Since the frequency doubles every 12 half steps, that means that the frequency of any note is the twelfth root of two times the frequency of the one before it.

Since the frequency doubles every 12 half steps, that means that the frequency of any note is the twelfth root of two times the frequency of the one before it. That's really all you need to know. (of course this doesn't account for octave stretching that is typically done on acoustic pianos)