RESUMO
A hyperbolic grid-generation algorithm allows investigation of the effect of vocal-tract curvature on low-order formants. A smooth two-dimensional (2D) curve represents the combined lower lip, tongue, and anterior pharyngeal wall profile as displacements from the combined upper lip, palate, and posterior pharyngeal wall outline. The algorithm is able to generate tongue displacements beyond the local radius of strongly curved sections of the palate. The 2D grid, along with transverse profiles of the lip, oral-pharyngeal, and epilarynx regions, specifies a vocal conduit from which an effective area function may be determined using corrections to acoustic parameters resulting from duct curvature; the effective area function in turn determines formant frequencies through an acoustic transmission-line calculation. Results of the corrected transmission line are compared with a three-dimensional finite element model. The observed effects of the curved vocal tract on formants F1 and F2 are in order of importance, as follows: (1) reduction in midline distances owing to curvature of the palate and the bend joining the palate to the pharynx, (2) the curvature correction to areas and section lengths, and (3) adjustments to the palate-tongue distance required to produce smooth tongue shapes at large displacements from the palate.