Input impedance of sheng pipes augmented with resonators

Abstract

The sheng is a free reed mouth organ constructed of bamboo pipes with a free reed in each pipe near one end. A version commonly available today has 17 pipes in a circular arrangement with the reeds enclosed in a wind chamber. The pipes are nearly cylindrical over a significant portion of their length, but the bore near the reed end becomes approximately conical. A traditional instrument of China, the sheng, has a long recorded history, but a number of enlarged and modernized versions were created in the twentieth century, some featuring keys and additional pipes. The sheng in the current study is a standard 17-pipe configuration, with cylindrical metal pipe resonators attached to most of the pipes. These resonators amplify the radiated sound and also alter the tone quality. Calculations of input impedance have been made for the pipes, with and without the resonators attached, taking into account the position of the reed along the pipe, tuning slots, finger holes, and non-circular pipe cross sections. These calculations are compared with the measured pipe impedances as well as the measured sounding frequencies and sound spectra. [Research supported by NSF REU grant PHY-1004860.]