If you expect anything less than a reinvention of the jazz-song repertoire from vocalist Sheila Jordan, you’re bound to end up either disappointed or shocked. Like Betty Carter–who also came to prominence in Detroit in the 50s and also appears in Chicago this weekend–Jordan takes enormous liberties with a song’s melody right from its first statement, at times warping it into something utterly unfamiliar and completely captivating. And like Mark Murphy, Jordan freely uses foghorn low notes, discomfiting high squawks, note-smearing swoops, and word-obliterating slurs in a relentless quest for greater expressivity; together she and Murphy have helped two generations of jazz vocalists shed their inhibitions. Jordan manipulates her willowy sound to communicate complicated feelings–her love and yearning often come twisted up with wisdom and irony. The merely pretty doesn’t interest her much; even on romantic ballads, Jordan claws at the more dangerous concept of true beauty, in all its naked, unconventional splendor. She never really stops improvising, but her scat solos stand out nonetheless, proceeding with an economy of notes–a stinginess, almost–that other scat singers would do well to emulate. Jordan will perform with the same Chicago trio she spouted admiration for after her last visit: the effortlessly empathic pianist Bradley Williams, bassist Dan DeLorenzo, and drummer Anthony Pinciotti. Friday, 9 PM, and Saturday, 8 PM, Green Mill, 4802 N. Broadway; 773-878-5552. Neil Tesser

Art accompanying story in printed newspaper (not available in this archive): photo by Lauren Deutsch.