It sounds like something out of a film script. A Greek man in his early 20s fights for his homeland as part of the Communist resistance at the end of the second world war. Shrapnel from a blast from a British tank causes a horrendous facial injury that means the permanent loss of sight in one eye. He is sentenced to death after his exile to Paris (a sentence that was later commuted to a prison term, with his conviction finally quashed with the end of the junta in 1974). By the time he returns, he has become one of the leading creative figures of the century: an architect who trained, worked, and often transcended the inspiration of his mentor and boss, Le Corbusier; an intellectual whose physical and mathematical understanding of the way individual particles interact with each other and create a larger mass - atoms, birds, people, and musical notes - would produce one of the most fertile and prophetic aesthetic explorations in musical history; and above all a composer, whose craggily, joyously elemental music turned collections of pitches and rhythms and instruments into a force of nature, releasing a power that previous composers had only suggested metaphorically but which he would realise with arguably greater clarity, ferocity, intensity than any musician, before or since. This is the music of Iannis Xenakis.

When you hear Xenakis's music – any piece of what we recognise as his mature work, starting with 1954's Metastasis, onwards – you're confronted with an aesthetic that seems unprecedented according to any of the frames of reference that musical works usually relate to. You won't hear vestiges of things like familiar forms, or shapes, or languages. Even the furthest-out reaches of early 1950s serialism sound resolutely conventional next to Xenakis's works of the same period. It's music whose sheer, scintillating physicality creates its own territory in every piece, whether it's for solo cello or huge orchestra. As Ben Watson has put it, Xenakis's work is "an alien shard, glimmering in the heart of the West". When Xenakis approached Olivier Messiaen in Paris for composition lessons, Messiaen turned him down, because, "I think one should study harmony and counterpoint. But this was a man so much out of the ordinary that I said… 'No, you are almost 30, you have the good fortune of being Greek, of being an architect and having studied special mathematics. Take advantage of these things. Do them in your music'."

And that's exactly what Xenakis would do, and was already doing - which is both one explanation of his music's shocking otherness (it was heard as "alien" even by the hipsters of the early 1950s; the 1955 premiere of Metastasis at the Donaueschingen Festival was one of the scandals of postwar music) and a revelation of this music's deep, primal rootedness in richer and older phenomena even than musical history: the physics and patterning of the natural world, of the stars, of gas molecules, and the proliferating possibilities of mathematical principles. Xenakis resisted the label of being a mere mathematician in music just as surely as he refused the idea of his music's political or social message, and it was of course how he used those scientific principles (outlined in his book, Formalized Music) to create pieces of shattering visceral power.

His architectural output offers ways into his music's imaginative world. Take the Philips Pavilion that Xenakis designed for the Brussels World's Fair in 1958 and for which he and Edgard Varèse wrote electronic music to animate its still gorgeously futuristic-looking parabolas, swoops, curves. The maths underlying its construction, and the shapes it makes, have a direct correlation in the way Xenakis uses the instruments of the orchestra in Metastasis, organising the entries of the instruments, and the pitches they play, according to the working-out of mathematical and statistical formulae, translating the space of architectural planes into musical time. (Take a look at his near-contemporary design for a "Cosmic City", a gloriously sci-fi vision of the metropolis of the future - and what happens when Dan Dare meets curvy brutalism.) Xenakis also designed what he called "polytopes", high-art son-et-lumière installations that involved his lighting designs, his sets, his music, and his sound projection to create vivid multi-media experiences, in places from Canada to Iran to Greece. And he designed a system for the conversion of graphic stimuli into sound, a programme he called UPIC and which has now morphed into more sophisticated computer software like IanniX. (More than a decade before Boulez founded IRCAM, Xenakis had set up his own institute for music-technological research in Paris called EMAMu, which now exists as CCMIX.)

Those are some clues to the elemental concerns of his music. But what happens when you hear his music goes beyond even the sensation of teeming natural phenomena or landscapes transmuted into music. Listen to this piece - Synaphaï - for piano and orchestra. You'll hear a piano part of mind-bending complexity, which has the unique distinction, as far as I'm aware, of having a separate stave for each finger. You did read that right: Xenakis uses 10 staves in this piece. You'll hear clouds of minutely detailed orchestral sonority wrap around the solo part, like flocks of small birds mobbing an avaricious raptor; and you'll hear a near-continuous rhythmic intensity and textural violence that takes your breath away. Hearing this piece is as awesome an experience as watching some life-changing natural spectacle. Synaphaï has all the teeming unpredictable power of a glacier, the thrilling complexity of shape and movement of a mass animal migration.

But there's something else as well. This music is expressive: not in a conventionally emotional way, perhaps, but it has an ecstatic, cathartic power. Xenakis's music – and its preternaturally brilliant performers - allows its listeners to witness seismic events close at hand, to be at the middle of a musical happening of cosmic intensity. (That's literally true in Terratektorh, in which the orchestra perform from within the audience – it would have been fun to be part of this performance conducted by Matthias Pintscher…) Xenakis has said that his war-time experience informed his desire to create his new kind of sound-experience. (He described the play of sirens, gunfire, and spotlights in Athens in the 1940s as like a "large-scale spectacle") Yet his music sounds, to me at least, to be purged – or perhaps to be a purging - of the sort of existential darkness that György Ligeti's music, say, never escapes. (Among the closest Xenakis comes to a direct emotional utterance is in his Nuits for chorus; music that sounds like a primordial cry, an impassioned scream.)

There's a huge amount to discover in Xenakis's music, and much of his vast output is out there on YouTube. Some highlights: the non-stop dynamism of Keqrops for piano and ensemble, the epic scale of the 75-minute long Kraanerg for ensemble and tape; the dagger-like pointillism of Khoai for solo harpsichord; or the devastating virtuosity of Tetras for string quartet. The piece that converted me, though, was Jonchaies for orchestra, composed in 1977, and quite simply one of the most exciting experiences you can have in music. Listen to it as loud as you can and convert all your neighbours to Xenakis too.

Jonchaies embodies the elemental truth about all of Xenakis's music. Beethoven described nature in the Pastoral Symphony, Sibelius was terrified by it in Tapiola, but it took Xenakis for music to become nature. On holiday in Corsica, Xenakis would pilot his canoe into the teeth of the biggest storm he and his paddle could manage. When you're listening to his music, you also go out there into the eye of a musical storm that will invigorate, inspire, and awe. See you out there…

Five key links

Synaphaï

Jonchaies

Keqrops

Tetras

Terratektorh