INTRODUCTION

Physical modelling of woodwind instruments with application to musical sound synthesis requires a digital tonehole model that 1) can represent toneholes of any physically and musically feasible dimensions, 2) can be applied in the efficient travelling-wave formulation (such as a digital waveguide model), 3) closely approximates acoustical tonehole theories in the low-frequency-limit, 4) characterises all tonehole states from open to closed, and 5) is computationally efficient. Tonehole models that were previously developed in this context [5, 7, 8, 9, 10] do not meet all of these requirements. The three-port tonehole model described in [9], in which wave propagation in the tonehole is modelled using a short delay-line, meets all criteria except the first. This is because the model is only computable for tonehole lengths that correspond to a round-trip time of at least one delay. For an audio sampling frequency $f_s=44.1$kHz and a wave velocity $c=342$m/s, the tonehole length is restricted to a minimum of $t=c/ (2 f_{s}) \approx 3.8$mm. Since increasing the sample rate is undesirable for a variety of reasons, simulation of woodwind instruments that contain holes of shorter length (such as the saxophone) requires an alternative modelling approach.