Unfortunately it is definitely not the keyboard - I tested it alongside other instruments and it is the minidisc at fault. Yes, I do need it to be 'nearly' in tune - quarter tone out offends my ears so much I can't play.
The keyboard is a Roland XP50 and I am still trying to get to grips with the instruction book. It has a note bender so it might have a pitchwheel function somewhere (if I can find where).