I will first discuss the importance of an inner product on the space of spectra. Since “Cohen's Matrix R” depends on this inner product for its definition, the choice of inner product affects the structure of fundamental space (and thus color space) in a nontrivial way. The choice has to be made on considerations of physics and physiology. Usually this goes unnoticed and a choice is made implicitly. With the metric of the inner product one proceeds to construct a distortion free color space that reflects the metric of the space of spectra veridically.Next I will discuss the structure of the Schroedinger object color solid. Although Ostwald's original constructions are attractive because firmly founded on colorimetric principles (whereas e.g., Munsell's atlas is not based on colorimetry but on “eye measure”), they are marred by a number of unfortunate flaws: Not all object colors can be represented, the structure depends on the spectrum (not just the color) of the illuminant, and the “Principle of Internal Symmetry” used to mensurate the color circle is flawed because the locus of “full colors” is not a planar, but a twisted space curve. I show how to amend these flaws in a principled manner.When Ostwald's mensuration of the color circle (which result from purely colorimetric calculations) is compared to eye measure results (e.g., Munsell's) I find that (perhaps surprisingly, because colorimetry concerns only judgments of equality) they correspond closely.