I was most interested in the O/P's initial comment:
Nevertheless, there appears to be dissonance between the chords of the BB song (I usually use real-track styles) and the notes I'm playing. It may not be a lot, perhaps a semitone or less, but it's just not 'quite right'.
A
semitone would sound extraordinarily terrible, in fact it would be completely "unlistenable" to. So I suspect that this might be related to a tuning issue(?) (only a guess, I'm not a horn player, so many other influences could come into play), but I'll be the tonality difference is much less than a semitone. Nevertheless, it's a concern and needs resolving.