Related to the recent thread on mounting an anvil:
One quick way to stop an anvil from ringing is to put something in the pritchel hole. An L shaped piece of round stock works well. If the short leg of the L is only an inch long it is pretty much out of the way. Consider personal safety when you decide on a shape. I often drop a holdfast into the hole when I am at someone else's anvil and the ringing annoys me.