Though I'm not a dealer in stones, my thinking matches sachem's on this: he's testing for cracks. Notice he holds the stone at the very top, allowing maximum vibration. Then he taps down low, near what looks like a line, then higher, then back down low. If a crack went all the way through the stone, the vibrations and sound would be very different depending on where you tapped--as in finding studs or space shuttle defects.

Seems to me the only real test for hardness/fineness is putting a blade on the stone.