On one level, classical music concerns a dialogue between old and new. This is a programming specialty of the Knights, a New York chamber orchestra that presented an homage to Bach at Dumbarton Oaks on Monday evening. The adventurous musicians even tricked the audience into holding up its end of the musical dialogue in a stealthy final number.

As expressions of Bach’s virtuosity, solo pieces for cello, violin and harpsichord dotted the evening. Violinist Robyn Ballinger was most impressive in the sunny Prelude from Violin Partita No. 3, a constant stream of running notes from which contrapuntal lines emerged.

Playful Bach resounded in Colin Jacobsen’s “Back in Your Cage,” a work for chamber orchestra built on the musical theme C-A-G-E, an oddly pentatonic musical signature for the modernist composer. The driving rhythmic groove of the outer movements, propelled at times by the space-rocket sound of the flexatone, was balanced by the calmer middle section, featuring a mysterious melody sung by some of the musicians.

The same frenetic spirit infused Judd Greenstein’s Flute Concerto, from 2017, featuring much virtuoso figuration from soloist Alex Sopp. Just as the flowing notes grew tiresome, a reflective flute cadenza, answered by shuddering strings and melancholy vibraphone, provided a respite.

Earlier composers offered more sober tributes to Bach with music in contrapuntal styles, such as Stravinsky’s “Double Canon” and Gyorgy Kurtag’s “Hommage à Bach,” both for combinations of string instruments. Most delightful were Ligeti’s “Six Bagatelles” for wind quintet, played with equal parts circus parody and pastoral reflection. Schnittke’s “Prelude in Memoriam Dmitri Shostakovich” came with a surprise, as Jacobsen’s second violin part crept in from the back of the room to join Ariana Kim on the first part.

The turkey platter of this Thanksgiving repast was Bach’s Brandenburg Concerto No. 3, featuring nine solo string parts braided together. Actually, it was more like a turducken, with something stuffed inside, in that the enigmatic second movement, a simple cadence that probably indicated the end of an improvisation of some kind, was replaced by an arrangement of Paul Simon’s “American Tune.”

Simon derived his melody from the chorale set to many different sets of words, most famously “O Sacred Head, now wounded.” In the place of the expected Christmas carol singalong of December concerts, the Knights asked the audience to sing that chorale, in English, as the final piece. The instrumental accompaniment trailed off, leaving just a few brave voices singing this ancient tune in the darkened music room like a ghostly echo.