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Acoustic Modeling and Optimization of the Xiao

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Flutes exist in varying forms around the world and play important roles in many musical cultures. Despite their long history, many flutes remain imperfect in tuning, tone range, and high note playability. All these imperfections can be described and solved by studying the acoustical impedance. This paper reports such a case study on the xiao, the Chinese end-blown flute. The xiao was modeled by the transmission-matrix method. The model was verified by impedance measurements to be accurate within a few cents. Then the model was used to predict the playing frequencies of a xiao with arbitrary tone hole positions and sizes, and bore diameter. Numerical optimizations were made to improve the xiao and a routine was devised to obtain a set of optimal fingerings. Several xiaos made from PVC pipes of uniform bore with optimized tone holes show good tuning over three octaves (deviations of all notes within 20 cents). A xiao with optimized bore shape was machined out of acrylic, showing further improved tuning, high notes playability and rich harmonics. The model and optimization methods can also be used to improve many other wind instruments.
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Document Type: Research Article

Publication date: November 1, 2016

More about this publication?
  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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