An Acoustic Analysis of Single-Reed Woodwind Instruments, with an Emphasis on Design and Performance Issues and Digital Waveguide Modeling Techniques

by Gary P. Scavone

Current acoustic theory regarding single-reed woodwind instruments is reviewed and summarized, with special attention given to a complete analysis of conical air column issues. This theoretical acoustic foundation is combined with an empirical perspective gained through professional performance experience in a discussion of woodwind instrument design and performance issues. Early saxophone design specifications, as given by Adolphe Sax, are investigated to determine possible influences on instrument response and intonation. Issues regarding saxophone mouthpiece geometry are analyzed. Piecewise cylindrical and conical section approximations to narrow and wide mouthpiece chamber designs offer an acoustic basis to the largely subjective examinations of mouthpiece effects conducted in the past. The influence of vocal tract manipulations in the control and performance of woodwind instruments is investigated and compared with available theoretical analyses. Several extended performance techniques are discussed in terms of acoustic principles.

Discrete-time methods are presented for accurate time-domain implementation of single-reed woodwind instrument acoustic theory using digital waveguide techniques. Two methods for avoiding unstable digital waveguide scattering junction implementations, associated with taper rate discontinuities in conical air columns, are introduced. A digital waveguide woodwind tonehole model is presented which incorporates both shunt and series impedance parameters. Two-port and three-port scattering junction tonehole implementations are investigated and the results are compared with the acoustic literature. Several methods for modeling the single-reed excitation mechanism are discussed.

Expressive controls within the context of digital waveguide woodwind models are presented, as well as model extensions for the implementation of register holes and mouthpiece variations. Issues regarding the control and performance of real-time models are discussed. Techniques for verifying and calibrating the time-domain behavior of these models are investigated and a study is presented which seeks to identify an instrument's linear and nonlinear characteristics based on periodic prediction.