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Schnittke's second sonata for violin and piano (1968) was his first "polystylistic" work. He subtitled it "Quasi una sonata," which means "like a sonata," or "in the manner of a sonata." Schnittke called it "a sort of borderline case of sonata form," explaining that it was, in a sense, about the process of writing a sonata. "The form is called into question; it seems not to be achieved - and then the sonata is already over." He also called it "a report of the impossibility of the sonata."

The "impossibility of the sonata" for a composer steeped in atonality is that sonata form is based on tonality: it is, in essence, a journey from tonic key to the dominant key and back again. A composer who eschews the whole idea of key is likely to eschew the idea of the sonata. Indeed, after years of avoiding major and minor chords, Schnittke was changing course significantly. "The Sonata begins with a loud, short G-minor triad. That was very important for me," he wrote, "after a very long period of writing exclusively serial music. Suddenly I had to write this piece, without rules of construction. It was, so to speak, a mutiny against everything else. There is a continual exchange between this triad and a dissonant violin chord: the piece seems to stammer. Then, suddenly, the motif B-A-C-H appears…at the end it stands out clearly as the solution. The solution consists of the fact that nothing is solved," concluded Schnittke, since both the minor chord and the atonal material "remain as contrasting elements which are balanced against each other."