Saturday night’s free concert at Central Park Summerstage amounted to three and a half hours of intelligent groove, informed by jazz but rarely beholden to it, with improvisation as a binding but nonidiomatic force. With three bands on the bill — Medeski Martin & Wood, Josh Roseman and the King Froopy All-Stars, and Jim Black’s AlasNoAxis — there were innumerable on-the-fly decisions about timbre and color, rhythm and counterrhythm. Each set was impressive in its own way, but there was continuity among them.

The show was jointly presented by Summerstage, the Blue Note Jazz Festival and the Undead Jazzfest. Of these three it seemed to belong most to the Undead Jazzfest, which doesn’t technically begin until next week. Adam Schatz, one of that event’s organizers, took the stage between sets to hype the bands and congratulate the audience for its good taste and hardy constitution. (A cool breeze and the threat of rain apparently prevented some would-be attendees from showing up. Then again, maybe they were at Bonarooo.)

Members of all three bands on the bill spent overlapping stretches studying in Boston during the 1980s, either at the New England Conservatory or the Berklee College of Music. This was little more than subtext onstage, a matter of shared history and common experience.

Still, it meant something. Higher jazz education was a more rigid proposition 25 years ago, and each of these musicians sought out an alternative current to the swinging mainstream. Free jazz, funk and noise-rock were outré departures then, and to align oneself with any of them, never mind all of them, was a self-marginalizing act. That the situation is so different now can largely be attributed to this generation of players; consult present-day undergraduates at a jazz program and you’re likely to draw that conclusion.