This is a real poser to my limited knowledge. I have developed over the past few days a buzz on my first string but it is very specific. It only buzzes outright when the string is fretted at the third fret, although there is something zingy about the tone on that string at other times.
But here's the thing. This only happens if I also have the sixth string fretted at the third fret as well. As I say, I can hear a hint of a first-string problem at other times but that's the only situation that has a frank buzz at moderate to loud volumes. A couple of other things...
If I drop the sixth string down to D instead of E the first-string buzz goes away (even if I fret at the fifth fret instead of the first!)...
If I press on that third fret on the bass side without fretting the string it does not buzz...
The first-string buzz starts the moment the sixth string just barely contacts the third fret but continues no matter how hard or softly I fret either the first or sixth string...
Finally, I noticed a slightly high fourth fret on the treble side so I tapped it back down a few thousandths. All the frets are now dead level and it made no difference in the buzz. These are 12-54 gauge 80/20 Martin strings on a handbuilt OM guitar, 24.9" scale with an ebony fingerboard and nickel-steel frets. Very low action and about 0.008" relief at the sixth fret. Bone nut and saddle.