Figure 2.

The physical properties of a given phonological unit vary considerably depending on its context (e.g., Kent & Minifie, 1977; Liberman, Cooper, Shankweiler, & Studdert-Kennedy, 1967; Öhman, 1966). Much of this context dependence emerges lawfully from the use of task dynamics. An example of this kind of context dependence in lip closure gestures can be seen in the fact that the three independent articulators that can contribute to closing the lips (upper lip, lower lip, and jaw) do so to different extents as a function of the vowel environment in which the lip closure is produced (Macchi, 1988; Sussman, MacNeilage, & Hanson, 1973). The value of lip aperture achieved, however, remains relatively invariant no matter what the vowel context. In the task-dynamic model, the articulator variation results automatically from the fact that the lip closure gesture is modeled as a coordinative structure that links the movements of the three articulators in achieving the lip closure task. The gesture is specified invariantly in terms of the tract variable of lip aperture, but the closing action is distributed across component articulators in a context-dependent way. For example, in an utterance like [ibi], the lip closure is produced concurrently with the tongue gesture for a high front vowel. This vowel gesture will tend to raise the jaw, and thus, less activity of the upper and lower lips will be required to effect the lip closure goal than in an utterance like [aba]. These microscopic variations emerge lawfully from the task dynamic specification of the gestures, combined with the fact of overlap (Kelso, Saltzman, & Tuller, 1986; Saltzman & Munhall, 1989).

Gestural Structures

During the act of talking, more than one gesture is activated, sometimes sequentially and sometimes in an overlapping fashion. Recurrent patterns of gestures are considered to be organized into gestural constellations. In the computational model (see Figure 1), the linguistic gestural model determines the relevant constellations for any arbitrary input utterance, including the phasing of the gestures. That is, a constellation of gestures is a set of gestures that are coordinated with one another by means of phasing, where for this purpose (and this purpose only), the dynamical regime for each gesture is treated as if it were a cycle of an undamped system with the same stiffness as the actual regime. In this way, any characteristic point in the motion of the system can be identified with a phase of this virtual cycle. For example, the movement onset of a gesture is at phase 0 degrees, while the achievement of the constriction goal (the point at which the critically damped system gets sufficiently close to the equilibrium position) occurs at phase 240 degrees. Pairs of gestures are coordinated by specifying the phases of the two gestures that are synchronous. For example, two gestures could be phased so that their movement onsets are synchronous (0 degrees phased to 0 degrees), or so that the movement onset of one is phased to the goal achievement of another (0 degrees phased to 240 degrees), etc. Generalizations that characterize some phase relations in the gestural constellations of English words are proposed in Browman and Goldstein (1990c). As is the case for the values of the dynamic parameters, values of the synchronized phases also appear to cluster in narrow ranges, with onset of movement (0 degrees) and achievement of goal (240 degrees) being the most common (Browman & Goldstein, 1990a).

An example of a gestural constellation (for the word “pawn” as pronounced with the back unrounded vowel characteristic of much of the U.S.) is shown in Figure 3a, which gives an idea of the kind of information contained in the gestural dictionary. Each row, or tier, shows the gestures that control the distinct articulator sets: velum, tongue tip, tongue body, lips, and glottis. The gestures are represented here by descriptors, each of which stands for a numerical equilibrium position value assigned to a tract variable. In the case of the oral gestures, there are two descriptors, one for each of the paired tract variables. For example, for the tongue tip gesture labeled {clo alv}, {clo} stands for -3.5 mm (negative value indicates compression of the surfaces), and {alv} stands for 56 degrees (where 90 degrees is vertical and would correspond to a midpalatal constriction). The association lines connect gestures that are phased with respect to one another. For example, the tongue tip {clo alv} gesture and the velum {wide} gesture (for nasalization) are phased such that the point indicating 0 degrees–onset of movement–of the tongue tip closure gesture is synchronized with the point indicating 240 degrees–achievement of goal–of the velic gesture.

Each gesture is assumed to be active for a fixed proportion of its virtual cycle (the proportion is different for consonant and vowel gestures). The linguistic gestural model uses this proportion, along with the stiffness of each gesture and the phase relations among the gestures, to calculate a gestural score that specifies the temporal activation intervals for each gesture in an utterance. One form of this gestural score for “pawn” is shown in Figure 3b, with the horizontal extent of each box indicating its activation interval, and the lines between boxes indicating which gesture is phased with respect to which other gesture(s), as before. Note that there is substantial overlap among the gestures. This kind of overlap can result in certain types of context dependence in the articulatory trajectories of the invariantly specified gestures. In addition, overlap can cause the kinds of acoustic variation that have been traditionally described as allophonic variation. For example in this case, note the substantial overlap between the velic lowering gesture (velum {wide}) and the gesture for the vowel (tongue body {narrow pharyngeal}). This will result in an interval of time during which the velo-pharyngeal port is open and the vocal tract is in position for the vowel–that is, a nasalized vowel. Traditionally, the fact of nasalization has been represented by a rule that changes an oral vowel into a nasalized one before a (final) nasal consonant. But viewed in terms of gestural constellations, this nasalization is just the lawful consequence of how the individual gestures are coordinated. The vowel gesture itself hasn’t changed in any way: it has the same specification in this word and in the word “pawed” (which is not nasalized).