Models for the formant-frequency contours of vowels in CVC′ context are presented and illustrated with an American English database comprising isolated syllables with C, C′=/b,d,g/ and V=/i,i,q,æ,a,c,U,u,v,W/. Both established and reinterpreted regularities among context effects are cast in a series of successively elaborated mathematical models. The first model (model I), in common with all its successors, embodies the notion of the superposition of CV and VC′ transitions, according to which a formant trajectory FCVC′(n) is modeled as fCV(n)+TV+gVC′(n), where n is duration-normalized time, TV is a vowel target, and fCV(n) and gVC′(n) are initial- and final-consonant transition functions. The rms errors for F1, F2, and F3 (30, 89, and 111 Hz) against independent test data are near the minimum theoretical values (32, 69, and 100 Hz) predicted from interrepetition variation and its contribution to uncertainty in the model elements. Subsequently, the elements of the additive model are individually characterized by further incorporating per-consonant transition shape similarity (model II), target-locus scaling (model III), exponential transition shapes (model IVa), and exponential duration dependence (model IVb).
In model II, the CV and VC′ trajectories are respectively defined as L+k f*(n) and L′+k′g*(n), with contour shape functions f* and g*, scale factors k and k′, and consonant loci L and L′. The loci are herein defined as baselines about which families of formant transitions are scaled. This model fits the data nearly as well as theory allows, except for F2 of C/i/C′ and C/ud/. Then, in model III, the scale factors k and k′ are represented by forms proportional to the target-locus distances T−L and T−L′. The vowel target T is then redefined to best fit these forms. The target-locus scaling hypothesis fares quite well except for F2 of CV sequences. In model IVa, the shape functions f* and g* are fit to exponentials with asymptotes associated with the vowel targets. Target-locus scaling is a corollary of this vowel target definition. Finally, in model IVb, the exponential model is redefined on a recovered real-time scale. The resulting context effect follows Lindblom’s [J. Acoust. Soc. Am. 35, 1773–1781 (1963)] in decaying exponentially with vowel duration.