It's very pretty just as it is, I think. There's lots of personality in the pearls and I love the clasp, too.
The small pearls close to the clasp that look dull, are typical of pearls that have had their nacre coating worn off. Natural pearls may wear to a layer of conchiolin that isn't especially shiny. It doesn't usually look blank, though, because it doesn't wear evenly through the layers, leaving some aragonite to show through.
Roll those small pearls around and see if they are dull over the entire surface area. Put on some high-power reading glasses or get a magnifying glass or a loupe and bend the strand between two good looking pearls until you can see into a drill hole. If they are cultured Akoyas, you should see a line just inside the drill hole that defines where the bead ends and the first (and sometimes dark) conchiolin ring begins. Look at a few pearls to get an idea. If you don't see any signs of a bead coated with nacre, they might be naturals.
Either way, they are very cool. I find myself liking graduated pearl strands more and more each time I see lovely examples like these. Congratulations on finding them.