My first impression of cornetist Rob Mazurek upon hearing the Chicago Underground Orchestra’s 1998 release Playground (Delmark) was that the guy had a lot of nerve. Where did he get off putting the label “underground” on a band whose sound was the direct outgrowth of commercially successful 60s recordings like Lee Morgan’s “The Sidewinder” and Herbie Hancock’s score for Blowup? My second take was that he was a marvelously lyrical, deeply swinging soloist. I’ve never budged on the latter point, and I also have to admit that Mazurek has since earned his avant-garde stripes. He’s taken up electronics, using them to explore ambient music and musique concrete on three solo albums (one under the alias Orton Socket) and to intensify the grooves of the Chicago Underground (which variously manifests itself as a duo, trio, and quartet). Mazurek left Chicago for Brazil in 2002, but well before then he’d moved beyond his pure-jazz comfort zone to tackle the cyclical compositions of Luc Ferrari, recombinant improvisation with the ensemble Hoffman Estates, and free improv with Tigersmilk, a democratic trio that includes local bassist Jason Roebke and South African-born, Vancouver-based percussionist Dylan van der Schyff. The music on their debut, Tigersmilk (Family Vineyard), ranges as far across the map as the band members’ home addresses. On “The Soft Releases,” van der Schyff erects a wall of arrhythmic clatter that engulfs the insectile chirps of Mazurek’s electronics, but on “Right On Agatite” he holds to a strict, echo-laden cadence, as though he were marching a regiment through a culvert, while Roebke’s imploring, bowed bass phrases and Mazurek’s swooping, brassy cries seem to protest the implacable momentum. Van der Schyff also plays the contrarian on “Secret Mask,” his thrashing cymbals exerting a powerful drag on a kinetic horn-and-bass sprint. Due to geographic circumstances, Tigersmilk concerts are rare; this is only their second time together in Chicago, but they’re making the most of the visit by playing two very different concerts. The trio will play at the Empty Bottle on Tuesday evening; two nights later at the Cultural Center they’ll swell to a double trio with Aram Shelton on reeds and electronics, Frank Rosaly on drums, and Matt Lux on bass. Thursday’s show is free. Tuesday, November 4, 9:30 PM, Empty Bottle, 1035 N. Western; 773-276-3600. Also Thursday, November 6, 7 PM, Claudia Cassidy Theater, Chicago Cultural Center, 78 E. Washington; 312-744-6630.