This is a decent enough book, which I expect from Amie Kaufman and Meg Spooner because they're good writers. The mystery and puzzle aspect of it wasn't quite as strong as I expected because the reader watched them solve puzzles rather than being asked to participate in solving the puzzles. Also puzzle have been done in tv shows and movies that it's really (REALLY) hard to come up with something unexpected.
The musical bridge reminded me of The Snow Queen by Joan Vinge. The ceiling falling and floor crumbling room were straight out of Indiana Jones (which in all fairness I think they were designed to be). There were also parts that felt like Stargate, though I couldn't tell you which episode. Probably Crystal Skull but there were several episodes with puzzles like the ones with Merlin. The language obelisk was new but not surprising that it was a portal since the message in the beginning referenced going through the aether.
I think the story was also meant to be surprising in other ways. The fact that I was not surprised is not a detriment to the authors. It's because they're good storytellers that I know they didn't put a loaded gun in the room for no reason. So I was not surprised that Mink and Charolette were the same person. Or that Mia and Jules were being followed. Or that the Undying were humans. I think they're the people sent off to Alpha Centauri but we'll see in the sequel. What Kaufman and Spooner do so well is legitimize the seemingly unexpected. It twists tropes in unexpected ways and yet still follows a logical path so that the “surprise” is actually the only reasonable conclusion.
The characters were good but not quite great. Interesting enough to follow into the sequel but not dramatically fantastic. Or perhaps that was simply my mood while reading. Maybe I was trying too hard to follow the puzzle so didn't get drawn into the characters. Or maybe I saw where the story was going too well to get caught up in it.