An assessment of acoustic contrast between long and short vowels using convex hulls

An alternative to the spectral overlap assessment metric (SOAM), first introduced by Wassink [(2006). J. Acoust. Soc. Am. 119(4), 2334-2350], is introduced. The SOAM quantifies the intra- and inter-language differences between long-short vowel pairs through a comparison of spectral (F1, F2) and temporal properties modeled with best fit ellipses (F1 × F2 space) and ellipsoids (F1 × F2 × duration). However, the SOAM ellipses and ellipsoids rely on a Gaussian distribution of vowel data and a dense dataset, neither of which can be assumed in endangered languages or languages with limited available data. The method presented in this paper, called the Vowel Overlap Assessment with Convex Hulls (VOACH) method, improves upon the earlier metric through the use of best-fit convex shapes. The VOACH method reduces the incorporation of "empty" data into calculations of vowel space. Both methods are applied to Numu (Oregon Northern Paiute), an endangered language of the western United States. Calculations from the VOACH method suggest that Numu is a primary quantity language, a result that is well aligned with impressionistic analyses of spectral and durational data from the language and with observations by field researchers.