Time-domain simulation of sound production in the brass instrument

Abstract

Sound production in brass instruments is formulated physically with two different models of lip vibration: the ‘‘transverse’’ model, where lips strike laterally to the direction of the air flow, and the ‘‘swinging-door’’ model, where lips execute an outwardly striking motion. This formulation is used to carry out time-domain simulation, which indicates that self-excitation of the brass instrument is possible with both of these lip models. Changing the lip resonance frequency provides sustained oscillation at the first through eighth air column resonance modes, which correspond to the musical tones in the harmonic series played on the brass instrument without valve manipulation. Oscillation probably also occurred at higher modes, but that region was not investigated. The harmonic structure of the simulated sound varies according to the fundamental frequency and sound level, as is the case in the sound produced by actual brass instruments. Unusual regimes of oscillation are also obtained: the pedal tone, whose fundamental does not participate in its sound production, a tone an octave below the third mode, whose odd harmonics do not contribute to the regime of oscillation, and a multiphonic, which is an oscillation perceived as having two fundamentals simultaneously.