Don’t be fooled by pianist Tom McDermott’s mild and unassuming demeanor. Just below the surface lies a sort of trad jazz revolutionary. Witness his nervy concert last month at the Contemporary Arts Center.

Frustrated by a lack of new material in what he terms “traditional New Orleans music,” he assembled some of the best of the jazz set—Tim Laughlin, Matt Perrine, Rick Trolsen, Jason Marsalis, an...