Regeneration in brass wind instruments

Abstract

This paper is concerned with the production of musical notes by the interaction between the lips of a player and a brass wind instrument. The mechanism of this non-linear oscillation, together with that in the voice and for woodwind instruments, is discussed and past theories reviewed. Each element in the interaction is then carefully delineated and reasonable approximations to the governing equations for the lip dynamics and flow conditions through the lip opening are deduced: the acoustic parameters of the instrument and pressure source from the lungs can be experimentally determined. In contrast to the case of woodwind instruments, for example, many of the important parameters controlling the interaction can vary over a wide range and are under the complete control of the player. The expressions describing each component of the interaction are then combined to form an overall theory of regeneration, following Helmholtz, which leads to a description of the conditions necessary for a note to be sustained, and to an expression describing the characteristic waveform of the mouthpiece pressure at low frequencies. Experimental measurements of this mouthpiece pressure are presented, together with measurements of the steady and alternating components of the pressure in the mouth, and of the velocity in the mouthpiece for blown notes on a trombone and trumpet. Good agreement was observed between the harmonics of the measured mouthpiece pressure and those deduced from theory. Measurements are presented of the intonation of a trombone, and the range and characteristics of notes “buzzed” on a mouthpiece alone are discussed. Finally the steady pressure in the mouth and the average flow down the instrument are used to calculate the average lip opening, and hence the effective mass of the moving parts of the lips for a variety of notes played on a trombone and trumpet.