For more than a decade, the Neville Brothers and the Radiators closed the main stages on the final Sunday of the New Orleans Jazz and Heritage Festival presented by Shell.

But the Radiators closed the Gentilly Stage for the last time in 2011, and the Nevilles were the last act for the last time on the Acura Stage in 2012.

Since then, the Gentilly Stage has seen a variety of closers, while Trombone Shorty and Orleans Avenue has settled into the symbolic space the Neville Brothers once occupied.

Shorty started a busy festival week Saturday when he headlined the Saenger Theatre for the first time for a show he titled “The Tremé Threauxdown.” He and Orleans Avenue started the show, but it became a jam with Allen Toussaint, Kermit Ruffins, New Breed Brass Band, and Mystikal — all people who were influential on his music, Troy Andrews said last week during a rehearsal for the show.

On Thursday night, he’ll host Shorty Fest at Generations Hall, a fundraiser for The Trombone Shorty Foundation, before playing at the Fair Grounds Sunday.

Andrews had a good year in 2014. His stock rose nationally; he recorded with Foo Fighters and played before them when the rock band performed at Voodoo in City Park last fall.

When Prince played the Essence Music Festival last July, he brought Shorty onstage, then kept him there for the next half-hour to jam. Shorty’s blend of funk, R&B, rock and hip-hop can speak to those very different audiences, but it is also true to the New Orleans tradition.

He credits the broad reach of his music and his ability to fine-tune it for the audience in front of him to his musical upbringing in New Orleans.

“Playing with the Neville Brothers, with Kermit, with Danny Barker, you learn those skills,” Andrews said.

He wants the Trombone Shorty Foundation to be part of that education for the next generation. The organization aspires to “preserve and perpetuate the unique musical culture of New Orleans by passing down its traditions to future generations of musicians,” according to its mission statement.

For Shorty, it’s an extension of the kind of organic education he received from Tuba Fats, his brother James Andrews, and the countless musicians he encountered while growing up in Tremé.

The idea came to him three or four years ago while on tour in Miami.

“I was watching the news and it was talking about murders in New Orleans, and that made an impact to see how we were perceived outside New Orleans,” Andrews said. “I wanted to see if I could save some kids’ lives through music.”

His first response was to buy some instruments and approach Mayor Mitch Landrieu — Andrews calls him “Mitch” — about how to get the instruments to students who needed them. But that was a stop-gap effort. He wanted to do something more lasting, so the foundation was born.

Bill Taylor is executive director. His personal shorthand version of its mission is simple: “To create more Trombone Shortys,” he said.

“It’s to help provide a platform through which kids who have grown up in similar situations to Troy can follow their dreams, musical and otherwise.”

There are a number of organizations that focus on music education with an eye toward helping children beyond their musical dreams, and Taylor wants the foundation to be the bridge between high school band programs and NOCCA, which can only take a finite number of students.

“We want to give these children, who you’d call underserved, the opportunity to take it to the next level,” Taylor said. “That’s a combination of skills in performing as well as business acumen.”

Shorty Fest at Generations Hall is a fundraiser for the foundation. Students in the program will perform in a show that will also include a tribute to Big Chief Monk Boudreaux of the Golden Eagles, with an all-star band that features Bill Kreutzmann of The Grateful Dead, June Yamagishi, Kirk Joseph, Nick Daniels, Raymond Weber, Davell Crawford, and Luther Dickinson of North Mississippi Allstars. Corey Henry and The Treme Funktet, New Breed Brass Band, Tank and The Bangas, TYSSON, Sweet Crude, and MainLine will also perform, and Ivan Neville will sit in with Shorty and Orleans Avenue.

“He’s a part of the band when we can have him,” Andrews said. “We learn so much from him. Whenever he’s free, we’ll take him.”

Earlier this month, Andrews also became the subject of a children’s book. He and Taylor co-wrote “Trombone Shorty,” which was illustrated by Caldecott Award-winning artist Bryan Collier.

Neither Andrews nor Taylor were thinking about a book, but when Taylor asked Shorty for stories to help align the foundation’s activities with his real-life journey, he realized they had possibilities.

“It’s an unbelievable story, and some of the things that happened to him early on are remarkable,” Taylor said. While listening, it occurred to him that it was an inspiring tale that would make a good kids’ book.

The book is on sale now, and Andrews will sign copies at Shorty Fest, with part of the proceeds from sales going to the foundation.

“I was reading it and felt like a kid again,” he said. “I looked at the illustrations without reading the words and it made my imagination create my own story, even though it’s my story. I was thinking about some things that really weren’t me.”