Modal analysis of the input impedance of wind instruments. Application to the sound synthesis of a clarinet

International audienceThis paper investigates the modal analysis of wind instruments as seen from the input of their air column. Beside the treatment of analytical models, a particular emphasis is given to the analysis of measured input impedances. This requires special care because the measurements cover only a limited frequency band and are affected by some unknown errors. This paper describes how the Prony analysis and the Least Squares Complex Exponential (LSCE) classical techniques can be used in this context and how the main pitfalls can be avoided in their application. A physically acceptable method of reconstruction of the low frequency band is proposed. A technique using fictitious points in the high frequency range is described in order to ensure the passivity of the resonator in the whole frequency band. The principles of a real-time synthesis of clarinet sounds based on the modal representation of the resonator is given as an application, with a method to efficiently handle the modal representation during the transition between fingerings

External Tonehole Interactions in Woodwind Instruments

The classical Transfer-Matrix Method (TMM) is often used to calculate the input impedance of woodwind instruments. However, the TMM ignores the possible influence of the radiated sound from toneholes on other open holes. In this paper a method is proposed to account for external tonehole interactions. We describe the Transfer-Matrix Method with external Interaction (TMMI) and then compare results using this approach with the Finite Element Method (FEM) and TMM, as well as with experimental data. It is found that the external tonehole interactions increase the amount of radiated energy, reduce slightly the lower resonance frequencies, and modify significantly the response near and above the tonehole lattice cutoff frequency. In an appendix, a simple perturbation of the TMM to account for external interactions is investigated, though it is found to be inadequate at low frequencies and for holes spaced far apart