One of the beauties of a jazz jam is the players also become composers, improvising solos and holding musical conversations on stage.

At the Madison Jazz Jam, the conversation also is about learning.

The monthly gathering, just half a year old, is designed to bring together veterans and learners, regardless of age and level — that means everybody from gifted high school players to retirees who’ve dusted off their band instruments from college and want to play again with a group.

The jam’s website at promises two sets each Sunday it meets, one for experienced players and one where feedback “will be given gently” — and publicly, “so everyone can learn together.”

“A lot of people cringe when they hear that,” said Bob Kerwin, the jam’s emcee and coordinator. But the critiques by Dan Wallach, director of jazz studies at Edgewood College, “always start with the positive, and then provide constructive advice” such as the importance of maintaining eye contact with other players during a jam, Kerwin said.

“It’s nothing like ‘American Idol’ and Simon” Cowell, he said.

The Madison Jazz Jam was founded at the Washington Coffee House (and more recently moved to Liliana’s Restaurant at 2951 Triverton Pike, Fitchburg, where jazz is an entertainment staple) in part to fill a void left after the New Breed Jam lost one performance home after another. The New Breed Jam since was resurrected Tuesday nights at Cardinal Bar.

“Playing with the New Breed could be a little intimidating,” Kerwin said. “Those guys are such incredible musicians.”

The Madison Jazz Jam, on the other hand, was intentionally designed to be instructional as well as entertaining, and to provide the essential experience and connections a drop-in session can offer.

“I feel that’s the heart and a soul of a jazz community,” said Kerwin a physician who picked up the saxophone as a student but struggled to find places to play as an adult. “A lot of what we’re trying to do is keep the jazz scene going.”

While schools provide great opportunities for jazz learning, there are too few options after graduation, he said.

“If we would have had something like this for me as a kid,” he said, “I would have really loved it.”

The next all-ages Sunday jams will be at Liliana’s from 4-7 p.m. on May 15, June 12 and July 10.