From time domain simulation of diatonic harmonica, proposal of a minimal free reed model

Abstract

Chromatical playing on diatonic harmonica can be explained and reproduced using a temporal model. This model features a nonlinear vocal track, two free reeds and interaction of these three elements. The agreement between numerical simulations and experiment will be illustrated. From these results, and considering the sinusoidal reed motion during normal playing, a minimal description of free reed will be proposed. The equivalent reed oscillator will be derived from comparisons between quasistatic and modal description of the reed displacement; it will be shown that the modal description is a good choice. Then, a sufficient description of the flow through each reed will be built. Waveforms and related sounds will be presented for each tested assumption and will illustrate the fact that this flow must rely on the local reed displacement. Application of this model will be discussed in the case of other free reed instruments.