Dispersion Theory [DT; Liljencrants and Lindblom (1972). Language 12(1), 839-862] claims that acoustically dispersed vowel inventories should be typologically common. Dispersion is often quantified using triangle area between three mean vowel formant points. This approach is problematic; it ignores distributions, which affect speech perception [Clayards, Tanenhaus, Aslin, and Jacobs (2008). Cognition 108, 804-809]. This letter proposes a revised metric for calculating dispersion which incorporates covariance. As a test case, modeled vocal tract articulatory-acoustic data of stop consonants [Schwartz, Boe, Badin, and Sawallis (2012). J. Phonetics 40, 20-36] are examined. Although the revised metric does not recover DT predictions for stop inventories, it changes results, showing that dispersion results depend on metric choice, which is often overlooked. The metric can be used in any acoustic space to include information about within-category variation when calculating dispersion.
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Many thanks to Schwartz et al. (2012) for providing the data for use in this project and helpful commentary. Thanks are also due to Kristine Yu, John Kingston, UMass Sound Workshop, Robert Staubs, Joe Pater, and audiences at the ASA 2017 Boston meeting. The author is supported by the National Science Foundation Graduate Research Fellowship under Grant No. 1451512. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.