary interest for a musical instrument maker. An original method of continuation (path-following method) based on the combination of the Harmonic Balance Method (HBM) and the Asymptotic Numerical Method (ANM) is applied to a physical model of the {player-trumpet} system. It consists in studying the evolution of the system where one parameter of the model varies, and enables to calculate bifurcation diagrams for different configurations of the model. Especially, this allows to compare different instruments on the basis of quantitative descriptors computed from the continuation outputs.