Digital Waveguide Modeling of Woodwind Toneholes

This paper demonstrates a digital waveguide implementation of a six-hole woodwind tonehole lattice, based on theory and measurements published by Keefe (1981). Woodwind tonehole transmission-matrix parameters are converted to traveling-wave scattering parameters suitable for digital waveguide implementation. Second-order digital filters are designed to approximate the reflection and transmission transfer functions implied by the Keefe data. In this way, the tonehole is implemented by a two-port scattering junction which accounts for both series and shunt complex impedances. Alternatively, the tonehole can be implemented as a one-multiply, one-filter, threeport scattering junction. The results of a digital waveguide six-hole flute bore implementation using both models are compared to Keefe (1990), with excellent agreement. In this way, the best available acoustic theory regarding toneholes is efficiently and accurately simulated in discrete-time. 1 Two-Port Tonehole Model The fundamental acoustic properties of toneholes have been extensively studied and reported by Keefe (1981, 1990). The model described by Keefe (1990) is an accurate representation for a tonehole unit, assuming adjacent tonehole interactions are negligible. In this description, acoustic variables at the tonehole junction are related by a transmission matrix of series and shunt impedance parameters. Keefe’s original derivation of the tonehole parameters was based on a symmetric T section, as shown in Fig. 1 (Keefe, 1981). The series impedance terms, Za, result from b b b b Za/2 Za/2