Most of these songs emerge from perceptive readings of outsized feelings generated by ordinary events, like a comic tune about your grandmother getting a new boyfriend or a sweetly romantic one about seeing a white lady crying on the streets of New York. “Once you keep your eyes peeled,” Mulaney tells his co-stars, “you’ll see crying white ladies all over New York City.”

Mulaney mixes in cameos by beloved character actors like André De Shields (who plays a stylish, eye-patch-wearing crooner preaching the virtues of algebra) and Richard Kind (who chats with three girls in a segment called “Girl Talk”). This hodgepodge aesthetic is tied together by a running joke that the special (and often the kids) makes cultural references that are more The New Yorker than Nick at Night. This has got to be the only show for children that has references to Fran Lebowitz, Federico Fellini and Ed Koch.

The jokes will alienate some young viewers. They annoyed the two-kid focus group in my home: my 5-year-old lost interest, while my 10-year-old felt talked over, if also intrigued by these adult-world references. It’s hard to see the audience for a sketch imagining a focus group for a movie, where kids act like showbiz veterans, talking about Elizabeth Banks or Mark Ruffalo. Children will be confused, while adults who chuckle may grow tired of the name-dropping many bits.

At the same time, these knowing jokes reflect how committed Mulaney is to rejecting any note of condescension, which earns the trust of kids, so often patronized by adults. Death is a frequent subject here, often comically, which might strike some as odd, but youngsters have much darker senses of humor than adults tend to believe. There’s an interlude offering a fun fact about the number of people who died from volcanoes and an irreverent sketch with a blue Barney-like character named Googy that is interrupted by news that the man in the costume died. It’s a risky joke that some children (and adults) will love, and some might not.

That’s the assumption behind most art put out in the world. Taste is subjective. Yet kids’ entertainment can be overly cautious and homogenized, anxious about upsetting or confusing its audience. But there are worse things. Perhaps because Mulaney doesn’t have children, he sees this more clearly than some parents. And it makes his special stand out.

And yet, as committed as he is to his taste, Mulaney also has the instincts of a crowd-pleasing entertainer. So he knows his final musical number must include the broadest, most flamboyantly silly performance. As Mr. Music, Jake Gyllenhaal pops his eyes and flops his limbs in a calypso number that tries to explain how ordinary sounds can be musical, but he keeps stumbling, an escalating pratfall of a comic turn.

He’s a grown-up who comes off like a fool. What kid wouldn’t love that?