Can you give us a close up of the clasp, front and back?
Can you take a close up photo of one of the drill holes?
Obviously I can't diagnose from your photo, but your necklace looks a lot like my grandmother's Richelieu pearl necklace, which were imitation pearls. Don't believe the Richelieu wikipedia entry which says they made cultured pearls. They did not. Richelieu made good imitation pearls by painting ground up fish scales on a mother of pearl bead. My grandmother's are quite old, golden colored, and have a sterling silver clasp with the same sort of bead cap attachment between the pearls and the clasp. There are no knots between the pearls.
Having said that, yours could still be real, as the Richelieu ones were imitations of real necklaces.
However, your pearls, like mine, have no overtones, luster or orient.
I have never had good luck doing the "grit" test. Good imitation pearls will pass the grit test. Cheap plastic or glass pearls will not.
UPDATE: I've updated the Wikipedia entry to remove the bit about Richelieu making cultured pearls, and I entered that they made faux / fake pearls of high quality.
