Secant lines in a preliminary study of phonetic reduction of /I/ and /epsilon/

Two subjects from the X-Ray Microbeam Speech Production Database were examined in their production of the vowels /I/ and /epsilon/ in alveolar and dental consonant contexts. Secant lines, or first-order splines, between the three most anterior pellets were examined at vowel critical times. These critical times were zero crossings in the tangential acceleration of the midpoints of the secant lines. We expected and found, in general, that vowel reduction occurred as a function of vowel duration in measures of the secant line midpoint-to-palate distance and secant line orientation at vowel critical times. The shorter the vowel, the smaller the distance of the secant line midpoints to the palate and the less downward the orientation of the secant lines at the vowel critical times. Phonetic reduction was also apparent in the formant frequencies. There were differences between the speakers in terms of the range of vowel duration and degree of reduction. The subjects differed in the functional parts of the tongue spanned by the secant lines and the shape of their palates. These differences were factors in the observed relations between formant frequencies and the articulatory, secant line measures for each subject.