Vibration patterns and reed - pipe coupling in the free reeds of the hulusi

Abstract

The hulusi is a free-reed instrument from Yunnan, Western China, known for its unique sound. Its reed and frame are cut from a single brass sheet in a symmetric shape, the free end narrower than the clamped end. Its free reeds are coupled to tubes that determine the instrument's pitch during normal playing. With reduced playing pressure, the reed frequency takes over the instrument sound. We report point-by-point laser Doppler vibrometry on the reeds of six handmade hulusi, two each in the keys of F, B$\flat$ and C, measured at 29 points on every reed or tongue over nine fingerings and two supply pressures. Steady-state spectra carry two components: a tube-dominant frequency $f_\mathrm{tube}$, locked to the air-column resonance and carrying a complete harmonic series, and a reed-dominant frequency $f_\mathrm{reed}$, which is not an integer multiple of it. Their difference $Δ= f_\mathrm{tube} - f_\mathrm{reed}$ runs from 38 to 523~Hz across the dataset, from about three semitones to more than an octave. The reed-dominant frequency rises with the pressure at the reed, by $28.0 \pm 10.3$ Hz/kPa once $f_\mathrm{tube}$ is controlled for. At low pressure supply the oscillation loses its lock to the air column, falls silent for about 100~ms, and returns at the reed frequency within 0.1 Hz. The spatial patterns are forced oscillation shapes of one limit cycle at its fundamental and harmonics rather than eigenmodes: the measured frequencies stand in strict 1:2:3 ratios, far from the bending ratios of a cantilever. The reed-dominant pattern is pure bending and holds across fingerings and supply pressures, whereas the tube-dominant pattern breaks up near the oscillation threshold.