This is a second image of the same specimen taken under two 200watt tungsten globes and with the camera white balance set in tungsten / incandescent:
If I took the photo under tungsten light using the camera's auto white balance setting, it comes our far too yellow. I don't have info on the CRI for either lighting system.
Interestingly, its only the euhedral, gemmy sugilite crystals that are difficult to photograph. The more common massive variety of sugilite gives accurate colour rendition under both tungsten and fluorescent lights. Here's an example of a polished slab of massive sugilite, taken under fluorescent lights, camera on auto white balance (the angular grey fragments are banded iron formation):
The use of the camera settings for white balance is only approximate, especially for fluorescent lamps. If the white balance is correct in both images the background material should very close to the same color, unless the material is very sensitive to color temperature, i.e., metameric like alexandrite. Electronic flash is better as a daylight substitute than fluorescent lamps. Use a spectrally flat gray card to do a custom white balance under both lamps and the results should be much better.
Tungsten, tungsten halogen, and electronic flash have a CRI of 100. Daylight fluorescents, with very few exceptions, do not have high CRIs due to the mercury vapor lines in their spectrum.
A grey card WB should be performed at intervals with the same lamp(s) on the order of once a week, or month depending on bulbs. Electronic flash needs a grey card WB as well as it can vary with intensity of use and age.
A proper spectrally flat grey card can be obtained from many sources like Amazon, Gretag-McBeth, Robin Myers Imaging, etc. You can google more sources as well and they are not expensive. 
Color balance your images either before (by setting the WB in the camera using the K setting and a gray card) or after in the software. The Auto WB is almost never totally accurate.
