A new metric for calculating acoustic dispersion in stop inventories

Abstract

Dispersion Theory (DT; Liljencrants and Lindblom, 1972) claims that acoustically dispersed vowel inventories should be typologically common. Literature on DT has focused on vowels, where the predictions are robust, and less work has been done on consonants. This paper uses vocal tract model data of stops (as in Schwartz et al. 2012) to extend the predictions of DT to consonants, revealing problems with the conventional method of calculating dispersion. Dispersion is often quantified using triangle area between three category means as points in acoustic space. This approach ignores distributions and reduces entire acoustic categories (which have large variances and different distribution shapes) to single points. Within-category variance is a factor in DT (Lindblom, 1986) and experimental data shows that it affects perception (Clayards 2008), yet conventional dispersion metrics do not take it into account. Here, a new metric based on the Jeffries-Matusita distance is proposed and compared with the more conventional mean to mean distance approach. The incorporation of covariance better reflects human perception, which has implications for considering dispersion in any acoustic space. Nevertheless, this does not recover the predictions of DT, suggesting DT does not apply to consonants and vowels in the same way.