Direct computation of modal parameters for musical wind instruments

Parameters of modal expressions for the input impedance of wind instruments can be computed from the Telegrapher equations with radiating boundary conditions at the bell. One dimensional finite elements are used for spatial discretization. Provided that the models can be put under a specified form, the modal parameters can be computed directly by solving a generalized eigenvalue problem. Viscothermal effects can also be accounted for, as well as open or closed toneholes. Modal shapes can be visualized along the instrument. Parameters of modal expressions for the input admittance of flute-like instruments can also be computed.

Automated summary

This article investigates the computation of modal expression parameters for the input impedance and input admittance of wind instruments. The Telegrapher equations with radiating boundary conditions and one-dimensional finite elements are used for spatial discretization. By solving a generalized eigenvalue problem, the modal parameters can be directly computed, taking into account viscothermal effects and open/closed toneholes. Modal shapes can also be visualized along the instrument.