A central pianist of our time, Alfred Brendel, played a recital of central repertory in Carnegie Hall. This was on Monday night. The venerable Austrian is celebrating his 75th birthday this year. And, in his recital, he displayed considerable experience, wisdom, and skill.

The program was Haydn, Mozart, and Schubert – but not in that order. Mr. Brendel chose an unusual order, and a satisfying one. He began with a Haydn sonata, and moved on to a Schubert one. After intermission, he played two works of Mozart, neither a sonata! These were the Fantasia in C minor and the Rondo in A minor. And he completed the program with another Haydn sonata – kind of a full-circle deal.

That first Haydn sonata was that in D major, Hob. XVI:42. This is in two movements, not to be confused with another Haydn sonata in D major, long popular with students (and others). In any case, Mr. Brendel handled his sonata nicely.

In the first movement, he showed charm and grace, and also balance: balance between the hands, balance of thought – simply balance. This is a lovely quality for Haydn, and other composers. Every voice was clear, although sometimes Mr. Brendel was on the verge of overpedaling. (Which is not quite the same as overpedaling, is it?)

You have heard the second movement (Vivace assai) done more sparklingly. Impishness and merriment are not Brendel specialties. But he certainly had enough of Haydn’s spirit, and he ended the movement, and the work, with a suave matter-of-factness (if you can imagine).

His Schubert sonata was No. 18 in G major, D. 894, rarely heard. In fact, most of the Schubert sonatas are still relatively rarely heard. Artur Rubinstein, the late, great pianist, used to play all the Schubert sonatas, at home, for himself. He would read through them, for his own edification and pleasure. But he did not think they could be presented to the public – they were too long, too repetitive, too strange. Audiences would not sit still. Pretty late in his career, he played but one sonata, in public: the famous B-flat major, Op. posth.

In Mr. Brendel’s hands, the opening of the G-major sonata was beautiful, chorale-like. And he provided some more of that balance we heard in the Haydn. His octaves sang pleasingly. Some of his trills and turns were a little sluggish, but not ruinously so.

And Mr. Brendel displayed a fierce musical concentration (all through the recital). Don’t they all concentrate? No, not like this, not like Mr. Brendel. This concentration – this artistic focus – is especially important in Schubert, with his “heavenly length” (to borrow a famous phrase). (Sometimes length in Schubert does not seem so heavenly.)

As the sonata progressed, Mr. Brendel’s passagework was not always the smoothest. But we have bigger fish to fry in this work. Mr. Brendel conveyed its happiness, its satisfaction, its occasional holiness. Always, he was unforced, rather internal. Sometimes Schubert gives the impression of having composed for himself – not for the public. Mr. Brendel seemed to be playing for himself, while we were listening in. In this sense, Mr. Brendel did not put on a “performance”; he simply let his Schubert unfold.

Mozart’s Fantasia is an ingenious, bravura work, and it must be played with musical confidence and authority. Mr. Brendel did indeed. His understanding of the rhythm was excellent, and so was his phrasing. He unified the various sections neatly. There was not a lot of fire – Classical fire – where you might have expected it, but this pianist’s spine was unquestionable.

And the Rondo in A minor? This is one of Mozart’s most cherished piano pieces, for good reason: It is a small masterpiece, ever remarkable. When Mr. Brendel began, he provided great relief, because he had chosen a sensible tempo: This rondo is often killed, or harmed, by slowness. He was undawdling while being in no way rushed.

Moreover, he was fairly straightforward in this piece, while not too plain. Others have played the Rondo more hauntingly, sinuously – but Mr. Brendel got the message across. Again, some of the ornamentation was blurred and slurred, but otherwise Mr. Brendel was all clarity.

The Haydn sonata serving as the finale was that in C major, Hob. XVI:50, one of Haydn’s greatest works for the keyboard, and quite possibly his most popular sonata. Mr. Brendel started with some nice puckishness. The ensuing chords did not exactly ripple, in Richard Goode style (that American pianist is a master of this sonata). But they were okay. While never wayward, Mr. Brendel showed nice musical imagination, giving us some variety in repeats.

He barely paused before launching the second movement (Adagio), which he lent a wonderful shape and character. Rather, he brought out the shape and character that Haydn has written. And in the closing movement, he was crisp, forceful … and witty. What was I saying about merriment not being a Brendel specialty? This music, this playing, was undoubtedly merry, witty, and everything else it needed to be.

Through the decades, many people have considered Alfred Brendel the great heir to the Schnabel tradition, the great purveyor of the canonical, Austro-German repertory. Others of us have not quite seen their point. But on Monday night, Mr. Brendel showed where they got that point. He played like the wise, expert man of his reputation.