Sibelius on his Sixth Symphony: "Whereas most other modern composers are engaged in manufacturing cocktails of every hue and description, I offer the public pure cold water". Benjamin Britten on the same piece: "He must have been drunk when he wrote it."

There's already an irony in Sibelius's description of his apparently austere Sixth, given his personal predilection for alcohol. But you can sense what he means right from the start of this less-than-half-hour, four-movement (an outwardly conventional shape of first movement, slow movement, scherzo, and finale) symphony, in its invocation of ancient musical arcana in the strange polyphony he writes for the strings, to be played at music's plainest and most inexpressive dynamic - mezzo-forte, neither loud nor soft; simply, unavoidably, there.

Jean Sibelius - manipulating music's fourth dimension. Photograph: Rex Features

The economy of Sibelius's material, its avoidance of anything approaching emotionally charged rhetoric or expressionist trauma, its repudiation of any ultra-modern clichés, mark this as a very strange symphony indeed for 1923. Sibelius may have thought of it as a purifying corrective to a musical world of modernist angst, but perhaps it was that very plainness that perplexed Britten. How could you write a symphony that seemed, if anything, to retreat in musical time to an era before tonality, a symphony of weird modes and ambiguous scales? And how could you conceive a work that seemed to be about so little: a tension between the scales of C major and a modally inflected D minor, which ends even less demonstratively than it began, with a pianissimo chant for the strings and timpani, music that's the opposite of grandiloquent resolution (such as the end of Sibelius's previous symphony, the huge chords that wrench the Fifth Symphony to a conclusion). Instead, this is music that's so self-effacing it's the equivalent of going for a walk in the snow and covering up your tracks, a symphony that seems to want to leave no mark in the musical landscape at all. Yet if all that's true, how is it that it's this piece - not the more obviously radical Seventh (which Sibelius compresses into a single 20-minute movement), or the single-mindedly dissonant Fourth - that is the single most influential of Sibelius's symphonies for later generations of Finnish composers, such as Magnus Lindberg and Kaija Saariaho?

The autograph score of opening page of Sibelius's Sixth Symphony, kept in the Sibelius Museum. Photograph: Alfredo Dagli Orti/© Alfredo Dagli Orti/The Art Archive/Corbis

I found a clue when I went to the Sibelius Museum in Turku in Finland, where the manuscript of the symphony, one of Finnish music's holiest of holies, is housed. Seeing the symphony in the flesh revealed something even more intriguing than the liquid fluency of Sibelius's handwriting. It was to do with the bar-lines. The rest of the score was in pencil, but the bar-lines, those dividers of musical time, had seemingly been written after Sibelius had written down the notes, in a thick red pencil, and in impressionistic, curved lines rather that straight, rigid marks. That's an extraordinary thought, that Sibelius could have written the piece without those usually essential markers of time to manage his musical imagination. (Even if it's possible, I admit, that Sibelius did exactly the opposite, and made those impressionistic red marks before he wrote the notes, but bear with me for the purposes of this argument…) Seeing the score seemed to make sense of the way the opening of the symphony sounds: clock time - the world of beats, or marked-out bars and rhythms - is suspended in the flow of the strings' and then woodwinds' music, before the symphony suddenly picks up energy, catalysed by a repeated rhythm in the harp. The point is, it's the way time works, the way Sibelius manipulates music's fourth dimension, that's among the great mysteries of this symphony, and one of the reasons it's become so important for contemporary composers: the strange layers of different kinds of time in the slow movement; the way the scherzo sets up structural expectations which it then pulls from under you; and how the final movement explodes with all the ferocious speed and energy of a sudden, white-out blizzard before subsiding into the cold, uneasy calm of its final bars.

Sibelius's Sixth Symphony is an enigma because its sheer musical concentration achieves the opposite of what its composer thought it would. He may have thought of it as pure, cold, and clear, but paradoxically, that very focus and intensity means that it teems with musical thinking whose depths are only now being acknowledged. Enjoy your plunge into this musical ice-bath!...

Three very different sixths

Osmo Vänskä/Lahti Symphony Orchestra: white-cold and white-hot, Vänskä's performance has an elemental austerity.

Thomas Beecham/Royal Philharmonic Orchestra: Beecham finds an expressive - yet non-intoxicating - warmth at the symphony's heart.

Herbert von Karajan/Berlin Philharmonic Orchestra: Karajan's high-octane orchestra give you every ounce of red-blooded emotional intensity they players can find can find in this supposedly pure-cold symphony.