This paper presents a technique to resynthesize the sound generated by the vibrations of two piano strings tuned to a very close pitch and coupled at the bridge level. Such a mechanical system produces doublets of components generating beats and double decays on the amplitudes of the partials of the sound. We design a waveguide model by coupling two elementary waveguide models. This model is able to reproduce perceptually relevant sounds. The parameters of the model are estimated from the analysis of real signals collected directly on the strings by laser velocimetry. Sound transformations can be achieved by modifying relevant parameters and simulate physical situations.

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In this short paper, we address the numerical simulation of the single reed excitation mechanism. In particular, we discuss a formalism for approaching the lumped nonlinearity inherent in such a model using a circuit model and the application of wave digital filters (WDFs), which are of interest in that they allow simple stability verification, a property which is not generally guaranteed if one employs straightforward numerical methods. We present first a standard reed model, then its circuit representation, then finally the associated wave digital network. We then enter into some implementation issues, such as the solution of nonlinear algebraic equations, and the removal of delay-free loops, and present simulation results.

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