The Hyde Park Jazz Festival celebrates its seventh anniversary this Saturday and Sunday, September 28 and 29, with the boldest, biggest, most comprehensive program in its history. Kate Dumbleton signed on as the festival’s executive director in spring 2012, giving her only a few months to put together her first effort, and this year’s event has clearly benefited from the extra planning time—no other fest showcases the breadth of Chicago jazz better. Thirty-two acts perform at 11 venues, all but two of which fit into a square of Hyde Park less than five blocks on a side. The 30 local groups cover such a dazzling array of styles and approaches that you’d never notice the absence of out-of-town acts, but a couple visitors sweeten the pot anyway, both playing Saturday—a trio led by New York-based pianist Gerald Clayton (7 PM, Logan Center) and a duo of agile Israeli reedist Anat Cohen and Brazilian guitarist Douglas Lora (11 PM, Rockefeller Chapel). The majority of the festival’s sets fall on Saturday, and other highlights that day include a trio set from pianist Willie Pickens (2 PM, DuSable Museum), a rare performance by the Jeff Parker Trio (7 PM, International House), Ken Vandermark’s powerful Music of the Midwest School (9:30 PM, Logan Center), and the inventive quartet led by cellist Tomeka Reid (9:30 PM, International House). Sunday’s program takes place all over the Midway Plaisance and wraps up at 7 PM with a concert by powerhouse singer Dee Alexander. This year’s schedule also includes a handful of events that aren’t jazz performances: a Sun Ra panel, a DownBeat magazine “blindfold test” with Jeff Parker (conducted by yours truly), and DJ sets from Eternals front man Damon Locks. All shows are free and all-ages, though some small venues will likely hit capacity and turn people away. Admission is first come, first served (the sets by Clayton’s trio and Frank Rosaly’s Green and Gold are ticketed, but the free tickets, available at the Logan Center box office, are also first come, first served). Donations of any size are gladly accepted, of course, and for $125 you can get a Jazz Pass that guarantees you preferred seating for indoor shows. The festival provides free shuttles between shows; for a complete schedule and a list of venues, visit hydeparkjazzfestival.org.