Consider playing the tune straight - no scooping up to pitch. The lack of a center to the pitch may occur because you don't have a solid concept of where it is. Steve (aka Nefertiti) has some great ideas above for learning to hear and respond to pitch deviations. And for what it's worth, not every note on your horn is exactly correct either. Even when you nail one note on the tuner, the next one will be off. You'll need to actively listen to your pitch as you play.
Same thing for time. You have to know where the time is before you can intentionally play either in front or behind it.
Enjoy the path!
Same thing for time. You have to know where the time is before you can intentionally play either in front or behind it.
Enjoy the path!