What constitutes musical truth? Is there really such a thing as musical authenticity (by which I don't mean using period instruments, or playing without vibrato) in the sense of giving voice to an absolute sincerity of emotional or expressive utterance? Or is music a combination of stylistic convention and structural formula that means composers conceal their true identity – whatever that might be – so that the search for the single true voice of a composer is always a confusing game of shadows?

The huge output of Russian composer Alfred Schnittke raises these sorts of questions – and some even more profound ones about musical meaning and historical signification. Take this monstrous music for example, his First Symphony, during whose composition Schnittke coined the phrase "polystylism" to cope with a musical aesthetic in which the kitchen sink is just the start of what he chucks into his "symphonic" structure. On the surface, you're listening to a large-scale, four-movement symphony that lasts a Mahlerian 75 minutes or more, and which ought to be the heir to a symphonic tradition whose immediate predecessor, in Russian music, is Shostakovich. It's also a piece that should signal the start of the mature composer's style, written when Schnittke was in his mid-30s. But what you actually hear is an hour-and-a-quarter-long pile-up of musical quotations and strange symphonic theatre. There are references – more like unabashed thievings – to melodies and whole musical chunks from Tchaikovsky, from Strauss and from Chopin; there's even a full-on jazz improvisation in the middle of the second movement, a set for violin and piano; and the whole thing is framed by an apocalyptic version of Haydn's Farewell Symphony. The players come on to the stage during the opening few minutes of the symphony and they troop off during the final movement leaving a solo violinist playing Haydn's symphony, only to reassemble to play a gigantic unison C as the symphony's conclusion. But this is more than a music-historical joke. Had it lasted a mere 10 minutes or so, you could hear Schnittke's mashup of the whole of western music as a sophisticated symphonic gag, a parody of the end of history. But the sheer size of Schnittke's symphony demands that you take it seriously. And just as he does not limit himself to any single genre, style or period for his outrageous symphonic pilferings, you have a range of options as to how you take this piece.

You could hear it as one of the great embodiments of musical post-modernism, a defiant and even joyous two fingers to the denizens of stylistic purity who had held sway, in the West at least, during the immediate post-war years. At the other extreme, you might feel that this symphony is among the most nihilistic ever written: instead of even attempting an originality of voice, instead of a belief in the possibility of musical renewal, all that remains is to regurgitate the past as a grotesque cavalcade, an enterprise for which the moniker "symphony" is nothing more than a cynical sticking-plaster, since any pretence of "symphonic" coherence belongs to another musical universe than the surreal space that this piece creates.

I'm not sure. I think Schnittke's First Symphony (he wrote eight, left a ninth unfinished at his death, and there's a Bruckner-style symphony number zero that he didn't acknowledge as part of his canon) is probably both, neither, and more than either of those extreme interpretations. Above all, it's a thrilling and disturbing musical riot if you ever have the chance to hear it live. But it's also a fragment – albeit a massive, hulking planetoid of a fragment – of the whole of Schnittke's catalogue of orchestral, vocal, chamber, theatre and film music, all written in his 63 short years, the last of them scarred by the series of strokes that would end his life in 1998.

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There's much to explore, and much of it is available on YouTube, but to give you a sense of the range of Schnittke's voices – or masks, or truths – listen next to his Piano Quintet, written shortly after the First Symphony in the wake of his mother's death. Where the symphony is a cataclysmic colloquy, the Quintet sounds like a single-minded expression of lament and loss. That's because of the directness and the bleakness of its emotional expression above all in its third and fourth movements, music that Schnittke said "are real experiences of grief which I would prefer not to comment on because they are of a very personal nature". The final fifth movement is a surreal lullaby in which a short melody in the piano part is encircled by sinister string lines; the music resolves into an image of limbo, as the piano repeats its tune into the infinite.

So is the quintet the "real" Schnittke, the harbinger of his echt-compositional voice? Probably not, if you listen now to this piece, one of his most famous: the Concerto Grosso no. 1, which returns to the hyper-real world of the First Symphony, but in a more compressed and in a sense still more stylistically extreme form. In the Concerto Grosso, Schnittke said he wanted to realise "one of my life's goals … to overcome the gap between 'E' (Ernstmusik, serious music) and 'U' (Unterhaltung, music for entertainment), even if I break my neck in doing so!". That means that beneath and within its frame of pseudo-baroque figuration, you'll hear, as Schnittke's biographer Alexander Ivashkin says, "the transformation of a cheerful song chorale of Soviet schoolchildren, a nostalgic atonal serenade, quasi-Corellian allusions" – as well as Schnittke's grandmother's favourite tango, and quotations from his film scores. The recitativo central movement, the work's "atonal serenade", though, rhymes with the Quintet's grief-stricken passages; as if this movement were the skull beneath the work's polystylistic skin.

So if it's not in the Concerto Grosso, perhaps Schnittke's real voice is music like this, his Concerto for Mixed Chorus, composed in the mid-1980s, music that strips back any playing in the mud of music history to make an avowedly spiritual statement, a piece that confirms Schnittke as a composer of some of the most important religious music of the late 20th century (born to an atheist Russian Jewish father in 1934, he converted to Roman Catholicism in 1982). You can hear the same essentially devout spirit animating the Fourth Symphony, especially its final few minutes, a setting of the Ave Maria that Schnittke wanted to bring together Jewish, Orthodox, Catholic and Lutheran ideas and musics.

In his last years, Schnittke composed some of his most austere music, which seems, on the surface, to be the distillation of his life in music, and a radical simplification of its means and methods: listen, for example, to the last movement of the Eighth Symphony, or any of the Ninth, deciphered from Schnittke's handwriting: because of the strokes he suffered, he was forced to write with his left hand. Is this, as Gerard McBurney thinks, the Schnittke whose music will prove the test of time, or will it be his more notorious polystylistic pieces that will continue to be heard as the heart of his achievement? Your idea of the real Schnittke will differ from mine, or from anyone else's for that matter; the real legacy of Schnittke's music lies precisely in its multidimensional exploration of what musical truth in the 20th century might be, from chaotic polystylism to heartfelt spirituality – and everything in between.

Five key links

Symphony no 1

Concerto Grosso no 1

Concerto for Mixed Chorus

Piano Quintet

Symphony no 8