The harmonic on the E string, normally reached with a stretch of the fourth finger from 3rd position, is sounding flat. If a play an arpeggio from 1st finger E on the D sting, the harmonic is a half step flat. I've put on a new string but no change. Does my bridge need moving?The harmonic on the A is perfect.
It varies from person to person, but once we get "off the staff" the tone can seem flat (and very low notes can seem sharp), but not necessarily in an even progression.
Also, the harmonic in question is in a very sensitive part of our hearing range, and the strength of a tone has a noticeable effect on our perception of its pitch.
there are a number of solutions to this problem but the one I have found to be most efficacious over ther years which I always teach my students is to shout 'woof!' as loud as possible as you are playing the note.
not only does this cover up the offending sound but it clears the room of any stray cats that may not belong to you, thus protecting you from a slew of law suits ranging from cat napping to 'nefarious acts with animals while crossing a bar line,'
Hope this helps,