Yeah.. I would follow RPs train of thought first. Google dead spots or wolf tones (they ARENT wolf tones but then again people dont seem to agree what a dead spot is either)
It took a year to notice but D does that on my Epi EmpReg. It does it acoustically (and electrically). It is most noticeable 3rd string 12th fret. If I detune to Db the deadspot moves to the 13th fret so it is definitely pitch specific. I was able to move it out of the way by adding mass to the top of the guitar (two really heavy hard drive magnets). I didnt leave them there. Just did it as a test to confirm my theory. You see it on electric guitars and more often on electric basses. In that case guys clamp a weight in the headstock (google fathead or fatfinger.. i forget which).
If it DOESNT do it unplugged disregard my previous paragraph
