Timo Andres. (Courtesy of The Phillips Collection)

Contemporary composers don’t have an easy time of it. If their music is performed at all, it’s usually shoe-horned in between Haydn and Dvorak, often to the alarm of all parties concerned. But the Phillips Collection has turned that clumsy model on its head by inviting a young composer — the gifted Nico Muhly — to design his own concert series, with free rein to choose everything from performers to programs. And if Sunday’s opening concert — which tied Muhly’s own music to that of Igor Stravinsky and Timo Andres — is any indication, the series will be a highlight of the Phillips’s winter season.

The concert showcased Andres himself at the piano, with the Russian American Yevgeny Kutik on violin. Opening with Muhly’s “Compare Notes,” a work premiered a few years ago at the Library of Congress by violinist Daniel Hope, Kutik immediately put his own distinctive stamp on the music. “Compare Notes” rings with a kind of direct, almost urgent authenticity. That seemed to suit Kutik perfectly; he turned in a vivid and captivating performance, and if his reading was perhaps less glowing than Hope’s, it was no less convincing — and maybe even more so.

Yevgeny Kutik. (Courtesy of The Phillips Collection)

That sense of directness and vitality set the tone for the entire concert, which may explain the program’s striking sense of cohesion. Or perhaps it was Kutik’s assured and full-bodied playing, which (supported impeccably by Andres) brought a kind of rough-and-tumble lyricism to two neo-classical works by Stravinsky, the 1932 “Duo Concertante” and the 1933 “Suite Italienne for Violin and Piano” (based on the Pulcinella ballet). Kutik, who was born in Minsk, Belarus, has a clear affinity for Stravinsky’s earthy, rich chamber music, and his reading of the “Duo Concertante” was the most characterful — and maybe most satisfying — you’re ever likely to hear.

But the violinist may have reserved his most insightful playing for the premiere of “Words Fail,” a one-movement “song without words” he commissioned from Andres last year. The work, Andres explained, was an attempt to grapple with his own aversion to vocal music (words are “one thing too many” in music, he said) by exploring the voice-like qualities of the violin. From a descending lament, the work slowly gathers power through overlapping variations, becoming darker, more ambiguous and more complex before building to a soaring climax. Kutik and Andres gave a persuasive, deeply thoughtful reading to this involving new work.