For history-minded clarinetists like Chuck Hedges, Benny Goodman’s small groups of the mid-30s are like the Holy Grail. While leading his sleek yacht of a big band, Goodman also cut loose in the swing era equivalent of cigarette boats: a trio, a quartet, and other combos that emphasized improvisation over arrangement. And after Goodman recruited the pioneering young electric guitarist Charlie Christian late in the decade, his sextet mixed the flowing, woody sound of his own clarinet, the hot clang of Lionel Hampton’s vibes, and the ripening glow of the guitar into a brand-new jazz flavor. Hedges used that sound as his model when he formed the Swingtet more than two decades ago, and today he and his band still play a style and a repertoire that were old when they started–except now they do it better. They’ve never been merely nostalgic about the swing era; they continue to investigate the music and grow within it. And though their leader is quite possibly the best swing clarinetist alive, at this point any of Hedges’s bandmates could step up and lead in his place. Dave Baney has steadily developed into a marvelous guitarist, influenced by Christian, Django Reinhardt, George Barnes, and Les Paul; Duane Thamm’s vibes work, while less flamboyant than Hampton’s, has a crisp, peppy lilt; and bassist John Bany and drummer Charles Braugham propel the group with no muss and no fuss. No band I’ve heard can match the Swingtet’s ebullient interplay and solo wizardry; it plays classic jazz without schmaltz or irony, re-creating–and reinvigorating–a signal moment in music history. Saturday, 9:30 PM, and Mondays, 5 PM, Andy’s, 11 E. Hubbard; 312-642-6805. NEIL TESSER