Introduction

Computer modeling of musical instruments has been an active area of research for nearly two decades. Because of inherent nonlinearities in such systems, time-domain models have been of particular interest. Most time-domain modeling techniques for complete woodwind instrument systems involve the convolution of a pre-calculated or measured instrument reflection function with a nonlinear driving mechanism [4]. Digital waveguide (DW) modeling [9] is a technique which simulates traveling-wave propagation along the length of a woodwind instrument bore using digital delay lines. Thus, a distributed model of the air column is used to continuously calculate the instrument reflection function, which allows variation of the resonator parameters in a physical manner during a simulation.

Most previously reported models of a woodwind tonehole have characterized only one state of the hole (open or closed). A dynamic DW tonehole model was presented [10], but this neglected the effects of closed holes.

Figure 1: Calculated reflection functions for a simple flute air column (see [3]). Transmission line model vs. DW two-port model with one hole closed (top), three holes closed (middle), and six holes closed (bottom).

Figure 2: Digital waveguide two-port tonehole implementation scheme, including delay-line length interpolation filters.