Curtain effect (scrolling)–or something close

Grateful for ideas for simple, this-ain’t-my-day-job kind of way to implement a “curtain” effect”. In other words, a way to have a <section> reveal the next, upcoming <section>.

Example: http://editsquarterly.com/

This feature is not in my theme. I’ve tried various parallax solutions/plugins and with some promise. But I’m not quite there. If you’ve done this, have ideas about doing this easily or cleanly, or know of a maintained plugin, I’ll come shovel out your driveway.

Seriously (and again), I’m grateful for ideas. Thanks!