Typological data shows a tendency for languages to exhibit harmonic (i.e. consistent) ordering between heads and dependents. However, some categories seem to contradict this tendency. Here we investigate one such case, the order of the noun with respect to two dependents—adjectives, which tend to follow the noun and genitives which precede. We report two silent gesture experiments examining (i) whether there are cognitive biases favouring postnominal adjective and prenominal genitive order in a single trial judgement task, and (ii) if those preferences continue to influence order when participants learn a complete word order system. Our results shed light on how biases for individual categories of elements interact with biases that affect the wider linguistic system. While participants strongly prefer postnominal adjectives and prenominal genitives when these are judged in isolation, when they learn a system of ordering, these biases are obscured and (at least in some cases) harmony emerges