The Emerson String Quartet is celebrating its 30th anniversary, and, in a way, Carnegie Hall is celebrating them: The ESQ is playing a slew of concerts in the hall, ending June 17. This is a huge and rare honor for a string quartet (or for anybody, really). You could even say that the series suggests that the ESQ is the preeminent string quartet in the world.

Or would that be New York- and Carnegie-centric?

Midst all the celebrating, the ESQ is celebrating Beethoven — playing his 16 string quartets, but playing them “in context”: interspersed with other works, written before, during, and after. The series includes two contemporary composers: Wolfgang Rihm and Kaija Saariaho.

The ESQ is bent on making musicological points — which is fine, provided they perform well.

Thursday night’s concert was all-Classical, starting with Haydn’s String Quartet in C major, Op. 33, No. 3, known as “the Bird.” (This opens up the following headline: “Emerson String Quartet Gives Carnegie Hall the Bird.”)

How do you want your Haydn? You want him refined but not prissy; respectful but not boring. The ESQ pretty much delivered on these fronts. But there were problems.

The beginning measures featured some scary intonation. And the playing throughout the first movement was a bit thick, texturally. (This despite the fact that the violist, Lawrence Dutton, produced some necessary nimbleness.) The biggest problem, however, was that the movement was a tad sleepy — almost boring, actually.

From my observation, the ESQ never plays outright badly. But like any other group, or individual, they can play without verve or insight — they can succumb to autopilot.

The second movement, too, had some bad intonation, or perhaps it was a question of tuning. But we also heard some attractive playing: some appropriate simplicity and innocence.

Can the third movement, Adagio ma non troppo, be played with more elegance and beauty? Oh, yes. But the final movement — a rondo — burbled nicely. The cellist, David Finckel, played with particular clarity, accuracy, and style. One may forget what a good cellist he is, because he doesn’t play major concertos with major orchestras every night.

In my view, Mr. Finckel should not hide his light under the bushel of chamber music. (No offense to chamber music, which, of course, we all revere.)

Next on the program was a Mozart quartet, that in C major, K. 465, known as “the Dissonance.” Why? For its unexpected, not quite tonal beginning. The ESQ handled this beginning fairly well – but there was a disappointment not long after.

Mozart’s first movement has two sections: Adagio and Allegro. And the transition from one to the other should be a delight, a relief, and a marvel. In this group’s hands, it was rather flat — unremarkable. But overall, the Emersons did much better in the Mozart than they had in the Haydn. Technical problems aside, they were more involved, more musical, and more convincing.

I should mention that, in that first movement, Mr. Dutton sent forth some serious beauty of sound. And the second movement, Andante cantabile, was nicely calibrated, from everybody. This is a long work, K. 465 — it’s important not to get bogged down in details, in passing moments. The Emersons seemed to keep the scope of the work in mind.

The minuet could have been lighter, more buoyant, more tense, more springy. And the finale could have been played with more gusto and heart.

Still, this was a distinguished, and ESQ-like, performance.

On the second half of the program was a single work: Beethoven’s String Quartet in C major, Op. 59, No. 3 (a “Razumovsky”). You may be aware that all of these string quartets — the Haydn, the Mozart, and the Beethoven — are in C major. Did we have too much of that key in one evening? Was Carnegie Hall swimming in whiteness? (I imply nothing racial.) Maybe — but you have to admit that these are pretty good composers.

Given that the ESQ’s series is essentially Beethoven’s party, it was only fitting that the best playing of the night should have come at the end: in Op. 59, No. 3. The Emersons were arresting, sensitive, and almost completely unified. They played up to their reputation, and venue.

In the opening movement, the first violinist did some struggling, but otherwise he was fine. Mr. Finckel gave the second movement the pulse and mystery it needs — he did this with dark, well-judged pizzicatos. The third movement, the minuet, was both smooth and marked. And the last movement — Allegro molto — was a rollicking good time.

Five years ago, the ESQ put out an album of encores (on Deutsche Grammophon). And the most exciting thing on it is that movement — Beethoven’s Allegro molto. Was Thursday night’s account as good as the studio recording? Maybe not — but it was still a technical and musical feat.

And, speaking of encores, I doubt anyone would have minded if the ESQ had repeated it.