The Metropolitan Opera season is over, and so is the Met Orchestra season: Last week, that extraordinary band gave a final concert in Carnegie Hall. They are an opera orchestra that plays like an orchestra orchestra — a top-flight one.

This is thanks to James Levine, the Met’s music director, who was on the podium at Carnegie. He began with one of his favorite composers: Elliott Carter. This was Mr. Carter’s Variations for Orchestra, composed in the mid-1950s. It is one of his best pieces.

A couple of seasons ago, Lorin Maazel performed it with the New York Philharmonic, in masterly fashion. Mr. Levine was this way too.

Under his baton, the music was neat and orderly — but also fluid. Mr. Levine conducted the entire work almost seamlessly. There was hardly a hiccup, and everything fit.

The orchestra’s sound was modern but not ugly (if you know what I mean). Every part was clear, but not sterile. The orchestra demonstrated great virtuosity, both collectively and individually.

The brass were robust and burly, but unblaring. The flute was lovely and scampering. In one variation, the unison playing of the strings was exemplary. Elsewhere, the timpani were forceful — even savage — yet somehow elegant.

Yes, this is a good piece, and it was played very well.

At the end, Mr. Carter took his bows, standing at the foot of the stage. He, and the music world, will celebrate his 100th birthday in December.

Following the Carter was the Schumann Piano Concerto, whose soloist was Jonathan Biss, the young American. He did not have his best outing, and the trouble began immediately: in Schumann’s famous opening passage.

Mr. Biss generated curiously little volume. And the passage was choppy, sort of picked at.

As the first movement unfolded, trouble continued. There were odd accents and emphases. There should have been more of a singing line. There should have been more darkness, when Schumann wanted to brood.

Many figures and passages were rushed and slighted. There was a general lack of authority, a lack of command. Much of the cadenza was muddy, in addition to rushed. And sound continued to be strangely weak and superficial.

Mr. Biss had his stylish moments — but too few of them. The middle movement was decent. And the closing movement was basically correct — but without flair. Without that enjoyment and sparkle and savoir-faire that makes this music great.

Mr. Biss is a talented man, who has played laudably well in the past. He will again.

As for Mr. Levine, he conducted his heart out, displaying huge vigor, in addition to knowledge and sensitivity. And the oboe, which has an important role in this concerto, was noteworthy.

When Mr. Levine returned after intermission, the audience screamed out its affection for him. And he gave them a strong, hard-driving performance of Tchaikovsky’s Symphony No. 4. Mr. Levine is not particularly associated with this composer. Though, as soon as I say that, I reflect that he is responsible for maybe the best-conducted “Eugene Onegin” on record.

The orchestra played with all the strength and alacrity that Mr. Levine wanted. The Scherzo — with all those pizzicatos — was especially good. Almost never will you hear it played with such precision.

This concert was marked by Mr. Levine’s energy, an energy that we have seen and heard a lot this season. After the Tchaikovsky ended, Mr. Levine wove in and out of the rows of the orchestra, hailing his players.

Mr. Levine will not stay at the Met forever. But maybe we can think about that another day.