Tuned two-dimensional vocal tracts with piriform fossae for the finite element simulation of vowels

The piriform fossae are two small side branches of the vocal tract that are located close to the larynx. They act as quarter wave resonators and introduce two deep dips around 5 kHz in the voice spectrum. These two cavities acoustically interact, which produce a significant shift in the antiresonance frequencies. Three-dimensional (3D) models can naturally account for these effects but at the price of a high computational cost, whereas the most common alternative, the one-dimensional (1D) approaches, speed up simulations but cannot deal with this interaction. In this work, these two cavities are incorporated in 2D tuned vocal tracts of vowel sounds, which have shown to provide a good balance between computational costs and accuracy in the numerical simulation of vowels and diphthongs. The 2D tuning methodology is thus extended to mimic the acoustic behaviour of a 3D vocal tract of circular-cross sections that also has the two piriform fossae. This methodology consists in introducing proper modifications on the vocal tract shape, wall losses and glottal flow so as to tune the location, bandwidth and energy of the planar mode resonances of the main tract (formants in the speech community) and the antiresonances generated by the piriform fossae. The finite element method (FEM) is used to perform the 3D and 2D simulations. Results are also compared against a 1D approach based on the transfer matrix method (TMM).