Miss Candy,
What a lovely gift from your Grandmother! Figuring they are dated to about 1950 or so, and if they pass the gritty test they would be cultured Akoya pearls from Japan. Your photo is still not quite close enough to see the pearls real well, but they look well matched. Is the clasp karat gold? Or silver? A clasp with a pearl on it seems to indicate genuine, not imitation pearls.