On Sunday night, Salzburg Festival offered a most interesting chamber concert. Actually, it was two-thirds a chamber concert, one-third a piano recital. On the bill were Schnittke, Tchaikovsky, and Schubert.

Alfred Schnittke was a Russian composer who lived from 1934 to 1998. And he composed his String Trio in 1985. It is a work of almost unrelieved despair: bleak, anxious, fearful. Every now and then, you get a churning outburst. And, once or twice, a ray of hope tries to break through. But it is quickly defeated.

The entire work smells of the Soviet Union, like much else in Schnittke’s corpus (and like much else from composers in that country).

And the trio was given a very good performance in Salzburg’s Mozarteum. The violinist was Leonidas Kavakos, who, though Greek, is something of a local hero: He is artistic director of the Camerata Salzburg. And you may recall that, last season, he gave two of the best concerto performances in New York (one of the Berg concerto, one of the Tchaikovsky).

The violist in this threesome was Kim Kashkashian, from Detroit. What is it about Armenian-American string players from Detroit? Two others are the Kavafian sisters, Ani and Ida, both violinists. And the cellist was the young Frenchman Gautier Capuçon, who sometimes forms a duo with his violinist brother, Renaud.

In the Schnittke trio, these three were composed and clear, not adding unnecessary emotion, letting the music speak for itself (which it does very well). To my mind, Mr. Kavakos’s chief characteristic is strength, in many senses. Ms. Kashkashian was alert and competent. And young Mr. Capuçon was absolutely self-possessed, confident in his technique and his thinking.

Mr. Kavakos ended the trio with some otherworldly effects — high, high in his instrument’s range — that were dizzying and chilling.

After about 35 minutes of Soviet suffering, an intermission was needed, and that’s what we got. When we returned, we had another trio, from another Russian composer — who worked in another time and place. This was Tchaikovsky’s famous Piano Trio in A minor (1881–82). And Messrs. KavakosandCapuçonwerejoined by Elisabeth Leonskaya, a pianist who left the Soviet Union in the late 1970s and settled in Vienna.

The first movement of the trio did not go well. Tempos were deliberate, not to say slow. And Ms. Leonskaya did not exhibit her best pianism: She was blocky, errant, and blunt. Phrasing and accents were strange, and not beneficial to the music.

On the plus side, Mr. Kavakos captured some of the nobility of the movement, and Mr. Capuçon played with considerable suavity. By the way, he has long virtuoso hair, which flops in his face, romantically.

In this movement, nothing could overcome the slow tempos, which simply killed momentum, and killed the music. There is more than one way to play this movement, of course. But Sunday night’s did not succeed. This interpretation was pretentious, wrong, and nearly insufferable.

The second movement — Theme and Variations — started no more promisingly. Instead of playing the opening measures straightforwardly, Ms. Leonskaya fussed with them, and she did so at a cruelly slow tempo. The variations were an improvement over the first movement, however, with some top-drawer playing. For example, Mr. Capuçon was delicious in a drunk and woozy waltz.

But the second movement as a whole did not rise above the adequate. The Finale (as Tchaikovsky calls the penultimate section) was a bit short on its tingling joy. The Coda wailed decently, but not especially movingly. The entire movement fell victim to okayness.

I must report, however, that the audience went positively mad for this performance. You should have heard the shouting, foot stomping, and cheering. The ovation went on and on. I don’t believe I have ever seen so many curtain calls for a chamber performance. Perhaps people were simply happy to have heard the piece. And everybody is happy to be at the Salzburg Festival.

After another intermission, Ms. Leonskaya returned to the stage alone, for a Schubert sonata. This was the Sonata in G major, D. 894, one of the composer’s grand, beautiful, and profound late works. Ms. Leonskaya played it in honor of Sviatoslav Richter, the great Russian pianist who died ten years ago. Ms. Leonskaya herself had an association with Richter: They played two-piano and four-hand music together.

The first measures of the sonata were a relief: Ms. Leonskaya played them perfectly, with nothing awkward, nothing willful. She just let the music flow. And she would continue to do so throughout the sonata.

She was warm, musical, and intelligent. She was smart about tempo, smart about rhythm, smart about pedal and phrasing and weight — everything. And, in her hands, this long, slightly unwieldy work cohered. You could hear the wisdom of years in Ms. Leonskaya’s performance. It was a fitting tribute to Richter, and to Schubert.