Sometimes ensembles just need a trip to New York to focus. This is a perennial problem at the Kennedy Center, where touring orchestras often turn in very good performances just before they go to Carnegie Hall and give truly terrific performances.

Even the National Symphony Orchestra and its music director, Gianandrea Noseda, aren’t immune from this phenomenon. On Wednesday night at their official home, the Kennedy Center Concert Hall, they gave a performance of Act II of Wagner’s “Tristan and Isolde” that went by so quickly, the outlines blurred, a love story seen through a train window. On Sunday afternoon at Lincoln Center, they played the same program so much better that Noseda, in particular, sounded like a different musician altogether.

The NSO and Noseda are on a roll — certainly where public recognition is concerned. Last week, the orchestra announced the launch of its own label with a recording to be released in February, featuring the pairing of Dvorak’s Ninth Symphony and Copland’s “Billy the Kid” suite that closed the NSO’s season last June. On Friday, its second performance of “Tristan” was streamed live on Medici.tv to viewers around the world. In March, the orchestra will embark on its first tour of Asia in 10 years; the following season will see a tour of Europe.

A lot of this attention, though, is about form over content: accepting invitations and raising the orchestra’s profile rather than looking too exactly at what it plays. Are Dvorak and Copland really Noseda and the NSO’s calling card? And for all of his lighthearted “smorgasbord” programs (such as the “dance” program earlier this month, from Strauss’s “Tales From the Vienna Woods” to Florence Price’s “Dances in the Canebrakes”), this season’s overall programming doesn’t significantly vary from the template of “overture, concerto, symphony,” from which Noseda vowed to break away when he arrived.

Even on paper, however, “Tristan” was a clear highlight. Opera, with its extra forces and extra expense, is always a big statement for an orchestra; the New York invitation was significant; and most significantly, the performances marked the American role debut of Christine Goerke, the popular American dramatic soprano who has become a frequent Brünnhilde in the “Ring” cycle but had yet to tackle this arguably even more formidable role. (She is scheduled to sing it onstage next season.)

Noseda, too, is fairly new to “Tristan”; he conducted one run of the opera in 2017 in Torino. At the Kennedy Center, he approached the score with his hallmark light fleetness, the way he conducts Beethoven, or the translucent Verdi Requiem he led here in 2018. Fleetness, though, doesn’t necessarily work with Wagner — not, at least, as Noseda demonstrated it Wednesday night, when he crashed into the piece in a messy flurry of offstage horns, and zoomed along so fast that he left the composer’s leitmotifs fluttering in a colorful, confused tangle in the breeze behind him.

The conductor’s velocity contributed to the urgency and anticipation when Isolde is waiting impatiently for Tristan and underlined the obsessive, consuming drive of their love. But for a listener, it was sometimes hard to tell whether you were nervous with the singers or for them, as Goerke and the American tenor Stephen Gould desperately tried to keep astride the bucking bronco of Noseda’s tempos and avoid being drowned in the waves of orchestral sound. Gould has a large, slightly phlegmatic voice, and on Wednesday he kept pushing dynamically into each note, giving each a little extra emphasis, which created the impression at times of plodding. Goerke, referring to the score on her music stand, sang with appealing warmth but seemed to be finding her way into the role both dramatically and vocally. The music never had time to breathe, and even the haunting “Habet acht” (take heed) of Isolde’s maid, Brangaene, usually a poignant counterweight to the surging love music, failed fully to register in Ekaterina Gubanova’s clear, slightly acidic voice.

The star on Wednesday was Günther Groissböck as King Marke, who enters at the height of the love music’s rapture to discover that his best friend is involved with his wife, thereby creating one of the most famous cases of coitus interruptus in Western art. The long bass ­monologue after the love music is generally either a letdown or a scene-stealer, and Groissböck was the latter, offering powerful singing colored with emotion down to a little, pained vocal shake as he choked out the words “Tristan betrayed me.” As Melot, who betrays Tristan by bringing Marke onto the scene, Neal Cooper showed a clear, strong tenor in a few telling lines before wounding Tristan with his sword — something this concert performance left to the imagination.

In Washington, the NSO is the familiar local team. In New York, under Noseda, they’ve become honored visitors. On Sunday afternoon at David Geffen Hall — the concert venue formerly known as Avery Fisher Hall, still awaiting its promised renovation — was crowded with fans and insiders. And whether inspired by the locale or more secure after two performances, or both, everyone onstage rose to the occasion. Noseda was still fast, but his driving, even panicky approach had softened into something more spacious. The tempos had become malleable rather than hurtling. The score had more shape, the motifs emerged more clearly and, as the singers found more room to breathe, moments that had flown by at the Kennedy Center, such as Brangaene’s “Habet acht,” took root and became moving. Gould found some melting pianissimos, and Goerke unsheathed a saber of sound that shone the way toward her interpretation of the whole role.

And in a city filled with good orchestras, which the night before had been treated to a memorable one-two punch of Prokofiev from the gleaming Chicago Symphony Orchestra under Riccardo Muti at Carnegie Hall, the NSO more than held its own. The NSO has always been an orchestra of unfulfilled potential; these days, it seems, it’s finally unlocking it. If Noseda’s interpretation shifted considerably over the week, the musicians were able to follow him, offering limpid winds and caressing horns, more effective with his restraint than they had been with force.

Even after years of concert-going, it’s always a joy and a bit of a surprise to be reminded how much performances by the same people can vary from one night to the next. There was more to this transformation, here, than just chance and chemistry: Noseda made different decisions on the podium and the orchestra followed him. There’s a humility in being able to change, and letting go of old ideas, to make something better. So it wasn’t even the New York performance of “Tristan” that gave me hope for the NSO’s future: It was the path that all the musicians had traveled to get there.

Correction: An earlier version of this story stated that these concerts marked Christine Goerke's role debut as Isolde. They were her American debut in the role. This story has been updated.

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