Time-domain simulation of harmonica pitch bending

Harmonica playing involves a technique known as bending, in which the pitch of a note is lowered by altering the shape of the player’s mouth (vocal tract). Johnston [Acoustics Australia 15(3), 69–75 (1987)] experimentally reproduced pitch bending using a variable-length cylinder as a substitute for the vocal tract and theoretically showed that vocal tract resonance causes pitch bending, based on a small-amplitude approximation. More recently, Okada et al. [Tech. Rep. Musical Acoustics 42(5), 17–22 (2023) (in Japanese)] replicated the experiment using cylinders of various diameters. This study proposes a physical model of harmonica sound production that incorporates both the self-excitation mechanism of the free reed and acoustic resonance on the oral cavity side. Time-domain simulations based on this model successfully reproduce pitch bends closely resembling those observed experimentally. The proposed model provides a clear physical explanation for the pitch-bending phenomenon in harmonica playing. To demonstrate the model's potential for practical applications, synthetic sounds are generated that simulate a player bending the pitch while drawing or blowing, and then returning it to the original pitch.