A comparison of nonlinear modal synthesis using a time varying linear approximation and direct computation

Modal synthesis is a common technique to model linear musical systems efficiently using a parallel bank of second-order digital filters to represent the modes of a resonating instrument. However, many instruments exhibit nonlinear behavior when driven at high amplitudes, often resulting in amplitude dependent mode center frequencies. This behavior can be modeled in a simplified manner using a time varying linear modal structure or could be directly modeled using a nonlinear mode approximation such as that of a Duffing oscillator. The time-varying linear approach is compared to the direct approach to gauge if the approximation is valid within perceptual limits. Particular emphasis is put on weakly nonlinear modes which may be found in a string instrument with thin vibrating plates.