couple of suggestions,
1. make sure your string it seated propely in the nut slot, if the slot does not have enough back slope to it the string will viberate in the slot and cause a tinny sound.
2. make sure your not fretting out up the neck, be sure that the string does not touch any frets as its plucked.
3. How is the break angle on your saddle? If your saddle is too low and there is not enough downward pressure on the crown of the saddle the string can have a tendency to dance on top and again, cause the tinny or buzzing sound.
There are a few things to look at, im sure others will think of some more
