Well, 8th fret on the A string is an F over an E, I'm not sure intonation is going to help much there, the F# and the G should sound OK though, considering the are more than an octave apart. What does the 7th octave or 14th fret a fifth sound like? if the intonation is out of whack then the octave should sound out of whack too. Tune up first of course
Maybe just your amplifier or room acoustics? Try with headphones or just acoustically.