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Human beings are thought to be unique amongst the primates in their capacity to produce rapid changes in the shape of their vocal tracts during speech production. Acoustically, vocal tracts act as resonance chambers, whose geometry determines the position and bandwidth of the formants. Formants provide the acoustic basis for vowels, which enable speakers to refer to external events and to produce other kinds of meaningful communication. Formant-based referential communication is also present in non-human primates, most prominently in Diana monkey alarm calls. Previous work has suggested that the acoustic structure of these calls is the product of a non-uniform vocal tract capable of some degree of articulation. In this study we test this hypothesis by providing morphological measurements of the vocal tract of three adult Diana monkeys, using both radiography and dissection. We use these data to generate a vocal tract computational model capable of simulating the formant structures produced by wild individuals. The model performed best when it combined a non-uniform vocal tract consisting of three different tubes with a number of articulatory manoeuvres. We discuss the implications of these findings for evolutionary theories of human and non-human vocal production.