Specifying surface reflectances in a simple and perceptually informative way would be beneficial for many areas of research and application. We assessed whether a 3×3 matrix may be used to approximate how a surface reflectance modulates the sensory color signal across illuminants. We tested whether observers could discriminate between the model's approximate and accurate spectral renderings of hyperspectral images under narrowband and naturalistic, broadband illuminants for eight hue directions. Discriminating the approximate from the spectral rendering was possible with narrowband, but almost never with broadband illuminants. These results suggest that our model specifies the sensory information of reflectances across naturalistic illuminants with high fidelity, and with lower computational cost than spectral rendering.