If you have a tapping noise along with burning oil, it does not sound good.

Can you tell if the noise is at engine speed or half engine speed? Is the noise more of a knock or heavy tapping noise rather than just tapping?
If the noise is half engine speed, then your problem could be two-fold. The hydraulic tappets, if fitted, are getting very tired and burning oil could be a piston problem.
If noise is at engine speed, then definately, I would say you have a piston problem.
I would like to suspect valve guide seals as this is a cheeper fix, but your symptoms indicate otherwise.

Try changing the oil, for a cheap brand for fault finding sake, and see what happens. If symptoms disapear, well you are lucky. Change oil again for a decent quality one.