Much has (and should be) written about the incredible job the cast of “Saturday Night” do in breathing new life into the comedy legends featured in the original “Saturday Night Live” lineup. It’s not perfect mimicry, of course, but it feels like what the best adaptations do: an interpretation that pulls us into the world of Studio 8H.

Another key component of the film mirrors what the cast is doing, both in how it was made and how it works inside the Jason Reitman film. The score, created live on set by composer Jon Batiste and the band he assembled for the film, embodies the clock ticking ever closer to showtime — the thing Batiste told IndieWire is the true villain of the story, however much Willem Dafoe’s NBC exec leers at the proceedings. But Batiste’s music also embodies the creativity of working in an intensely collaborative, almost improv-style,...