Acoustic characterization of the resonator in the Chinese transverse flute (dizi).

This article focuses on the linear acoustical behavior of the dizi, a traditional Chinese transverse flute distinguished by a hole covered with a wrinkled membrane. It presents a detailed acoustical model incorporating the dizi’s drilled toneholes, radially positioned back end-holes, membrane hole, and embouchure hole, using the transfer matrix method (TMM) and its extension with external interactions (TMMI) to predict input admittance. The study finds that TMMI more accurately models the dizi’s acoustics, particularly by accounting for mutual radiation effects among open holes, and that the membrane shifts resonance peaks to lower frequencies, reduces their magnitude, and generally improves harmonicity, though its influence varies with fingering and proximity to the membrane’s resonance frequency. Additionally, the analysis reveals that the upstream branch complicates cutoff frequency evaluation, suggesting it may be excluded to isolate tonehole lattice effects, which show distinct cutoff frequency groupings likely due to interactions between finger-hole and end-hole lattices. The modeling approach offers a scientific tool for instrument makers to assess tuning and design, with future work proposed on nonlinear membrane dynamics, improved radiation modeling, and sound synthesis applications.