Some singers celebrate their debt to Billie Holiday by covering her songs and noting her mannerisms. Sheila Jordan does neither, but she embodies the Holiday spirit more faithfully than most. Like Lady Day, Jordan eschews the merely pretty, finds the improvised notes nobody else wanted, and revels in the naked purity of a somewhat unorthodox vocal instrument. As Jordan snakes her way around a familiar melody, both she and the song seem to undergo a transformation: wringing the song line to squeeze out its essence, she contorts her face into unexpected caricatures. But Jordan’s alterations somehow reinforce her respect for the original melodies, reminding us that those melodies are strong enough to support her departures, which expand and comment upon them. The delicate power of her music reaches its zenith in her duets with longtime partner Harvie Swartz on bass; Swartz’s monumental tone and dart-sharp technique provide all the support one could want in this most vulnerable setting. In her improvising, Jordan will often allow the notes to slide into moans, the words to slur into blowsy neologisms. (This sinuous melisma–along with her rhythmically tense scat solos–helped teach two younger generations of jazz vocalists how to shed their musical and emotional inhibitions.) To the unadventurous or unsympathetic, such singing may seem almost otherworldly; in fact it is simply other–unique. Jordan and Swartz will be joined by Chicagoans Brad Williams on piano and Mike Friedman on drums. Friday, 9 PM, and Saturday, 8 PM, Green Mill, 4802 N. Broadway; 878-5552.