A geometric representation of spectral and temporal vowel features: quantification of vowel overlap in three linguistic varieties

A geometrical method for computing overlap between vowel distributions, the spectral overlap assessment metric (SOAM), is applied to an investigation of spectral (F1, F2) and temporal (duration) relations in three different types of systems: one claimed to exhibit primary quality (American English), one primary quantity (Jamaican Creole), and one about which no claims have been made (Jamaican English). Shapes, orientations, and proximities of pairs of vowel distributions involved in phonological oppositions are modeled using best-fit ellipses (in F1 x F2 space) and ellipsoids (F1 x F2 x duration). Overlap fractions computed for each pair suggest that spectral and temporal features interact differently in the three varieties and oppositions. Under a two-dimensional analysis, two of three American English oppositions show no overlap; the third shows partial overlap. All Jamaican Creole oppositions exhibit complete overlap when F1 and F2 alone are modeled, but no or partial overlap with incorporation of a factor for duration. Jamaican English three-dimensional overlap fractions resemble two-dimensional results for American English. A multidimensional analysis tool such as SOAM appears to provide a more objective basis for simultaneously investigating spectral and temporal relations within vowel systems. Normalization methods and the SOAM method are described in an extended appendix.