Christoph Eschenbach and the National Symphony Orchestra. (Scott Suchman)

People ask where the National Symphony Orchestra stands in relation to other American orchestras. Saturday night’s concert at Carnegie Hall exemplified it pretty well: It seems to be doing very well, while somehow remaining slightly apart from everyone else, engaged in an orchestral equivalent of parallel play.

The concert was a big deal. It was the NSO’s first concert at Carnegie since 2008 and its first there under its current music director, Christoph Eschenbach. And it was the final concert of the Spring for Music festival, a celebration of American orchestras and contemporary programming. All week long, orchestras large and small from around the country offered American works; the night before the NSO concert, the Detroit Symphony Orchestra performed all four of Charles Ives’s symphonies back to back, perhaps the first time the feat has ever been attempted. (Detroit’s music director happens to be the NSO’s former music director, Leonard Slatkin, a stout champion of American music.)

Spring for Music is also about hometown pride. Each orchestra was supposed to bring hometown fans; each fan got a banner in the orchestra’s assigned color to wave at appropriate moments; each concert was preceded by remarks by local luminaries — the Baltimore Symphony was introduced by Maryland Gov. Martin O’Malley. The Buffalo Philharmonic brought more than 1,500 people; the Detroit Symphony musicians draped their chairs with their red banners.

The NSO didn’t seem to be interested in any of this. Although the orchestra has done a lot of American programming over the years — since 1984, the Hechinger Commissioning Fund has been responsible for the creation of more than 60 new works — it opted to offer Spring for Music an all-Soviet program dedicated to Mstislav Rostropovich, who ended his 17-year tenure as the NSO’s music director almost 20 years ago. This was introduced not by a political figure but by Ted Libbey, the former NPR commentator, who, in lieu of uplifting platitudes about the importance of classical music, told personal anecdotes about “Slava” (Rostropovich’s nickname). There were only around 250 hometown fans in the audience; and onstage, though the women of the orchestra wore bright shawls, there wasn’t a hometown banner in sight. The Kennedy Center, one surmises, is not that interested in playing with others.

You could also say, though, that some of the Spring for Music shtick is a little cheesy, and that the NSO found a way to give a very good concert without toeing the party line. In which case its refusal to join in the game is less about cluelessness than arrogance.

And the concert was good enough to support at least some swagger. The NSO’s administration and players keep telling me how much touring focuses an orchestra and puts the players on the line, and this was borne out here. Hearing the familiar orchestra in an acoustically superior hall emphasized the richness of its sound and the improvement in some key areas — winds and brass! — from its last performance here. And in Shostakovich’s Fifth Symphony, the last piece on the program, there was a marked increase in focus and precision from the orchestra’s (already good) performance at the Kennedy Center the week before.

The “creative programming” part of the evening was furnished by Rodion Shchedrin and the late Alfred Schnittke. Shchedrin’s “Slava, Slava” is essentially a celebratory fanfare in honor of Rostropovich, evoking processionals and Mother Russia and appropriate to the occasion.

The Schnittke violin concerto is a bigger, more ambitious piece. By bringing together so many orchestras and works in a single week, Spring for Music creates some interesting resonances, like the juxtaposition of two very different composers’ approach to pastiche — the practice of creating a musical collage from snippets of other musical styles and genres — on successive nights. On Friday, Detroit offered Ives, who in the early 20th century wove bits of American hymns and anthems and popular songs into his symphonies to create an evocative wash of sound, mingling art music with the vernacular with ruddy good health. On Saturday, the NSO presented Schnittke, who, writing at the century’s end, snatched at scraps of bygone traditions to create a nervous and wistful ambiance. A long, pretty melody from the viola becomes, in Schnittke’s hands, a kind of aural minefield, less because it is layered with other instruments than because you are keenly aware that it is ephemeral, a mask, and may be snatched away or crumpled up at any moment.

Having missed the NSO’s performance of the concerto the preceding Friday in Washington, I was happily surprised to find it such a substantive work, and equally happy to hear it in the able hands of David Aaron Carpenter. Eschenbach tends to like very expressive soloists, and Carpenter, long and lean as a modern-day Paganini, fits the type, but to judge from my colleague Robert Battey’s review of his Washington performance, he must have toned down his physical mannerisms considerably for this Carnegie Hall outing. Apart from some soulful gazes heavenward in the long, slow final movement, he didn’t offer any noteworthy excesses. What he did offer was some very strong playing that helped bring alive a potentially difficult work.

The Detroit Symphony, the night before, offered some up-and-down playing of four up-and-down symphonies. Before the performance, Slatkin said, in print, that he didn’t care for Ives’s First, and you could certainly tell from the way he played it; the symphony is the most conventional and arguably the easiest of the four, but the orchestra sounded like amateurs, as if the conductor’s goal was simply to get through it at all. The readings got progressively better through the concise, hymn-studded Third to the ebullient Fourth, which Slatkin dissected a bit for the audience in engaging podium remarks before plunging in. He is no more precise than he was in Washington, and the NSO sounded quite a lot better by comparison, but the DSO offered an engagingly can-do spirit, particularly for an ensemble still recovering from a strike that many people thought might snuff it out altogether.

Overall, the week left a warm impression, although a wistful one: All this unconventional programming has not sparked huge ticket sales, even at $25 a pop, or found future funders, and the festival’s 2014 iteration will be its last.

As for the NSO, the question of how it wants to position itself remains open. It’s an ongoing debate how far an ensemble with the word “national” in its name should represent the music of its own country. Eschenbach was certainly able to play American music with some of his past orchestras — indeed, he led the world premiere of the Jennifer Higdon concerto “4-3” that the Baltimore Symphony Orchestra played on its Spring for Music program last Monday night. But at the NSO, Peter Lieberson’s tribute to JFK is his sole noteworthy nod in this direction. Does it matter?

“We’ve been a great Russian orchestra [under Rostropovich],” Rita Shapiro, the NSO’s executive director, said to me in a phone interview a few weeks ago. “We’ve been a great American-focused orchestra [under Slatkin]. Christoph is much more of a polymath.”

It remains to be seen what kind of identity this chameleon-like orchestra will take on next. But it’s striking that, at this festival, it chose to define itself by looking back rather than ahead, and abroad rather than home.