This article presents an interface for navigating a musical parameter space. The entire combinatorial space of a ten-parameter synthesizer is laid out as a two-dimensional surface on a multi-touch screen. The surface can be scrolled and zoomed using touch-screen swipe and pinch gestures, reminiscent of a map application. The user can place markers on the surface to flag favorites and to explore regions of different sizes around these points. The mapping from the two-dimensional surface to the higher-dimensional parameter space uses a space-filling curve. Hilbert curves constructed from Gray codes with long bit runs can be used to preserve locality as much as is possible, while still maintaining access to all possibilities. A user study was performed to compare this parameter mapping with a more traditional one-slider-per-parameter interface. Questionnaire responses indicate that different mapping strategies suit different stages of the creative process. The combination of the two interfaces was deemed more useful than either individually, reinforcing the notion that a combination of divergent and convergent processes is important for creative tasks.