Feathering collisions in beating reed simulation
Tamara Smyth, Jonathan S. Abel, Julius O. Smith · The Journal of the Acoustical Society of America · 2003
Pressure controlled valves are the primary sound production mechanisms for woodwind and brass musical instruments, as well as for many bioacoustic vocal systems such as the larynx and syrinx (the vocal organ in birds). During sound production, air flow sets a reed or membrane into motion creating a variable height in the valve channel and, potentially, periodically closing the channel completely. Depending on how this event is handled, an abrupt termination of air flow between open and closed states can cause undesirable discontinuities and inaccuracies in a discrete-time simulation—particularly at relatively low audio sampling rates. A solution was developed by re-examining the behavior of the differential equation governing volume flow through a pressure-controlled valve, paying particular attention to this rather troublesome transition. A closed-form solution for the time evolution of volume flow is given and used to derive an update for volume flow. The result is a smoother, more accurate, and nearly alias-free transition from open to closed. ‘‘Feathered collisions’’ of this nature can refine the sound quality produced by the numerical simulation of beating reeds, such as in clarinets, at typical audio sampling rates.