New Orleans and the shores of Cuba are about a thousand miles apart, close enough to have instigated a centuries-old cultural exchange and shared historical touchstones but, in other ways, so far from one another. NOLA’s Preservation Hall Jazz Band visited the island in 2015 and made a documentary film about their travels, and this collection is ostensibly its soundtrack, augmented by new tunes written on their return. Its diversity is its greatest strength: Cuba, like New Orleans, is not about one style of music, and A Tuba to Cuba does as much as possible within its 43 minutes to make that clear. Its leadoff track, all 49 forlorn and yearning seconds of it, features a lone tenor saxophone played in a small space somewhere in Havana by Clint Maedgen, but the mood picks up soon enough with “Tumba,” all pulsating polyrhythms and celebration. “Keep Your Head Up,” featuring a lead vocal by the alluring Eme Alfonso, is a spicy dish of condensed cream of party, irresistibly rhythmic—if the PHJB has ever had more fun cutting a tune, this fan would like to hear it. The liner notes liken the number’s spellbinding chanting to a Mardi Gras Indians march in the band’s hometown, and from there it’s nothing but a straight line to Havana. As for that tuba, it’s here, and there, but the Pres Hall folks aimed for, and discovered, something higher on this set, which runs the glorious gamut from the solo guitar of Alejandro Almenares, on “Las Palomas” (written by his father) to the sly Latin soul of “Kreyol” to the full-band blast of “I Am.”