Classicists who make hip-shaking music, Tiempo Libre brings its mix of Latin and European genres to concert halls, jazz clubs and even Dancing with the Stars. Growing up in Fidel Castro’s Cuba, band members balanced conservatory training with forbidden American music, snatched from the ether with a makeshift receiver. Immigrating to Miami, the Grammy-nominated band drew on the American funk and R&B they’d heard on their secret radio, fusing it to timba, a characteristically Cuban mix of Latin jazz, cha-cha and son. It’s an addictive, rhythmic concoction, but Tiempo Libre takes it one step further. Drawing on its classical chops, the seven-piece ensemble brings classical music to the pan-cultural table. Giving Johann Sebastian Bach a Latin makeover, the band folds “Sonata in D Minor” into an energetic cha-cha, while recasting “Air on a G String” as a lush bolero. On paper, this Afro-Cuban classical gas sounds like a baroque stunt, but Tiempo Libre effortlessly traces orchestral music’s DNA from its African origins to its ongoing development through Europe, the Caribbean and beyond. If there’s any drawback to this Tiempo Libre gig, it’s that music this propulsive shouldn’t be confined to the concert hall.