Note that CRI (Colour Rendering Index) is a bit bogus. It came about when florescent lights became a thing and was originally based on a sheet of printed colour swatches. RGB LED lighting promoters have pointed out that CRI doesn't really reflect the goodness of light sources other than florescent in practice.
I'd say CRI is a bit bogus in that a light source can have fairly high CRI and still look bad. For example, I've seen LEDs used in a flashlight with a CRI over 90 that had a significant green tint.
On the other hand, I have not seen a light source with low CRI that looked good illuminating people, natural materials, or anything else where subtle differences in color are relevant.
There are several other ways color rendering can be measured, but the ones used in the lighting industry tend to be based on comparing the rendering of specific samples much like CRI. One that's seeing a lot of use lately is IES TM-30, which is based on a much larger number of samples and includes a measurement of color gamut as well as fidelity.
