Early in his career Ben Allison wisely realized that recognition would come easier if he banded together with similarly inclined players. So in 1992, taking a cue from the AACM, he cofounded the Jazz Composers Collective; since then, each member has developed a sublime fluency in the others’ work. Allison is uniquely skilled at making conflicting musical ideas work together: his compositions feature contrasting melody lines, sharp rhythmic shifts, and more convoluted conceits–a piece on an early album was in two keys simultaneously. Buzz (Palmetto), the latest release by Allison’s group Medicine Wheel, is a rich contrapuntal concoction that encompasses a wealth of styles. Before it veers off into a bluesy groove driven by Frank Kimbrough’s funky piano, “Respiration” sounds like a chamber-jazz take on Radiohead; “Mauritania,” written by saxophonist Michael Blake, cribs some ideas from North African trance music, as Kimbrough’s piano underlines a circular groove sculpted by drummer Michael Sarin. On the title track, Sarin shifts between swift swing and choppy clatter while the rest of the band adds a dissonant tone via unusual treatments–bundles of pea pods wrapped around bass strings, coins and paper clips lodged in piano strings–but the elegant horn arrangement brings a steely balance. This is the long overdue Chicago debut for the group, which also features trombonist Clark Gayton. Allison also plays a free, all-ages show with his Kush Trio, which includes Blake and Sarin, Friday at 12:15 PM in the Randolph Cafe, Chicago Cultural Center, 78 E. Washington, 312-744-6630. Fri 1/21, 9 PM, Green Mill, 4802 N. Broadway, 773-878-5552, $12. Allison and Medicine Wheel also perform Saturday at the Green Mill, and on Thursday, January 20, they play a free, all-ages show at 7 PM in Preston Bradley Hall, Chicago Cultural Center, 78 E. Washington, 312-744-6630.