For the last several decades, two pianists have been associated with the Salzburg Festival, more than any others: Maurizio Pollini and Alfred Brendel. Why this selection was made, I can’t tell you. Whether it was made consciously, I can’t tell you. But Messrs. Pollini and Brendel are almost the mascot pianists of the Festival.

They are both giving recitals in the Great Festival Hall this year. Other pianists in the spotlight are Rudolf Buchbinder (another Festival favorite), András Schiff (ditto), and the superb Stephen Hough.

Mr. Pollini had his turn on Monday night. The first half of his program was all-Mozart, the second half all-modern (if we can call music composed in the 1930s and ’40s “modern” — and that is a debate for another time).

The pianist began with Mozart’s phenomenal Fantasy in C minor, K. 475. Its opening pages are chromatic and spooky, and Mr. Pollini made them seem quite modern. As he continued, he was intelligent and clear, pure and aristocratic.This was Mr. Pollini at his most effective. He calibrated the piece carefully but naturally. The faster and louder sections got a little muddy (despite the general clarity). But, on the whole, this was “good honest playing,” as a wise pianist I once knew would say.

Mr. Pollini then played the Sonata in C minor, K. 457, a most Beethoven-like work (or maybe, given chronology, we must call Beethoven Mozartean). How did the sonata go? I thought of an old expression: “Second verse, same as the first.” Mr. Pollini played K. 457 almost exactly as he had K. 475.

Tempos were fairly brisk, for Mr. Pollini does not like to linger. He knows how to use an enormous grand piano without making Mozart too grand. And here’s a detail: As a rule, Mr. Pollini plays chords strictly together. That may seem too small or obvious to mention, but you’d be surprised how many pianists fail in this basic task.

The Adagio was notable for its simplicity, and Mr. Pollini shaped this movement beautifully.The third and final movement is marked Molto allegro — and, from Mr. Pollini, it was more Allegro moderato.But, with his exactitude and penchant for definition, he made a case.

At this point, we had Mozart’s Adagio in B minor, K. 540, a brief piece, but utterly profound. Even when you feel saturated with Mozart, he can still stun you. And Mr. Pollini allowed you really to hear the piece. What I mean is that, eschewing interpretation — if such a thing is truly possible — he let you behold the piece in something like a natural state, with the performer to one side.

At his worst, Mr. Pollini is cold, severe, and mechanical. He can resemble an accountant going over his figures, more than a musician dealing with notes, and art, and life. But we had heard almost none of that so far.

We did in the next piece, unfortunately.That was the Sonata in D, K. 576. The first movement could have used much more of a smile, and some sparkle. Plus, Mr. Pollini’s clarity largely left him. He was stiff, muddy, and grim, which is a bad combination, certainly in this music.The middle movement needed more songfulness, and a more generous helping of feeling. Mr. Pollini traversed the closing Allegro with a decent zest.

Odd, though, how muddy he can be, for such a clinician.

I myself would not have done an all-Mozart first half and an all-“modern” second — I would have interspersed these pieces. But Mr. Pollini didn’t ask me, and he has done all right on his own.

Mr. Pollini returned from intermission with Webern’s Variations, Op. 27 (composed in 1935–36). Like most Webern, this is strikingly concentrated music, and Mr. Pollini is a pianist who can really concentrate. Thus we have a good marriage between composer and performer.

Also constituting a good marriage are Mr. Pollini and Pierre Boulez. The latter, incidentally, will conduct the Vienna Philharmonic in the Great Festival Hall on Sunday.Mr. Pollini played his Second Piano Sonata on Monday night. This was written in 1948, when Mr. Boulez was in his early 20s.

Paul Griffiths, in an article excerpted in the program booklet, quoted Mr. Boulez on his sonata. And the composer repeatedly uses the words “destroy” and “dissolve”: He wanted to “destroy what was the first-movement sonata form,” and to “dissolve slow-movement form,” etc. For all his destroying and dissolving, musical traditions survive.

Will Mr. Boulez? That is, will his music, after his departure from the mortal scene, and after that of his personal friends among performers? One can never know for sure, and one pops off at one’s peril, but I have my doubts.

In that article, Mr. Griffiths wrote that Mr. Pollini “always” plays the Boulez sonata “astonishingly from memory.” He did not on this occasion. Out came the music, and out came a page-turner. In any case, Mr. Pollini played the sonata manfully and devotedly, showing that Mr. Boulez is lucky to have this champion. Afterward, Mr. Pollini bowed charmingly to his page-turner, and applauded her.

The Salzburg audience applauded Mr. Pollini at length, and he sat down for an encore — Debussy’s “Sunken Cathedral.” Mr. Pollini had color, sensitivity, and the skill of a musical sculptor. For my money, this was his best playing of the night.

Salzburg Festival until August 31 (for more information, call +43-662-8045-500).