David Letterman is typically remembered for his more ridiculous interviews, like the time that Crispin Glover tried to kick him in the face, or when Chuck Norris also tried to kick him in the face. But, in retrospect, one episode of Late Night with David Letterman was an incredibly valuable part of music history.

Forty-one years ago to this day, January 10, 1984, Late Night with David Letterman welcomed Otis Blackwell to the show. While not a household name, Blackwell was, as Letterman stated in his introduction, “the most influential songwriter in rock and roll history.” Blackwell’s credits included hit songs like “Great Balls of Fire” and “Fever.” But, perhaps most notably, he penned several of Elvis Presley’s biggest tunes, including “Don’t Be Cruel,” “All Shook Up” and “Return to Sender.”

Elvis didn’t just record the songs, he arguably copied Blackwell’s singing voice. That’s because Blackwell...