A critic once wrote of his work that "it was so portentous, so downright antagonistic, that it was a wonder anybody listened to it".
But musicians did perform his music and audiences listened to it in concert halls throughout the world.
Music Russian to the core
Schnittke was born in the central Russian town of Engels. Half Jewish and half German, he had the misfortune to belong to two of the Soviet Union's least favourite ethnic groups.
His family moved to Moscow in 1948 where Alfred, by now bilingual in German and Russian, studied at the music Conservatory.
Although Schnittke later moved to Germany, his music remained very much rooted in his homeland.
There was an anxiety, foreboding and fury within it, which identified it as Russian to the core.
Symphony banned
He was occasionally compared with Shostakovich, and like him, was influenced by Jazz.
His First Symphony, performed for Soviet audiences initially in 1974, contained elements of Gregorian chant, Baroque and romantic music - and jazz.
The brooding style of composition did not endear him to the Soviet authorities.
The symphony was considered so experimental that it was banned.
But over the next decade, his reputation spread as Russian colleagues began to introduce his work to western audiences.
Prolific composer
He wrote a total of 35 live performance pieces, including an opera ('Life with an Idiot') and a further 60 film scores - a prolific output from a man who spent his last 13 years partially crippled by the effects of a stroke.
Schnittke had been living in Hamburg since 1990, but there are plans to return his body to Russia.
A spokeswoman for the Moscow Composer's Union said his body will be brought back for burial in Moscow's famous Novodevichy Monastery, alongside some of the country's most revered artists, such as Chekhov and Shostakovich.
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