> what is the range of the fine tune adjust knob supposed to be

For older A-110 it's about +/- 1/2 octave, for newer ones about +/- 1
semitone. We reduced the range many years ago (I don't remember the exact
date) as customers recommended that for better fine tuning. But the range
can be changed by replacing one resistor (R5, now 1M) by another value.
Reducing the value of R5 increases the range.

Best wishes
Dieter Doepfer