The problem is, that tension is something static. If your muscles are tense, you will not be able to play fast and with exact movements. You need fast reflexes - which come out of relaxed muscles. I think, your teacher is absolutely right, that you should play as relaxed as possible.
I thought, this is such a fantastic, concise, and perfect post, I was so pleased. Then I saw your next one and thought, HUH?! It's the old argument dating back to C.P.E. Bach - does your body have to experience what the music is expressing.My answer is a resounding No. Perhaps this was true in the days of C.P.E. Bach, whose music required a virtuosity which to us today is very limited.
She went so far as to state that my playing problems could be solved if I can eliminate ALL tensions in my forearm. I find the idea of playing without any tension in the forearm extremely alien. How can one exact strength on the keyboard without any forearm tension? When playing fast passages,surely the forearm needs some structure instead of swaying like the wind?
The basic anatomical process of playing is as follows1) the forearm rises without tension2) the forearm falls without tension3) there's an optimum alignment at the moment of the impact4) in the fraction of a second moment of the impact there's a short contraction5) the contraction allows the weight to be transferred from the torso to the arms/hands6) there's an instantaneous release7) the release allows the weight to be transferred back to the torso
Is it really possible, to play Mozart's Sonata facile 1st or 2nd movement this way?
Tension is never any advantage to a pianist.