In a dressing room behind the stage in the Metropolitan Opera House, Wynton Marsalis, the trumpeter and educator, intently watched a live feed of the big band representing the Osceola County School for the Arts, from Kissimmee, Fla. They were playing Dizzy Gillespie’s “Things to Come,” a piece that can expose any weaknesses in a big band. Being a good jazz musician isn’t just about playing fast and loud and high, but this song requires musicians to do all of that.

The school’s lead trumpet player was in the middle of a solo. A dexterous player who could hit the high notes, he sounded like a professional. “Watch, the director’s going to wave off the backgrounds here,” Mr. Marsalis said, using some colorful language to say the soloist had not gotten to his good stuff yet.

The director then made a small gesture to the rest of his band, telling them to wait to let the solo develop. It was a chart that Mr. Marsalis had surely heard live hundreds of times, but each time it is full of small decisions like these, making it a new experience.

It has been nearly a century since Duke Ellington’s orchestra became the house band at the Cotton Club on 142nd Street. Even there, where Ellington and his group of Black musicians played in front of all-white audiences, patrons were expected to be active listeners. Ellington is quoted in the book “Duke Ellington’s America” as saying the club “demanded absolutely silence” during performances, and that anybody making noise would quickly be ushered out the door.

Ellington knew his work had a signature. He wrote with particular members of his orchestra, like the saxophonist Johnny Hodges or the trumpeter Cootie Williams, in mind, and he believed that nobody else could sound like them, no matter how hard they tried.