David Letterman, who signs off from “The Late Show” on Wednesday, May 20, is not just a comedian or a broadcaster. He represents an entire comedic language that is now so common we don’t even notice it.

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In the most praised installment of his still-young stint as host of “The Late Late Show,” James Corden crashed a stranger’s home, set up cameras and recorded an entire episode. Corden called it an “experiment” and CBS promoted the show online as “making late-night history.”

But as with so many bold ideas that seem radically new in late night, David Letterman did it first. In 1980, on his short-lived NBC morning show, a kind of out-of-town tryout for his evening program, he took his band and crew to tape an episode in a home in Cresco, Iowa.

This doesn’t mean that Corden stole the idea or that, even if he did, there’s anything wrong with borrowing a good gimmick. But now that Letterman’s legacy is being celebrated as he prepares to retire from his long run as the star of “Late Night” on NBC and “Late Show” on CBS, the greatest evidence of his titanic impact remains what’s on other talk shows.

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Letterman’s last appearance as host is 11:35 p.m. Wednesday, May 20, on CBS.

Critics have lately focused on the differences between Letterman and his younger, sunnier, more digitally savvy peers. But today’s hosts still lean heavily on a playbook developed by Letterman. Any time a show tries something vaguely avant-garde, there’s a good chance that there is an antecedent involving David Letterman.

Corden has employed many ideas that longtime Letterman fans will find familiar, including prankish remote segments in which he ineptly moonlights in a sales job or takes a star to a fast-food drive-through. He also organized a first date in his studio that he checked on periodically throughout the broadcast. Letterman tried all of these concepts, although his 1982 blind date involved Peter Tork from the Monkees.

Last month, Fallon interviewed Helen Mirren after they had both inhaled helium. Letterman went on this lark in the mid-1980s, with Jane Pauley delivering high-pitched answers.

For today’s talk shows, Letterman is not just a comedian or a broadcaster. He represents an entire comedic language that is now so common we don’t even notice it. You see it when Jon Stewart slyly hints at his indifference as he asks stars about their movies or when Fallon turns to his piano player and says, “Hey, James, could I get some thank-you-note-writing music, please.” (Letterman would introduce phone-call segments by requesting “Some dialing music, please” from Paul Shaffer.)

In another example, Fallon, sitting at his desk, scratches his chin and looks upward thoughtfully before a flashback sketch begins. Letterman regularly used this same segue, and while he may not have been the first comic to come up with the idea, he performed it often enough to make it a kind of talk-show shorthand.

His fingerprints are also apparent in the broader structure of these shows. Take the evolution of the bandleader. It’s become common to cast comedians (like Fred Armisen and Reggie Watts) in this role. But Shaffer, who was briefly a featured player on “Saturday Night Live,” paved the way.

Letterman also popularized aggressive man-on-the-street segments that became common not only in late night but also on shows like “Billy on the Street.” And with the help of his head writer Merrill Markoe and his director Hal Gurnee, his creatively edited remote pieces expanded the ambition of the comedy before anyone thought about going viral. Such segments are now highlights of shows put on by Conan O’Brien and Jimmy Kimmel.

Of course, Letterman, a perceptive student of radio and television, didn’t invent all of these ideas. While he revered Johnny Carson, he borrowed from other predecessors, in particular Steve Allen.

Newer hosts depart from Letterman in their sensibility. They are more likely to break into song or dance or play games with celebrities than they are to rib them, and they jump into stunts with earnest enthusiasm.

Letterman filtered his forays through an acerbic sense of humor and a grand sense of the absurd. He didn’t proclaim giddily that he was trying an experiment so much as chuckle with self-deprecation at the stupidity of the undertaking.

Nowhere is this contrast clearer than in attitudes toward technology. Letterman’s stunts, like the Monkey Cam, often poked fun at the passion for new gadgets that has become pervasive.

Over the years, Letterman played with the form less, but he developed into a great conversationalist and storyteller. And his long-standing skepticism lent weight to moments of seriousness, like his reaction to heart surgery or the Sept. 11 attacks. He became that rare thing, a television comedian with gravitas.

A few political satirists approach something similar, but it’s unlikely that in the age of social media, another network star will replace his particular brand of common sense: a mix of goofy mischievousness and buttoned-up dignity. Once he is gone, what will remain is the aesthetic vocabulary he introduced, a vital achievement that cannot be measured in ratings or applause.