British saxophonist Trevor Watts was a cofounder of the revolutionary Spontaneous Music Ensemble in the 60s, a charter member of the London Jazz Composers Orchestra in the 70s, and guiding light of the bands Moire Music and Moire Music Drum Orchestra in the 80s. Like Moire (which played the World Music Festival here three years ago), Watts’s new project draws inspiration from Chris McGregor’s Brotherhood of Breath, a London group formed in the mid-60s around a racially mixed core of South African emigres. The Brotherhood combined tight structure and loose execution to achieve a vibrant big-band sound, and Watts recaptures much of this with a four-man sax section, a heavily African rhythmic base, and a riot of prearranged riffs that tightly frame the occasional solos. Trevor Watts & the Celebration Band, the group’s 2001 debut (ARC Records), emphasizes long-form Afrocentric melodies, reedy, damascene harmonies, and extended vamps built from repetitive patterns that subtly shift in and out of phase a la Steve Reich. Those tricky changes of musical perspective could stand as metaphors for Watts’s restless, lifelong oscillations between linear traditionalism and avant-garde freedom and, more recently, between European models of harmony and rhythm and those of the third world. This will be the Celebration Band’s first Chicago appearance. Sunday, October 5, 9:30 PM, Schubas, 3159 N. Southport; 773-525-2508.