Is the same note played by the finger shifted depending on whether it is pp or p or f or ff?

It should be as pitch (the brain perception) depends on intensity and not only on frequency.


This is why good musicians play by ear-brain.


And good conductors too.


And good synthesizer players-composers too. Each synthesizer is tuned according to how loud it plays and how high it plays.


The ear brain is the judge. Not the frequency.