What do you think of when you think of Italian music? Now here’s some Italian music that isn’t that. This, in a nutshell, is the concept behind the National Symphony Orchestra’s contribution to “Unexpected Italy,” a festival “lite” at the Kennedy Center this month. The final program, which opened Thursday, included two works the orchestra had never played before, and one familiar piece that was offered with a strong Italian accent.

There were other unexpected elements to both programs. The first one ended up being repeated at Carnegie Hall, to considerable acclaim, after the cancellation of Gianandrea Noseda’s scheduled tour with the Teatro Regio Torino left an open date into which the orchestra could jump. Unexpected about Thursday night’s program was that it was streamed live on Facebook, and it’s still up there, which means that all of you who weren’t there can hear the whole thing — and compare your reactions with my own. (It’s on the National Symphony Orchestra page on Facebook.)

The programs, of course, bore the heavy stamp of Noseda, whose local popularity seems to be growing as he nears the end of his second season as the orchestra’s music director — to judge, not least, from the fuller houses when he performs. In charming remarks to the audience from the podium, Noseda offered a thumbnail outline of the program, which presented three composers of roughly contemporaneous dates: Respighi, Rachmaninoff and Casella. Of these, Casella is the hardest sell because he is the least familiar, but Noseda treated him as if he were a known quantity, both in his remarks and in his performance of the 50-minute Second Symphony, which closed the program.

One “unexpected” feature in the first half was that the Respighi piece was something other than one of the famous Roman trilogy: the second suite of “Ancient Airs and Dances,” adaptations of lute music that retained a sense of crisp strumming in Noseda’s careful reading, set off with the light metallic sprinkles of four-handed harpsichord and celesta. The orchestra seems to have gained focus and precision under Noseda, although there still were moments when it had trouble playing together, the flutes especially sounding a little fuzzy; yet the whole thing was altogether tighter than Stravinsky’s “Pulcinella,” another 20th-century orchestration of early Italian music the orchestra played last year.

The Italianate element of the Rachmaninoff was Paganini, on whose work the “Rhapsody on a Theme of Paganini” is based. Not Italian, despite his name, was the debuting pianist Francesco Piemontesi, a Swiss protege of Alfred Brendel, who is known for his Mozart and who brought a very unexpected clockwork, light-fingered approach to a piece that is generally the quintessence of romance. Another theme of the program, according to Noseda, was pieces that adapted much earlier music, and his conducting brought out an unfamiliar sense of the archaic, offering light and air and, of all things, restraint around the pianist’s tinkling, giving a distancing sense of unfamiliarity even to the piece’s most cinematographic effusions. One might not want to hear it played often this way, and Rachmaninoff is not strictly in Piemontesi’s wheelhouse, but the audience was ecstatic, and the soloist thanked them with an encore, the second movement of Bach’s Italian concerto.

Noseda saved the big guns and the fortissimi for Casella, a composer he has energetically championed. The second symphony was written in 1908, and it exudes the spirit of Mahler, in zeitgeist as well as in its particulars: It has a Mahlerian size and sprawl and collagelike aspect, with military marches and rising strings and flecks of Wagnerian brass and even a touch of percussion reminiscent of sleighbells in the slow part of the wild second-movement Adagio. It isn’t Mahler, of course, but it does help flesh out our context for a bygone musical epoch, with a brooding dark angst and lowering of percussion and final apotheosis that’s all its own. Measuring it against the yardstick of masterpieces is not useful; I was very glad that it was played, and that I got to hear it.

The program repeats Saturday night.