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  1. Results are presented from a modeling study of the clarinet in which the air flow through the instrument is calculated using the Navier-Stokes equations. The reed is modeled as an Euler-Bernoulli beam with damping whose motion is driven by the pressure in the mouthpiece. Damping of the reed due to its contact with the lip is studied and shown to be crucial to achieve oscillations in which the reed vibrates at the lowest resonant frequency of the instrument, producing sound at that frequency. This finding is consistent with previous studies in which a clarinet is excited with an artificial blowing machine. 
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