Both surface color and imaging industries strive for minimum color inconstancy in the materials they produce, while trying to match as many colors as possible. In this context the aim of this paper is to look at the relationship between color inconstancy properties of surface colors and their relationship to their chromas - specifically with the intention of understanding whether the two are opposed. Following the generation of spectra that match a sampling of the gamut of all possible surface colors it is shown clearly that the two properties are indeed inter-related and that highly chromatic colors cannot be color constant. Finally, the results of this work are proposed as a basis for setting color inconstancy targets and for having realistic expectations in terms of this property.