I'd say they're definitely corroloated, a really low or high color temperature bulb will go much lower on the CRI since it won't be producing as much of the oth

I'd say they're definitely corroloated, a really low or high color temperature bulb will go much lower on the CRI since it won't be producing as much of the other end of the spectrum. But a good temperature bulb won't necessarily have a good CRI because a middle temperature bulb doesn't have to produce all the intermediate frequencies that a good CRI bulb will have.