In this study, we used a procedure called selective/divided rotation to investigate the role of dimensions in the perception of color. Ss performed either selective-attention or divided-attention tasks to paired dimensions created from each of 3 orientations of axes in color space: 0 degree, 22.5 degrees, and 45 degrees. We evaluated a Euclidean hypothesis, namely, that speeded classification of interacting dimensions is invariant to rigid rotation of stimulus axes. All experiments obtained evidence against this Euclidean hypothesis. Experiments 1 to 4 showed that selective attention was best at the orientation corresponding to saturation and brightness, suggesting primacy of these dimensions. The results were replicated with the pairs hue-saturation (Experiment 7) and hue-brightness (Experiment 8). We conclude that interacting dimensions can be primary and that dimensional primacy characterizes much of perceptual experience.