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For the better part of nine years, the unsinkable saxophonist Ed Petersen has appeared every week at the Green Mill, helming a band that matches his intensity and versatility–which alone would place it among the best bands in town. At the beginning of this week, during his penultimate Monday-night performance, Petersen called the catchy but booby-trapped Thelonious Monk tune “Criss Cross” and then proceeded to play a novella: his solo broke down into individual chapters of specific action, but the characters and themes still retained their integrity. On tenor, his main instrument, Petersen’s fat and malleable tone pushes the music forward, and his virtuosic articulation makes him sound as if he’s gobbling up the chords faster than his pianist (the exhilarating Laurence Hobgood) can dish them out. Petersen’s high-energy approach to the sax finds its roots in John Coltrane and Chicago sax giants Von Freeman and Johnny Griffin (whose hyperexpressive balladry has also left its mark). But his roots, as they should, lie under the surface, anchoring his highly personal and splendidly focused approach to improvisation: that’s what gives his often sprawling solos their shape and substance. Petersen–who will move to New Orleans next month for a prestigious teaching position–finishes out his Monday-night gig with special guest Dave Onderdonk joining in on guitar; his fans and friends will celebrate Petersen’s musicianship (and start missing his unpretentious presence) in a bon voyage party at week’s end. It marks the final appearance of Petersen’s other band, the Green Mill All-Stars, featuring pianist Willie Pickens. Monday and next Friday, August 5, Green Mill, 4802 N. Broadway; 878-5552.