Two cross-linguistic factors underlying tongue shapes for vowels.
Desirable characteristics of a vocal-tract parametrization include accuracy, low dimensionality, and generalizability across speakers and languages. A low-dimensional, speaker-independent linear parametrization of vowel tongue shapes can be obtained using the PARAFAC three-mode factor analysis procedure [Harshman et al., J. Acoust. Soc. Am. 62, 693-707 (1977)]. Harshman et al. applied PARAFAC to midsagittal x-ray vowel data from five English speakers, reporting that two speaker-independent factors are required to accurately represent the tongue shape measured along anatomically normalized vocal-tract diameter grid lines. Subsequently, the cross-linguistic generality of this parametrization was brought into question by the application of PARAFAC to Icelandic vowel data, where three nonorthogonal factors were reported [Jackson, J. Acoust. Soc. Am. 84, 124-143 (1988)]. This solution is shown to be degenerate; a reanalysis of Jackson's Icelandic data produces two factors that match Harshman et al.'s factors for English vowels, contradicting Jackson's distinction between English and Icelandic language-specific "articulatory primes". To obtain vowel factors not constrained by artificial measurement grid lines, x-ray tongue shape traces of six English speakers were marked with 13 equally spaced points. PARAFAC analysis of this unconstrained (x,y) coordinate data results in two factors that are clearly interpretable in terms of the traditional vowel quality dimensions front/back, high/low.