One of the leading string quartets in the world, the Alban Berg Quartet, is hanging it up. They will disband at the end of this season, after a 37-year run. They are a Vienna-based ensemble, and they began in that city, all those years back. Nixon was in his first term as president. And the president of Austria? Franz Jonas.

On Wednesday night, the Berg Quartet played its final New York concert. They did so at the Society for Ethical Culture, under the auspices of the Chamber Music Society of Lincoln Center. And it was a good concert.

You will want to know whether the Berg Quartet played the Berg quartet — the String Quartet, Op. 3, of Alban Berg. They certainly did. They also played a great string quartet of Haydn, father of the genre; and one of Beethoven’s last — which is also one of the greatest works of music we have.

This was a perfectly chosen program for a valedictory concert from this ensemble.

The Haydn quartet they played was the one in G major, Hob. III:81, Op. 77, No. 1. (A lot of cataloging, I know.) This is one of the master’s final string quartets, and it is full of his genius. The Berg Quartet played it with full maturity — with true understanding and proficiency. In their phrasing, dynamics, and overall conception, they were exemplary.

The first movement was appropriately marching and jaunty. And the players emphasized Haydn’s development of the music nicely. The slow movement, Adagio, was marked by unity — the players’ unity. And the cellist, Valentin Erben, made some really beautiful, dark sounds. Over time, this movement became practically symphonic (late Haydn, indeed).

The next movement is a minuet, having a Presto section. And, in this section, the players gave us what I can only call a shuddering merriment. It was extraordinary — and just the effect Haydn was after, I believe. As for the work’s Finale, it clipped along satisfactorily.

Please note that the totality of this performance was greater than its particulars. Musical values were greater than technical achievements. In general, the group’s sound was decent, no better; and the same goes for its intonation. There were some stray notes, and some scratchings. And the players were not always perfectly together.

But, again, that musical maturity — wisdom and spirit — won the day.

Alban Berg wrote his only string quartet in 1910, when he was in his mid-20s. The work is in two movements. And the Berg Quartet gave a fine account of it — as any group by that name had better.

The first movement was nervous, edgy — Bergian. The players were both clinical and musical. They were precise, exacting, and brainy; but they remembered that they were playing music, not working out a scientific experiment. In these hands, every line was clear; but the overall sound — the meshing — was what mattered. And the players breathed well, rising and falling together, and with Berg.

As for the second movement, it, too, was apt. It was gnarly but clean. The entire movement was fraught with a kind of searching, typical of this composer. And an impassioned solo flight from the cello was downright startling.

The Beethoven quartet chosen was the Quartet in A minor, Op. 132. This is the one with the beloved, miraculous slow movement in which Beethoven gives thanks to God for health recovered.

As earlier in the concert, the Berg Quartet did some quite sloppy playing. But they never did anything stupid, musically, and they never did anything departing from taste. These four know something about music; and they know something about string-quartet playing.

Beethoven’s second movement is marked Allegro ma non tanto, and it is a very interesting thing: It is earthy — very earthy — and it is heavenly. And this ensemble brought out both of those elements superbly.

And the immortal slow movement? The Berg Quartet simply went ahead and sang it. They were fairly straightforward. They were also more sinewy and vigorous than most ensembles are in this music. Their accents were sharp.

You have heard the movement more beautiful and elegant, and you have heard it more sublime. But what the Berg Quartet did with it was admirable: They sort of got out of Beethoven’s way. And that is a favor.

The artistic directors of the Chamber Music Society, David Finckel and Wu Han, wrote a program note. Of the evening’s guests, they said, “Their gifts have sustained and bettered the lives of thousands of listeners, and they have pushed the global standard and appreciation of quartet playing to ever higher levels.” Those are warm words — and true.