Results from a time domain clarinet model: Effects of non-harmonic air column resonances

A time domain model of a clarinet-like system was previously reported [S. C. Thompson, J. Acoust. Soc. Am., 150 A98 (2021)] . That model has been used to investigate the improvement in playing behavior when the instrument air column has accurately harmonic input impedance peaks. Two tube models were designed with an effective length to produce a 400 Hz first resonance frequency. Both tubes are terminated at the “closed” end by a SDOF reed with a reasonably high resonance frequency. The first tube is purely cylindrical terminated at the “open” end by a tone hole lattice with a cutoff frequency of 1500 Hz. This tube has two resonances below cutoff whose peaks differ from true harmonicity by approximately 7%. The second tube has a small region of slightly increased bore radius positioned to provide resonances whose inharmonicity is reduced to less than 1%. These tubes have very similar playing behavior in the model at low playing amplitude, but increasingly differ as the playing level is increased. The model has also been upgraded to include a mechanical hard stop for the reed position as it closes against the mouthpiece. Preliminary results with the beating reed will be presented.