We design and implement a comprehensive study of the perception of gloss. This is the largest study of its kind to date, and the first to use real material measurements. In addition, we develop a novel multi-dimensional scaling (MDS) algorithm for analyzing pairwise comparisons. The data from the psychophysics study and the MDS algorithm is used to construct a low dimensional perceptual embedding of these bidirectional reflectance distribution functions (BRDFs). The embedding is validated by correlating it with nine gloss dimensions, fitted parameters of seven analytical BRDF models, and a perceptual parameterization of Ward's model. We also introduce a novel perceptual interpolation scheme that uses the embedding to provide the user with an intuitive interface for navigating the space of gloss and constructing new materials.