This paper outlines a theoretical framework for creative technology based on two contrasting processes: divergent exploration and convergent optimisation. We claim that these two cases require different gesture-to-parameter mapping properties. Results are presented from a user experiment that motivates this theory. The experiment was conducted using a publicly available iPad app: “Sonic Zoom”. Participants were encouraged to conduct an open ended exploration of synthesis timbre using a combination of two different interfaces. The first was a standard interface with ten sliders, hypothesised to be suited to the “convergent” stage of creation. The second was a mapping of the entire 10-D combinatorial space to a 2-D surface using a space filling curve. This novel interface was intended to support the “divergent” aspect of creativity. The paths of around 250 users through both 2-D and 10-D space were logged and analysed. Both the interaction data and questionnaire results show that the different interfaces tended to be used for different aspects of sound creation, and a combination of these two navigation styles was deemed to be more useful than either individually. The study indicates that the predictable, separate parameters found in most music technology are more appropriate for convergent tasks.