Saxophonist Branford Marsalis is unconcerned that jazz musicians lack the popularity of mainstream artists.

“I chose to play this music, and I accept all the things that come with that, good, bad and indifferent,” he has said.

For those who envy the success of other musicians, Marsalis offers this advice: “Just shut up and play.”

Marsalis’ career is hardly lacking in success, however. He’s collected three Grammy awards, was nominated for a Tony, and last year was named a Jazz Masters fellow by the National Endowment for the Arts, as were his father and three younger brothers.

Marsalis will appear at the Schuster Center in downtown Dayton on Sunday as part of a tour promoting a new release by his quartet. The record features pianist Joey Calderazzo, bassist Eric Revis and drummer Justin Faulkner.

Marsalis offered high praise for the members of his band.

“When you hire people who you feel are talented, 95 percent of the time, they’re gonna play the right thing,” he said. “They know, and they’ve listened to enough music to know what’s gonna make the song work, and you just wait a second, and they’ll hook it up. They always do.”

While still a student at the Berklee College of Music, Marsalis performed with Art Blakey and the Jazz Messengers, and later in a quintet led by his brother Wynton. He has collaborated with popular musicians such as Sting, Bruce Hornsby and the Grateful Dead, and led Jay Leno’s “Tonight Show” band for two years.

Marsalis is comfortable in both the concert hall and jazz club. He’s performed classical works with the New York Philharmonic and Boston Pops orchestras, and will return to Ohio in November as soloist with the Cincinnati Symphony.

The Marsalis jazz dynasty had its origins in New Orleans, which profoundly affected their musical development.

“We grew up in a town where being a musician is actually associated with masculinity, not femininity,” he said. “It was great to live in a city where none of your friends would tease you for playing in an orchestra.”