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A physical modeling synthesizer is developed and used to parametrically represent digital audio recordings of clarinet soloists. Empirical data, in the form of acoustic impedance measurements, are incorporated in the model definition. Reed dynamics are also included. Algorithms which calculate control parameters from source recordings are presented and examples of both the impedance measurements and the synthesis output are provided. The synthesis results give further support to the idea that music can, in certain circumstances, be adequately represented by a few low bandwidth control parameters. Additionally, the governing equations of clarinet physical modeling are briefly reviewed.