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So When I fret an E note on the A string (7th fret) and play the open G string simultaneously I get this crazy zinging sound that disappears if I touch behind the 7th fret on the A string at the same time, removing the vibration behind the fretted note. Obviously the G note is causing some kind of sympathetic vibration with the A string behind my fretted note, but I've never seen this before. What could cause that, a too low fret behind, kind of like the reverse of when you press down on a low fret?

Back buzz! Raise the the nut a touch. You can put a piece of paper under the nut and raise it a touch and see if it goes away.

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When you fret a note at say the 7th fret, you are also "fretting" the section between the nut and the 6th fret. If your nut is the proper height that section of string is free to vibrate - ie it does not touch any of the other frets. If I pick this section of string my little chromatic tuner will fluctuate between several notes, but most of the time it will lock on to a G (maybe a hair flat). What I presume is happening in your case is that section of string is vibrating in sympathy with the open G string. Remember too that G is often one of the natural resonances of the air chamber.

Tried this on two guitars, both do the same thing. Don't know what you can do about it other than trying to dampen that section of string and I really don't know how to do that.

Edit to add, one way you could test this is to measure the distance from the nut to the 6th fret (any good fret calculator will give you that). Calculate the tension in the string using the standard equation (D'Addario's web site). Now solve that tension equation for frequency, plug the tension and string length back in and you'll get the fundamental frequency for that piece of string. I'll bet its a G.