The relationship between the sensory signal of the photoreceptors on one hand and color appearance and language on the other hand is completely unclear. A recent finding established a surprisingly accurate correlation between focal colors, unique hues, and so-called singularities in the laws governing how sensory signals for different surfaces change across illuminations. This article examines how this correlation with singularities depends on reflectances, illuminants, and cone sensitivities. Results show that this correlation holds for a large range of illuminants and for a large range of sensors, including sensors that are fundamentally different from human photoreceptors. In contrast, the spectral characteristics of the reflectance spectra turned out to be the key factor that determines the correlation between focal colors, unique hues, and sensory singularities. These findings suggest that the origins of color appearance and color language may be found in particular characteristics of the reflectance spectra that correspond to focal colors and unique hues.