I've been told that, ideally, a note like an e sharp or a b sharp should be slightly different in pitch from an f natural or a c natural. (especially when it is written as a leading pitch in a minor key, apparently)
I'm wondering, what direction that lean of pitch should be, slightly sharp or slightly flat? If it's flat, should I be in the habit of kicking out my first valve slide when an e sharp appears?
And do I need to adjust the pitch for double sharps and double flats if they appear in a classical piece?
Note: I play a lot of orchestral music and run into this issue relatively often. I know that, especially in the middle register of the instrument, it doesn't make a lot of difference. But when tone and tuning is already stressed in an above-the-staff or below-the-staff situation, I'll take any advantage I can.