Bob Brookmeyer joined Gerry Mulligan’s quartet in 1954–replacing Chet Baker, the jazz world’s equivalent of a matinee idol, in one of its best-known combos. He moved on to play in a high-profile band led by Clark Terry, then joined the brand-new Thad Jones-Mel Lewis orchestra in 1966. And Brookmeyer’s valve trombone, a seldom seen horn with pistons like a trumpet instead of a movable slide, would distinguish him further even if he handled it only half as well: when he picked it up, no one of prominence had used it in jazz since Juan Tizol, who’d joined the Duke Ellington band in 1929. So the fact that the jazz world knows Brookmeyer primarily as a composer and arranger doesn’t stem from any weakness in his playing, but rather from the remarkable quality of his writing for jazz orchestra. His arrangements were an integral part of the distinctive Jones-Lewis sound practically from the band’s inception: his almost emotional embrace of atonalism, a cerebral technique usually associated with 20th-century classical music, bumped up nicely against Jones’s analytical take on jazz’s traditional roots. By the time he returned as principal arranger in the late 70s, after Jones’s departure, he’d expanded on that approach and amassed a variegated, adventurous, and roundly respected body of work. Brookmeyer still performs on the valve trombone, an instrument that trades the flexibility of its cousin for increased precision. In his writing, though, he hasn’t had to choose between those assets, as evidenced by his latest project, Impulsive! (Stunt), which features his arrangements of songs by Brazilian pianist Eliane Elias; he segues effortlessly from big burnished horn charts to trio showcases for Elias’s solos, and brings heft to light Brazilian rhythms without weighing them down. And notwithstanding his reactionary writings about the contemporary music scene, some of which were circulated on the Web last year, he has scored impressively for postfusion soloists and instrumentation, including electric guitar and guitar synth–most notably on a 1991 recording called Electricity (ACT). In Chicago he’ll hook up with the always solid all-student big band at DePaul University, led by Bob Lark, for a week at the Jazz Showcase performing his own compositions–which definitely qualify as postgraduate work. By the end of the second night, Brookmeyer should have whipped the kids into shape for the live recording sessions that will take place during the weekend shows. Tuesday through Thursday, May 8 through 10, 8 and 10 PM, Friday and Saturday, May 11 and 12, 9 and 11 PM, and Sunday, May 13, 4, 8, and 10 PM, Jazz Showcase, 59 W. Grand; 312-670-2473.