Predicting vowel inventories: The dispersion-focalization theory revisited

Abstract

A revision of the dispersion-focalization theory (DFT) [Schwartz et al., J. Phonetics 25, 233–253 (1997)] is presented. Like DFT, the current computational model incorporates the center of gravity effect (COG) of 3.5-Bark spectral integration, but it deviates from DFT in that the COG contributes to the actual values and reliability weights of the perceived formants of vowels. The COG is reinterpreted as a domain of acceleration towards formant merger: the percepts of formants less than 3.5 Barks apart are perturbed towards one another in a nonlinear yet continuous fashion and their weights are increased, but perceptual merger and weight maximization occur only when the acoustic distance is about 2 Bark. Like other dispersion-based models, inventories are evaluated predominantly according to the least dispersed vowel pair, where dispersion is measured as the weighted Euclidean distance between the vowels coordinates (the first two perceived formants). Yet in the current model the weights are determined dynamically, in a well-principled manner. This model improves existing models in predicting certain universal traits, such as series of front rounded vowels in large vowel inventories, as emergent properties of certain local maxima of the inventory dispersion evaluation function, without sacrificing predictive adequacy for smaller inventories.