科研之友
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摘要
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.
- 出版日期2016-12
