Harmonic Generation in the Trumpet

Abstract

Various possible mechanisms for the generation of harmonics in the tone of the trumpet were investigated. By sounding the trumpet with a mechanical valve utilizing a sinusoidally varying opening, it was shown that nonsinusoidal motion of the player's lips is not an important mechanism for harmonic generation. Nonlinear behavior of the air column of the instrument due to high sound pressures was also shown not to be important by four different methods: (1) by a theoretical estimate of the amount of second-harmonic distortion to be expected; (2) by measuring the input resistance of the trumpet at resonance frequencies and finding that it did not vary significantly with sound pressure in the air column; (3) by measuring the intermodulation distortion produced when the air column was excited at two resonance frequencies simultaneously; and (4) by direct measurement of harmonic distortion produced in the trumpet output by different levels of excitation at the mouthpiece. It was found that the mechanism primarily responsible for harmonic generation is the relationship between the input impedance of the trumpet and the time-varying impedance of the player's lip opening during a cycle. Curves of mouthpiece pressure calculated on this basis showed good agreement with observed waveforms.