A Mathematical Model for Frequency Jumps in Phonation

Frequency jumps are a common phenomenon in voice production. They are perceived as discontinuities in voice pitch caused by smooth changes of physiological parameters, and may be observed in transitions between chest and falsetto vocal registers. Here, a recent model of birdsong production is used to model an oscillator source for the vocal folds coupled to an acoustic waveguide for the vocal tract, in terms of a delay differential equation. Numerical integration of the equation shows regions of coexistence of periodic solutions when the source-tract coupling is strong enough and the fundamental frequency is close to a resonance of the vocal tract. The coupling increases at larger subglottal pressures and smaller crosssectional area of the vocal tract. The results reproduce patterns of chest-falsetto transitions, as well as voice instabilities observed when singing into a tube with increasing pitch. Further, they match data obtained from a mechanical replica of the vocal folds attached to a waveguide of varying length. In general, these findings depart from the standard source-filter model of voice production, which regards the vocal tract as a mere filter to the glottal sound. The separation between the vocal source and tract holds as a valid approximation at low frequencies. However, source-tract interactions become relevant at higher frequencies, such as in cases of the singing voice and some animal vocalizations. The model may also find applications in the sound production in brass musical instruments, to describe interactions between the oscillating lips and the instrument’s tubing.