I'll go with the last post but the stone could be Amethyst.
Do you have any Selsun Blue Shampoo?
One drop would turn silver a cool Cobalt Blue color.
If it is White Gold this will not hurt your find.
Heat up some water. Just below Boil. Add One tea spoon of baking soda.
In a plastic dish place a sheet of Aluminum Foil.
Poor the Hot Mix in.
Place the Ring on the Foil.
If Silver, It will clean up most well. (What your doing is Reconverting the Silver Sulfide back to Silver and Just Loosing the Sulfer that Sulfided the Silver.)
This will not Hurt Gold or Platinum Items.. Or the Stone.
If Gold and or Platinum, it may take off some of the Crustation.
I think it is silver.
Any Marking on the inside of the Band?
http://en.wikipedia.org/wiki/Amethyst
Do NOT USE BOILING WATER! IT COULD SHOCK THE STONE AND CRACK IT!
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