Nonlinearity, complexity, and the sounds of musical instruments

Musical instruments can be treated to a first approximation as linear harmonic systems, but closer examination shows that they are, almost without exception, nonlinear and inharmonic. Sustained‐tone instruments such as violins and clarinets can be characterized as ‘‘essentially nonlinear’’ and owe their deceptively simple behavior to mode locking due to strong nonlinearity. When the nonlinearity is weakened, the behavior becomes complex, with inharmonic and multiphonic sounds that are sometimes exploited in modern music. In contrast, impulsively excited instruments, such as guitars, pianos, gongs, and cymbals, may be described as ‘‘incidentally nonlinear.’’ They would function quite acceptably if the nonlinearity were to be eliminated but, when it becomes strong, they exhibit physically and aurally interesting behavior such as period doubling, frequency multiplication cascades, and chaotic oscillation. This paper will explore some of these phenomena and demonstrate both their physical origins and musical ...