Time-domain simulation of harmonica pitch bending and overblowing

A physical model for sound production in the harmonica is proposed that is capable of pitch bending, and tested against experimental measurements on a real instrument. The model couples reed vibrations, airflow through the reed openings, and the acoustic resonance on the mouth side of a harmonica hole. By using one of three cylindrical tubes with different diameters as a resonator, time-domain simulations are conducted while the tube length is varied. The simulations successfully reproduce blow bending at hole 7 of a 10-hole diatonic harmonica, draw bending at hole 4, and overblowing at hole 6. The blow-bending simulation closely matches the experimental results obtained under the same conditions. Using a small-amplitude approximation, the conditions for self-excitation are derived, and the frequencies satisfying these conditions are calculated. The frequencies obtained experimentally, those from simulation, and those predicted by the theoretical analysis-each depending on tube diameter and length-show good agreement. A detailed examination of the sounding conditions further explains that, in the bending simulation, the sound frequency changes continuously with tube length, whereas in the overblow simulation, normal blowing is suddenly transformed into overblowing after a brief silent interval.