The prize has been haunted by that embarrassing episode, only partly rectified by special awards and citations granted posthumously to Ellington and other jazz legends like Scott Joplin and John Coltrane. A turning point came in 1997, when Wynton Marsalis won, the first time the prize recognized jazz. The guidelines subsequently eliminated an original reference to classical forms and, in 2004, dropped a requirement to provide a notated score, allowing for recording-only submissions.

There were critics. “I don’t think it’s a good idea at all,” Mr. Martino said of the new openness in 2004. “Let these people win DownBeat polls,” referring to the jazz magazine. (Characteristic of the history of the prize is the contradiction that some of the composers who have complained about its insularity have also vociferously defended its boundaries.)

Such changes, though, didn’t overturn the status quo. Since Mr. Marsalis, only two other jazz composers have won: Ornette Coleman and Henry Threadgill. Even Mr. Lamar’s path to victory last year was somewhat unusual: “DAMN.” had not been officially submitted. But during a weekend of deliberations, the five-member music jury weighed the merits of some classical submissions that drew on hip-hop influences, and came to the conclusion that hip-hop itself should be under consideration.

The jury introduced “DAMN.” into the process and ultimately decided it was worthy of the prize. “We’re there all day listening, reading, discussing,” one of the 2018 jurors, the jazz violinist Regina Carter, said in a recent interview. “We were all really respectful of one another and listened to each other. There was no fighting going on: We’d argue our cases, but it never got ugly.”

Ms. Canedy, who spent much of her career as a reporter and editor at The New York Times, became the Pulitzers’ administrator in 2017. She sees Mr. Lamar’s win as a step toward diversifying the submission pool. “The biggest thing we could have done to send a signal to the music industry that we’re serious about this is to award a Pulitzer to Kendrick Lamar,” she said in a recent interview. “That’s not why we did it; we did it because his work was spectacular. But if it sends a signal to the industry that we really are open to all kinds of amazing music, then that’s a good thing.”