Vocal tract effects in wind instrument regeneration

Abstract

Wind players are much concerned with vocal tract influences on tone production. Laboratory study has been inconclusive, in part from inadequate theoretical formulation. A reed valve is opened and closed by the pressure difference (pm − pM) across it: pm in the instrument's mouthpiece, pM in the player's mouth. The reed transconductance A = ∂u/∂(pm − pM) depends on its natural frequency ωr, and its damping, becoming large near ωr. The condition for oscillation is A[(Zm + ZM)//Zr] ⩾ 1. We note that the reed impedance Zr is paralleled by the sum of Zm and ZM. Oscillation requires Im(Zm + ZM) ≠ 0, with sign depending on the low-frequency sign of A (positive for woodwinds, negative for brasses); whence woodwinds play with ω ⩽ ωr, brasses with ω ⩾ ωr. These results extend to large amplitude (mode-coupled) regimes of oscillation in the familiar way. Available data show resonance bandwidths of ZM are much larger than those of ZM (with smaller magnitude fluctuations), explaining the difficulty of direct measurement of musical effects. During tonal startup on long instruments (e.g., horn tuba), Zm changes as successive reflections build up the standing wave. By itself Zm does not generally satisfy the regeneration condition during onset, thus giving a crucial role to the vocal tract. Results of experiments in progress will be presented. [Work supported by NSF.]