A fully quantitative, mathematical framework for the analysis of compensatory articulations is described. It is shown that the physics of speech production is best described by a spatial ‘‘potential function,’’ which, unlike cylindrical n‐tube approximations, accounts for dispersive wave phenomena in regions of rapidly varying cross section. It is demonstrated that many possible area functions, and hence articulatory configurations, correspond to a single potential function, and so it is claimed that the potential‐function descriptor is a both more accurate and more compact basis for the scientific investigation of phonetic systems. This work demonstrates that a 27‐vowel system may be simulated from just 8 binary, potential‐function parameters. The acoustic correlates of the individual ‘‘bits’’ are discussed, and it is found that they characterize the main vowel classes in a transparent way. Transformations from high to mid, and from mid to low, vowels are obtained, along with those involving the tense–lax and round–unround dimensions. It is shown that vocal‐tract area functions familiar from the literature can be deterministically recovered from the 8‐bit strings, although many others are also possible. It is claimed that the potential‐function vocal‐tract model has uniquely abstract and compact properties, and is suitable for development as a full phonological representation.