Every student who aspires to a career in classical music should be able to do what the pianist Jeremy Denk did on Sunday afternoon at Alice Tully Hall. I’m not just talking about playing beautifully, as he did in works by Beethoven and Ligeti for a program with the Chamber Music Society of Lincoln Center.

I’m referring to the chatty and insightful prep-talk Mr. Denk gave before performing Ligeti’s Trio for Violin, Horn and Piano, “Hommage à Brahms,” a seminal 1982 work by this giant, who died at 83 in 2006. Mr. Denk began by pointing to the oversized printed scores that his colleagues (the violinist Erin Keefe and the horn player Jennifer Montone) had placed on their music stands, a “sure sign,” Mr. Denk said, that we had come to “the notorious new music portion of the program.”

But Ligeti’s trio, he assured the audience, is a stunning masterpiece, an ingenious modern work that also looks back at music with “nostalgia, distance, loss and farewell.” The piece nods to Brahms’s trio for the same instruments. Ligeti uses one of the most familiar tropes in music, a horn call, as a crucial motif. Mr. Denk played that familiar flourish on the piano and showed how it has been used in ridiculous ways, quoting a passage from Tchaikovsky’s “1812” Overture, and sublime ones, playing the opening of Beethoven’s “Les Adieux” Piano Sonata.

He asked Ms. Keefe to demonstrate how Ligeti introduces the horn call in the violin in a tweaked, unsettled way. Then he had Ms. Montone show how the horn sometimes spins off into passages of high harmonics that are not “out of tune, as you may imagine,” but natural sounds meant to be a little jarring.