I dragged the photos into my iPhoto to enlarge them, but they are blurry.
Is there a hallmark on the gold-colored chain with the pearls strung on? These could be akoyas in an add-a-pearl type necklace that was not completed.
The full graduated necklace gives me the impression that it may be imitation, but better photos would help. Check the clasp for a hallmark, too. If it is real, then it could be a "3.5 momme" strand from the 1940s or 1950s, sold to servicemen and others in Japan during wartime to take home to their sweethearts. Momme is a unit of weight; pearls are sold by weight so the graduation would lower the cost of the strand. But I have seen imitation versions of these strands.