Editing Phonetics (section)

===Articulatory models===
When producing speech, the articulators move through and contact particular locations in space resulting in changes to the acoustic signal. Some models of speech production take this as the basis for modeling articulation in a coordinate system that may be internal to the body (intrinsic) or external (extrinsic). Intrinsic coordinate systems model the movement of articulators as positions and angles of joints in the body. Intrinsic coordinate models of the jaw often use two to three degrees of freedom representing translation and rotation. These face issues with modeling the tongue which, unlike joints of the jaw and arms, is a [[muscular hydrostat]]—like an elephant trunk—which lacks joints.{{sfn|Löfqvist|2010|p=359}} Because of the different physiological structures, movement paths of the jaw are relatively straight lines during speech and mastication, while movements of the tongue follow curves.{{sfn|Munhall|Ostry|Flanagan|1991|p=299|ps=, ''et seq.''}}

Straight-line movements have been used to argue articulations as planned in extrinsic rather than intrinsic space, though extrinsic coordinate systems also include acoustic coordinate spaces, not just physical coordinate spaces.{{sfn|Löfqvist|2010|p=359}} Models that assume movements are planned in extrinsic space run into an [[inverse problem]] of explaining the muscle and joint locations which produce the observed path or acoustic signal. The arm, for example, has seven degrees of freedom and 22 muscles, so multiple different joint and muscle configurations can lead to the same final position. For models of planning in extrinsic acoustic space, the same one-to-many mapping problem applies as well, with no unique mapping from physical or acoustic targets to the muscle movements required to achieve them. Concerns about the inverse problem may be exaggerated, however, as speech is a highly learned skill using neurological structures which evolved for the purpose.{{sfn|Löfqvist|2010|p=360}}

<!-- See Bizzi et al. 1992 on equilibrium-point model -->
The equilibrium-point model proposes a resolution to the inverse problem by arguing that movement targets be represented as the position of the muscle pairs acting on a joint.{{efn|See {{harvtxt|Feldman|1966}} for the original proposal.}} Importantly, muscles are modeled as springs, and the target is the equilibrium point for the modeled spring-mass system. By using springs, the equilibrium point model can easily account for compensation and response when movements are disrupted. They are considered a coordinate model because they assume that these muscle positions are represented as points in space, equilibrium points, where the spring-like action of the muscles converges.{{sfn|Bizzi|Hogan|Mussa-Ivaldi|Giszter|1992}}{{sfn|Löfqvist|2010|p=361}}

Gestural approaches to speech production propose that articulations are represented as movement patterns rather than particular coordinates to hit. The minimal unit is a gesture that represents a group of "functionally equivalent articulatory movement patterns that are actively controlled with reference to a given speech-relevant goal (e.g., a bilabial closure)."{{sfn|Saltzman|Munhall|1989}} These groups represent coordinative structures or "synergies" which view movements not as individual muscle movements but as task-dependent groupings of muscles which work together as a single unit.{{sfn|Mattingly|1990}}{{sfn|Löfqvist|2010|pp=362–4}} This reduces the degrees of freedom in articulation planning, a problem especially in intrinsic coordinate models, which allows for any movement that achieves the speech goal, rather than encoding the particular movements in the abstract representation. Coarticulation is well described by gestural models as the articulations at faster speech rates can be explained as composites of the independent gestures at slower speech rates.{{sfn|Löfqvist|2010|p=364}}