Hi,
I finished building an electric guitar. It has developed a "sitar sound" (suddenly a high harmonic "seperates" from the fundamental and is very audible) which is consistent on the B string and happens sometimes on the thin E string. I know it is not fret buzz/rattle, because it will do it with a very light pluck and I can see that the string is not hitting the frets. The action isn't that low anyway. This happens whether the string is fretted or open, so it's not at the nut. I think it's at the bridge.
Here's what I think the problem is: I adjusted the intonation at the bridge. Perhaps it was unnecessary, but I tuned each string down significantly (maybe a 3rd or 4th down) when adjusting the saddle, mostly not to pull the string too tight when moving the saddle back. I think in tuning the B string back up, it caught some sort of kink right where it leaves the bridge.
Here's why I think that: I can tune the string down a 3rd or so, and it won't do the sitar sound. As I tune it back up, it doesn't do it. Then, as it reaches a half step away from correct pitch, the sitar sound reappears and is there "in full force" when the string is back at correct pitch. It seems like the kink moves back off the edge of the saddle as the string is tuned down, and then pulled back up as the string goes to the correct pitch.
One more thing... I have not changed strings to test this. I will, but I don't have any strings right now. I just wanted to throw this out there and see the more experienced folks think.