Concerts of holiday favorites, the “Messiah” and other seasonal staples are the norm this month, but the American Symphony Orchestra offered an antidote to festive cheer last week at Carnegie Hall with a program called “Requiem for the 20th Century.” Appalled at the state of the world? Well, just remember that the last century was even grimmer, the lineup seemed to suggest.

The ensemble has a reputation for intriguing programs (and sometimes uneven performances), but on this occasion standards were high throughout, with Leon Botstein leading polished and exciting interpretations lifted by the superb work of the Bard Festival Chorale.

The program featured works by three composers deeply affected by the traumas of the 20th century. The British composer Ralph Vaughan Williams, a medic and lieutenant in World War I, eventually became deaf after extensive exposure to gunfire. The Hungarian-Jewish composer Gyorgy Ligeti, who survived labor camps during World War II, lost most of his immediate family in concentration camps. Alfred Schnittke struggled to compose under the dictums of Soviet ideology.

The program concluded with Schnittke’s “Nagasaki” (1958), a memorial to the Japanese city destroyed by an atomic bomb in 1945 and set to a poem by Vladimir Sofranov and translations of texts by Toson Shimazaki and Eisaku Yoneda. Influenced by Carl Orff, Stravinsky and Shostakovich, the colorfully scored oratorio, written while Schnittke was a student at the Moscow Conservatory in the eclectic style that would become his hallmark, attracted the ire of the Soviet authorities.

Mr. Botstein led a bristling performance; ominous and driven in the opening “Nagasaki, City of Grief” and brighter toned in the ensuing “Morning.” The cluster chords, colorful textural effects and outbursts of the striking third movement were vividly rendered here. The mezzo-soprano Sara Murphy sang with poise and emotive force in the ominous third movement, her words underpinned by an insistent ostinato. The chorus sang potently, meshing with the orchestra for a radiant sound at the work’s optimistic conclusion.

The program opened with Vaughan Williams’s dark-hued Symphony No. 6, completed just after World War II. Mr. Botstein conducted a vigorous interpretation, with the sardonic brass fanfares and eerie string motifs boldly executed. The Scherzo could have been rendered with more bite, but the Epilogue unfolded with apt tension, the shimmering violins creating a moody undercurrent.

The program also offered a welcome chance to hear in entirety Ligeti’s arresting “Requiem” (1960), whose score is well known from Stanley Kubrick’s “2001: A Space Odyssey.” The work’s micro-polyphonic textures were superbly rendered here by the choir; Ms. Murphy and the soprano Jennifer Zetlan sang the startling solo excerpts with expressive intensity. The dense vocal counterpoint of the opening section creates a mournful buzz, a searing wave of pain so intense that the more vigorous outcries of the ensuing movements, while haunting and alarming by turn, almost come as a relief.