The nonlinear physics of musical instruments

Musical instruments are often thought of as linear harmonic systems, and a first-order description of their operation can indeed be given on this basis, once we recognise a few inharmonic exceptions such as drums and bells. A closer examination, however, shows that the reality is very different from this. Sustained-tone instruments, such as violins, flutes and trumpets, have resonators that are only approximately harmonic, and their operation and harmonic sound spectrum both rely upon the extreme nonlinearity of their driving mechanisms. Such instruments might be described as 'essentially nonlinear'. In impulsively excited instruments, such as pianos, guitars, gongs and cymbals, however, the nonlinearity is 'incidental', although it may produce striking aural results, including transitions to chaotic behaviour. This paper reviews the basic physics of a wide variety of musical instruments and investigates the role of nonlinearity in their operation.