No instrument can match the malleability of the vox humana, and few human voices are as malleable as Sheila Jordan’s. She turns her notes over and around, discovering every microtonal facet, and licentiously redesigns a song’s melody to fit her peculiar style. On ballad solos, her quarter-tone warbles and trademark intervals–swooping up a fifth, stepping down a minor second–often give her music uncanny similarities to Native American chant. To the uninitiated or impatient, it may seem Jordan can’t find the center of a pitch, but in fact it’s her awareness of that center that allows her to drift all around it with the hyperexpressivity of speech. Reedmen Jackie McLean, Eric Dolphy, and Ornette Coleman were doing the same kind of thing in the late 1950s, back when Jordan, now 71, first came on the scene. Inspired by bebop but following her own quirky course ever since, Jordan has outlasted most of her contemporaries–including fellow Detroiter Betty Carter–to earn admiration for her artistry and iconoclasm. Many aging singers rely increasingly on experience to compensate for their declining vocal flexibility, and Jordan has indeed grown wiser as she’s grown older, filling her music from a deep well of life’s lessons. But she’s not compensating for anything: her voice has actually improved, deepening over time; the pinch that characterized some of her earliest recordings has softened, and I’d swear her tone gets rounder and more lustrous every year. Of course, on a typical weekend at the Green Mill she’d still need a megaphone to be heard over the crowd, but owner Dave Jemilo always makes sure Jordan’s weekends aren’t typical: he insists that revelers keep their conversations sotto voce, bans cigarettes near the stage, and stops admitting patrons if audience noise even approaches its normal decibel levels. So Jordan keeps coming back, aglow from the red-carpet treatment and enticed by the simpatico accompaniment of her regular Chicago group, bassist Dan DeLorenzo, drummer Anthony Pinciotti, and pianist Bradley Williams. (Dennis Luxion replaces Williams on Friday only.) Friday, 9 PM, and Saturday, 8 PM, Green Mill, 4802 N. Broadway; 773-878-5552.