This is not an easy subject and I think you've done well with it, but a couple of suggestions.... A non-textured background would be better, because with this background it is going in and out of focus, which is distracting. The colour has also reflected on to the ring itself, this can be avoided by a neutral background (preferably black velvet or black glass) or by suspending the item (normally with a wire behind it). The focussing is also out, although this is easily corrected. The main problem is the lighting, which is flat. I think you would produce a much better photo using backlighting, with a second light or a small mirror to direct light on to the stone. Hope this helps.
If this is a product shot the ring should be very sharply in focus. I like my jewelry to really sparkle. Also - the deep color of your background washes out the tanzanite.
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