Numerical Simulation of the Production of Pedal Notes in Brass Instruments
Simulations numériques de notes pédales pour des instruments de la famille des cuivres.
Résumé
Conical brass instruments, such as saxhorns, show an input impedance with almost harmonically distributed peaks, which allows to play notes whose frequencies approach a harmonic series. Conversely, all brass instruments with a long cylindrical section (notably trumpet and trombone) have their first impedance peak heavily shifted towards low frequencies (38 Hz for a trombone instead of 62 Hz if the first resonance frequency was belonging to the harmonic series formed by the upper peaks). However, trombonists can play the so-called "pedal note" despite its frequency close to 62 Hz, around a minimum of the input impedance. Previous publication showed interesting numerical and experimental results when using alternatively a saxophone reed and a brass mouthpiece on both a trombone and a saxhorn. In this paper, we try to reproduce numerically and extend the simulations results with a mouthpiece using Moreesc, a numerical tool based on the modal decomposition of the bore which allows changing parameters during the simulation. By simulating brass mouthpiece coupled with modal fits of measured trombone and saxhorn impedances, we examine this mysterious regime of oscillation. This allows to check the robustness of this phenomenon regardless of the numerical method. The influence of the number of modes taken into account is particularly investigated.
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