Scientific Article

On the tonehole lattice cutoff frequency of conical resonators: applications to the saxophone

LMA, CNRS, UPR 7051, Aix-Marseille Univ, Centrale Marseille, 13453 Marseille Cedex 13, France

^* Corresponding author: erikalanpetersen@gmail.com

Received: 17 January 2020
Accepted: 20 July 2020

Abstract

The tonehole lattice cutoff frequency is a well-known feature of woodwind instruments. However, most analytic studies of the cutoff have focused on cylindrical instruments due to their relative geometric simplicity. Here, the tonehole lattice cutoff frequency of conical instruments such as the saxophone is studied analytically, using a generalization of the framework developed for cylindrical resonators. First, a definition of local cutoff of a conical tonehole lattice is derived and used to design “acoustically regular” resonators with determinate cutoff frequencies. The study is then expanded to an acoustically irregular lattice: a saxophone resonator, of known input impedance and geometry. Because the lattices of real instruments are acoustically irregular, different methods of analysis are developed. These methods, derived from either acoustic (input impedance) or geometric (tonehole geometry) measurements, are used to determine the tonehole lattice cutoff frequency of conical resonators. Each method provides a slightly different estimation of the tonehole lattice cutoff for each fingering, and the range of cutoffs across the first register is interpreted as the acoustic irregularity of the lattice. It is shown that, in contrast with many other woodwind instruments, the cutoff frequency of a saxophone decreases significantly from the high to low notes of the first register.