My first thought was these are elaborate fakes, but the more I look at them... they're not that elaborate.
Perhaps it may be photo quality, but I see too much metal and not enough butter (nor depth) for gulf origin.
While the strand appears graduated, it's not. The third photograph the tape measure indicates from 2 to 12mm the pearls are 3.5 and 5mm in diameter. Three or five slightly larger than 5mm pearls embellish the low point between the same 3.5mm pieces. The give away being the left side greatly mirrors the right side with chain and sprocket precision. We only see that in the most elegantly crafted strands and pretty much never in limited inventory pieces.
The graduation of the pearls toward the clasp is uneven.
Yes, not an oversight to expect from one creating natural strands.
You'd certainly want to know if they were natural. Do these merit a trip to the lab? Not at this moment.
Candling would reveal the nuclei. I'd expect uniformity, but you'd pleasingly surprise me if they weren't. I'd suggest this strand was crafted to look natural in times more recent than the 30s. Nothing nefarious nor deceptive, though. Perhaps a piece from what they had on hand, or commissioned for a purpose/styling (ie) wedding etc.
Sometimes (though not a lot) we see mix strands, but I don't think this is that either. It's an alluring piece. Considering the clasp, the otherwise good condition and quality of the pearls, you did alright. Not just for gazing, but wondering or learning about pearls is fun too. Restring... perhaps they can tweak that graduation thing at the ends while their at it.