Most of the afterfest activities around town this Jazz Festival weekend are jam sessions or sets from locals hoping to attract listeners still hungry for music after the main event wraps up for the night. But on Saturday at 10 PM the Hungry Brain hosts a killer double bill that would be notable any night of the year.

Brilliant Dutch pianist Misha Mengelberg, coleader of the ICP Orchestra (which plays the fest Sunday night), opens the show with a rare solo performance. The circuslike atmosphere of a typical ICP performance, where the emphasis is on playful collective give-and-take, sometimes makes it hard to fully appreciate his imagination, skill, and command of jazz history, but Mengelberg, who turned 73 in June, has absorbed the lessons of Ellington, Monk, and Herbie Nichols like few other pianists. Both his slightly cranky, unkempt persona and his blase demeanor at the bench belie the subtle genius of his playing. When I’ve caught him solo before, he’s seemed to have no idea where he’s headed at first, tentatively striking some keys, but within minutes an improvisation guided by sharp logic has taken shape. That shape is always thoughtfully structured and always different, and that’s part of his singular appeal.

Following Mengelberg’s set wonderful drummer Gerald Cleaver (pictured) will lead his group the Violet Hour (no relation to the Wicker Park cocktail bar of the same name) in its Chicago debut. Like keyboardist Craig Taborn, a fellow Detroit native, Cleaver is a selfless musician who improves any group he works with, and he’s worked with an impressively wide variety. He’s collaborated extensively with Taborn, Roscoe Mitchell, Matthew Shipp, Joe Morris, Lotte Anker, and Liberty Ellman, among many others. I recently heard him in Lisbon with pianist Sylvie Courvoisier’s superb Lonelyville band, and his careful, evocative texture-based playing gave the classical-flavored music an elegant pulse and heightened its drama.

Despite a lengthy discography, Cleaver has only cut two albums as a leader; this Saturday his group will focus on material from the most recent, Gerald Cleaver’s Detroit (Fresh Sound New Talent). In this context he wears his hard-swinging postbop hat, and he’s got an excellent lineup to elucidate his tunes’ graceful melodies and pungent, carefully wrought harmonies: pianist Ben Waltzer, bassist Chris Lightcap, reedists Andrew Bishop and J.D. Allen, and the trumpeter Jeremy Pelt (who’s not touring with the group). In other contexts Cleaver excels at creating different kinds of opposition: timbre versus groove, melody versus melody, chaos versus calm–but here he functions mostly as a propulsive timekeeper and elegant composer. In fact, he sits out entirely on the lovely Monkish ballad “Grateful,” a duo by Waltzer and Bishop.

I’m particularly excited to hear tenorist Allen in the flesh. Earlier this year the Detroit native released the trio set I Am I Am (Sunnyside), and so far it’s one of my favorite albums of 2008. Ably supported by bassist Gregg August and drummer Rudy Royston, Allen swings like a motherfucker, and his skill at embroidering his pithy postbop themes when he solos brings to mind the master, Sonny Rollins. It’s a lean outing, even by sax-trio standards, but it’s not minimalist. Succinct, deliberate, and hard-charging, Allen knows how to trim down his improvisations till they’re nothing but meat.

Today’s playlist:

John Anderson, Eye of a Hurricane (Collector’s Choice/Warner Brothers)
Frank Rosolino, Free for All (Specialty)
Dieb 13, Tomas Korber, Jason Kahn, Zirkadia (1.8 Sec)
Oneida, Preteen Weaponry (Jagjaguwar/Brah)
Jon Balke, Book of Velocities (ECM)