The timbre space of the Chinese membrane flute (dizi): Physical basis and psychoacoustical effects

Abstract

The Chinese membrane flute (dizi) has a membrane covering a hole in the wall of the instrument between the mouth hole and the uppermost finger-hole. The membrane is driven by the acoustic pressure in the pipe, producing rich harmonics through its nonlinearity. The dizi timbre is multidimensional and varies with pitch. Inhomogeneity of the dizi timbre is well known by musicians. It reflects a general aesthetic tendency in traditional Chinese music that a skillful musician should produce a variety of timbre with a solo instrument. The major spectral features of dizi tones, i.e., (1) formants, (2) the predominance of odd harmonics, and (3) harmonic-to-subharmonics ratio at high frequencies, can be explained by a Duffing oscillator model of the membrane. They constitute the three dimensions of the dizi timbre space, where the ‘‘trajectory’’ of the changing timbre of a dizi melody is embedded. Psychoacoustical effects associated with them are discussed, including (1) spatial effects due to abrupt brightness changes, (2) multi-pitch effect due to the predominance of upper odd harmonics, and (3) roughness induced by subharmonics.