Sir Andras Schiff will present the third and final “Last Sonatas” concert in February. (Dieter Mayr)

Certain artistic projects are steeped in an air of reverence from the moment of their conception. So it is with Sir Andras Schiff’s “The Last Sonatas,” a three-part exploration of the three final sonatas written by the four quintessential composers of the Classical era: Haydn, Mozart, Beethoven and Schubert. (Washington Performing Arts presented Part 1 here in March.) The very idea is permeated with the air of the elegiac, of lost perfection, channeled by a performer who sometimes seems to move in his own atmosphere, stirred by some inner breeze or lit by an inner light, and certainly to follow his own tempos.

Which added up, in the second installment on Monday night at Strathmore, to something that sometimes threatened to succumb under the weight of its own greatness.

Schiff has a caressing, gentle touch; even at his most emphatic, he draws music from the keys rather than banging it out of them. He spoke at the start of the evening of playing in the Viennese dialect, although his simile specifically referred to his instrument of choice, a Bösendorfer, which he introduced in a few words to the audience before the concert. “I would like to challenge the preconceived idea that a piano has to be a Steinway,” he said, noting the wide range of instruments that were available in Mozart’s and Beethoven’s Vienna. “I think it’s a good opportunity to listen to something else.”

But the idea of dialect extended, in his performance, from the creamy rich sound of the instrument — like a good Viennese coffee with whipped cream — to the way that he drew music out of it, with a kind of lingering sweetness. It would be too facile to describe his performance as smooth when he made such a point of observing nuance; even runs down the keyboard in the Haydn D Major sonata that started the program’s second half were gently subdivided into little groupings rather than offered as one single fluid run. But there was a sense of flow that in the longer works — Beethoven’s Op. 110 and Schubert’s D. 959 — led at times to a sense of exalted torpor: music as opiate, exuding golden dreaminess.

Mozart’s K. 570 in B-flat major, which opened the program, was a glorious appetizer, simple and clear, though exposing a slightly brassy quality in a few ­lower-middle notes on the otherwise superb piano. The Beethoven, however, was a conundrum: Schiff was precise in details, but restrained even in his most emphatic outbursts, pushing at each phrase until he achieved a slightly muted sense of distance: veneration in place of immediacy.

In a program note, Schiff highlighted the difference between “late” works by composers who died young and one like Haydn who lived a long life; there is also a distinction between pieces (like Mozart’s and Haydn’s) written several years before the composer’s death to the quasi-valedictory of Schubert’s final sonatas. The Schubert was in every sense the climax of the night: the Andante tugging almost palpably on the senses, the Scherzo laid out artlessly with Schiff’s distinctive ability to play both a note and the space around it, seemingly at the same time. And yet as the richness of the final movement intensified toward a noble conclusion, the brilliance of the performance became almost cloying. Schiff was perhaps not insensible to the effect, offering two carefully chosen encores to help bring the evening back to earth: first continuing the mood with Schubert’s Klavierstuck No. 1, D. 948, and then abruptly moving into a different dialect with Schumann’s “Ghost Variations.” It seemed, in this context, as refreshing as cool air flowing through a warm room.

The final installment of “The Last Sonatas” project will take place on Feb. 24.