More than just an American city, New Orleans is historically a gateway to the Caribbean, inextricably tied to the slave trade and all the complex cultural transference that it entailed. New Orleans jazz, therefore, has always had an Afro-Caribbean component. The documentary film A Tuba to Cuba captures the Preservation Hall Jazz Band, one of New Orleans’ premier institutions, doing exactly what the title says: bringing its traditional Crescent City sound into direct contact with Cuban musicians and stylistic idioms, exploring a historical connection freighted with meaning. The soundtrack album, naturally, is a blast, ranging widely from the street parade feel and exuberant horns of “Tumba” and “El Manicero” to the crisp, bright strings of the tres on “Descarga del Son” and “Las Palomas.”