Analysis of the tonehole lattice of the northern xiao flute

Abstract

The northern Chinese xiao is an end-blown flute characterized by an array of two to three pairs of holes that separate the main bore from an extended foot. The top pair are tuning holes and the lower ones are described as vent holes, but the design of the latter have shown an influence in the attainability of the third octave as well as the timbre of the notes (G. Ellis, personal communication, 3 March 2014). We analyze these holes in the context of an infinite lattice with a cutoff frequency fc determined by the geometry and spacing of the top holes, and compare the results to that of the pole frequency of the calculated impedance of the actual, irregular lattice below the tuning holes. The input impedance of a cylindrical pipe with a tonehole lattice is calculated, and pressure standing waves are predicted for the peaks of the resulting admittance spectra. The standing waves are compared to experimental results to confirm the high-pass filter properties of the lattice above fc. The effects of varying lattice dimensions on fc and the alignment of upper harmonics with peaks in the spectra will be presented.

Deep Development of Yuping Flute Products and Development of Xiao Flute Culture

“…The discussion is of great practical significance. Two, the necessity of speeding up the deep development of the Shaxiao flute in Yuping [1] …”