Generation of vocal-tract shapes from formant frequencies

A microcomputer program has been developed to generate midsagittal vocal-tract shapes from the corresponding formant frequencies. The concept of formants is usually presented in textbooks and references for courses in the science of sound. The frequencies of these resonances are used to obtain the vocal-tract configurations for different vowel positions of the tongue. Ladefoged et al. [J. Acoust. Soc. Am. 64, 1027–1035 (1978)] have devised an algorithm that uses only the first three formant frequencies of vowels for generating vocal-tract shapes as seen on midsagittal x-ray diagrams. Ladefoged et al., gave a procedure for estimating the width of the vocal tract at different positions, but not the two-dimensional shape. In order to graph the midsagittal vocal tract shapes with a microcomputer having limited memory, an arbitrary, standardized, upper surface of the vocal tract was constructed. The equation of a catenary was used as a reference curve. A parametric form was found useful for generating graphs and relating path length to distance along the vocal tract.