Chicago’s nationally recognized jazz repertory orchestra has often tipped its hat to director William Russo’s two biggest heroes, Duke Ellington and Stan Kenton; this weekend’s celebration of the music of Woody Herman is less expected but wholly laudable. Unlike the other two, Herman did little of the important writing for his jazz orchestras of the 30s and 40s, and as an improvising clarinetist he could barely hold a candle to contemporaneous clarinetist-bandleaders Benny Goodman and Artie Shaw. But Herman had great ears and a genius for coaxing thrilling, groundbreaking big-band music out of the talent around him. What’s more, his orchestra, dubbed the Herd toward the start of the 40s, had as much to do with the popularization of bop as any other outfit: Dizzy Gillespie led the most explosive of the bop big bands, but Herman’s was more stable (and therefore ultimately more credible to the public). Reorganized in 1947 to include an unusual sax section of three tenors and baritone, the Herd really hit its stride. Nicknamed “the Four Brothers band” (a nod to the song of that name, designed to showcase the sax section), it exemplified the transition from swing to bop: the “brothers,” including Al Cohn, Stan Getz, and Zoot Sims, pledged equal allegiance to Charlie Parker and his swing-era equivalent Lester Young, and the rest of the band followed their lead. “Four Brothers” was the work of reedist Jimmy Giuffre, one of the many Herd members encouraged to arrange for the band; others included trumpeter Shorty Rogers, the great songwriter Johnny Mandel, Neal Hefti (who went on to write the theme for TV’s Batman in the 60s), and the recently departed pianist Ralph Burns, who achieved a rare blend of swing and orchestral pastels in his four-part “Summer Sequence.” That piece, Burns’s famous “Bijou,” “Four Brothers,” and the band’s much-admired version of “Tenderly” form the bulk of the program here. Wednesday, April 17, 7 PM, Columbia College Concert Hall, 1014 S. Michigan, and Saturday, April 27, 8 PM, North Shore Center for the Performing Arts in Skokie, 9501 Skokie Blvd., Skokie; 312-344-6245.