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.
Highlights
Woodwind instruments such as the clarinet and saxophone have resonators that are composed of an acoustical duct for which the downstream section has a lattice of toneholes that can be opened and closed to change the playing frequency of the instrument
For a real instrument of finite length, the tonehole lattice cutoff frequency separates these two bands, no definition is universally agreed upon and a precise definition does not exist because the toneholes do not constitute a perfectly periodic lattice
The tonehole lattice cutoff frequency has been studied for various instruments, the clarinet, but relatively little application to the saxophone exists in the literature [1, 2]
Summary
Woodwind instruments such as the clarinet and saxophone have resonators that are composed of an acoustical duct for which the downstream section has a lattice of toneholes that can be opened and closed to change the playing frequency of the instrument. The global cutoff frequency is a global property of a lattice for which each element has exactly the same natural frequency, in which case fcG 1⁄4 fcT 1⁄4 fcP It is only strictly valid for an infinite, lossless lattice, but it is a good approximation for a tonehole network with at least three open toneholes and is used for finite lattices in this article. For conical resonators, which cannot be geometrically regular due to the taper of the main bore’s internal radius, a lattice can be periodic following the interpretation of acoustical periodicity While these derivations are only strictly valid for an infinite, lossless lattice, the theory works well for lattices with as few as three toneholes.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
