Relating articulation and acoustics through a sinusoidal description of vocal tract shape

Abstract

A description of vocal tract shape for vowels is given in terms of a weighted sum of two sinusoids, displaced from each other along the length of the tract. The impetus for the description comes from uncovering a particularly simple relationship between F2 and a function on the parameters of a model of articulatory data. When the statistically derived articulatory model is simplified as displaced sinusoids, the relationship can be easily understood in terms of the physics of acoustic tubes. Thus, while the description is based on articulatory data, it relates simply to acoustics. The function (the sum of the weights of the two sinusoids) creates sets of articulatory shapes that can be said to trade in the amount of tongue front raising and the amount of tongue back raising to produce a constant F2. Alternatively, these equivalence classes of shapes can be said to trade in place of articulation and amount of constriction: this is so despite the fact that neither of these two variables are explicit parameters in generating the shapes. In embodying this compensatory property, it is also a description that is consistent with theories of motor control based on specifying functional equivalence classes, which are controlled with few degrees of freedom and allow context-conditioned variability.