Forget the ammonia. Hard water is generally caused by too much calcium in it and you need a mild acid to disolve it. I live in San Antonio, hard water heaven, and white vinegar does a good job with my stones. Just soak your ring in full strength vinegar for a 30 min or so, then clean with a soft brush.
If you use tap water to clean/rinse your jewelery, don't use a heat source (hair dryer) to dry them. It sets the calciun deposits and makes them more difficult to remove.
You should use vinegar fairly frequently to prevent build up in your coffeemaker, too. The calcium coats the inner workings and eventually will destroy it, if you don't prevent it.