Vienna Waltzes was one of the New York City Ballet’s greatest hits. It premiered in 1977, a decade in which George Balanchine was often off balance for any number of reasons (he would die six years later, in 1983). Balanchine had explored the waltz before, in the doom-laden La Valse (1951) and the ornate Liebeslieder Walzer (1960). But in Vienna Waltzes he gives his audience a history lesson in five movements—from the waltz in early folk form to its sweeping sensual refinement in European ballrooms. The New York City Ballet ends it 2021 digital season with Vienna Waltzes, a performance that was filmed in 2013. The heart-stopping fifth movement, set to waltzes from Richard Strauss’s 1911 opera Der Rosenkavalier, captures fin-de-siècle romanticism at its pinnacle. —L.J.