Tuning can effect the ring. But if you need a quick fix moon gels, masking tape, tissue and duct tape.......... work to get rid of some ring when applied to the batter head.
If tuned properly it won't ring.
A high pitch ring is usually a result of the heads working against each other.
Once it's tuned and you still want to dampen it dry, just add a snare dead ringer to the top.