UBC Theses and Dissertations
Acoustics of the xiao : a case study of modern methods for the design of woodwind instruments Lan, Yang
The xiao is a Chinese end-blown flute with a history over a thousand years and well known in China for its elegant sound. The xiao is little known outside China, but its close relative, the Japanese shakuhachi, is better known internationally. The xiao has not been well developed or standardized (because of the bamboo's varying geometries) for the contemporary musical requirements and is imperfect in tuning, tone range, tonal stability and playability of high notes. In acoustics, all these imperfections can be characterized by the acoustical impedance. As an air-reed instrument, the xiao plays at its input impedance minima. In the work reported in this thesis, the xiao was modelled by a modified transmission-matrix method, and an impedance tube was built for measuring the xiao's acoustical impedance to validate the model (accurate to a few cents). Then player effects were taken into account by an empirical formula, and the model was able to predict the playing frequencies of a xiao with any tone hole positions, sizes, and arbitrary bore shape along the symmetry axis. Based on this model, numerical optimizations were applied to improve the xiao, and a set of optimal fingerings for the xiao were obtained systematically. Several xiaos made from PVC pipes with optimized tone holes show good tuning over three octaves. A xiao with additionally optimized bore shape was machined out of acrylic, showing improved tonal stability and rich harmonics.
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