The Chicago Symphony Orchestra has performed Mahler’s symphonies and song cycles enough times to give the Mahler estate a king’s ransom. Germanic to the core–though music director Daniel Barenboim’s effort to lighten its tone seems to be taking hold–the CSO brings drama, precision, and a romantic sensibility to Mahler’s emotional and philosophical odysseys. It’s the main reason maestros with different outlooks, from Bernard Haitink to Pierre Boulez, have welcomed the opportunity to put their own stamp on a CSO Mahler performance, and the more the orchestra tackles these works the more supple and insightful it has become. In the first three weeks of the new season, Barenboim and the CSO return to Mahler in programs that cast him as a link between late European romanticism and American modernism. Each program pairs a Mahler symphony with one or two American works, though the four Americans singled out as his heirs–Gershwin, Varese, Elliott Carter, and Augusta Read Thomas–seem to owe more to Debussy, Schoenberg, and the American vernacular than to Mahler. The first of these concerts is being offered free to the public on Saturday as part of the Symphony Center’s “Day of Music.” The First Symphony, which has been played by the CSO more than 80 times since its debut in 1914, is grouped with Gershwin’s An American in Paris and Carter’s Parita. Barenboim may not be the most lucid of Mahler conductors, but he knows how to find both the frenzy and pathos in this music. On Saturday, a recital of songs related to the symphony follows in the Grainger Ballroom. Saturday, 7 PM, and Tuesday, 7:30 PM, Symphony Center, 220 S. Michigan, Chicago; 800-223-7114 or 312-294-3000.