Nonlinear dynamics and chaos in musical instruments

Abstract

Nonlinear phenomena are essential for the production of harmonic sounds from musical instruments with sustained tone through the phenomenon of mode locking. Under conditions where mode locking is circumvented, the sound of the instrument is 'multiphonic', an effect sometimes used in modern compositions. Simple impulsively excited instruments such as guitars and bells have nearly linear behaviour, with all modes simply decaying exponentially with time. Gongs and cymbals with shallow curvature, however, exhibit a range of striking auditory effects such as pitch glide and energy cascade towards high frequencies, which are commonly used in Eastern music. These effects all depend upon dynamic nonlinearity, and in some cases upon chaotic vibration. More detailed investigation of the forced vibration of an orchestral cymbal shows period multiplication and a transition to chaos, both of which are clearly and characteristically audible.