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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.

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.