Towards the end of his life, German composer Karlheinz Stockhausen decided that he came not from Earth but from the planet Sirius.

He believed that he was in contact with angels, like William Blake. Stockhausen was a strange man. He designed his own house with no right angles and lived there with two women at once.

He wrote music that required three orchestras and four helicopters. He could be shockingly rude or utterly charming. The composer Jonathan Harvey thought of him as a sort of shaman. Luigi Nono described his methodology as "spiritual suicide". The Fluxus movement picked outside his concerts with banners reading: "STOCKHAUSEN - PATRICIAN 'THEORIST' OF WHITE SUPREMACY: GO TO HELL!" When the conductor Thomas Beecham was asked whether he'd heard any music by Stockhausen he replied, "No, but I think I've trodden in some."

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The vast mythology around Stockhausen can go either way, sometimes souring, sometimes glorifying his music. He was the composer who took mathematical serialism to its furthest limits and beyond; Gyorgy Ligeti compared the fearsome rigour of his formulas to a Soviet five-year plan. Photographs of Stockhausen at Darmstadt (the institute where he taught summer schools) tend to show him at a scary-looking bank of knobs and dials, a bit like a flight pilot, maybe on his way back to Sirius.

But forget the Darmstadt laboratories for a minute. There might be little mystique behind his compositional process, but there can be plenty of magic in the effect of Stockhausen's music. Take Kontakte. The 1959-60 piece for piano, percussion and electronics counts among the most important works of 20th century music - a major breakthrough in electronic techniques and one of the first scores to combine electronics and acoustic instruments with such blazing interactivity.

Of course, no electronic music can impress us nowadays like it must have then, before computer programmes could generate new noises at the click of a mouse. Despite his primitive tools, Stockhausen had faith in technology: the pianist David Tudor once asked him why he didn't construct his own electronics and he replied, "because industry will provide me with what I need". Yet a 13-minute score like Gesange der Junglinge - a recording of a choirboy singing "Praise the Lord" remixed until it becomes abstract phonetics lost in a sea of electronic sounds - took him two painstaking years to create. For the Cologne audience at the 1956 premiere, the pioneering nature of the sounds they were hearing must have been a huge part of the thrill.

Stockhausen began work on Kontakte in 1959, long before synthesizers or digital computers were around to help him materialise the unprecedented sounds in his head. He used tape recorders and machines designed for radio stations to create the 34 minutes and 32 seconds of electronic scoring. The name (Contacts) is deliberately plural, referring variously to the contact between electronics and live instruments, between percussionist and pianist, between piano hammers and strings, between drum stick and skin, between soundwaves and eardrums.

For a percussionist like Colin Currie, Kontakte is a meat-and-potato staple of his repertoire. Last month he played it with the pianist Nicolas Hodges to a sold-out audience at the Southbank Centre; next week he and Hodges perform it at the Old Fruitmarket in Glasgow.

"I'm always reminded of how theatrical this music is the minute we get it into the surround sound of performance," Currie says. "It is so convincing in its abstract nature. And for all its extreme modernity it's also upbeat and fun." Tape glitches? Upbeat and fun? Currie explains that it's the musical drama and the element of ritual involved that keeps this piece so deeply compelling.

"It's intricate and interestingly confusing. You never know where the sounds are coming from. We [the pianist and percussionist] are designed to be obfuscating, so that it's never clear for the listener what they're hearing. And that can be really magical."

Stockhausen's pioneering electronic work often sounds woefully dated now; as the composer Christopher Fox pointed out, "nothing dates faster than the future". Currie agrees. "There are moments in Kontakte when the retro-ness will bring a real smile to your face. But does that lessen the impact of the piece? No, because of the strength of Stockhausen's musical ideas. To me it all still sounds futuristic. It's incredibly inventive and highly abstract. Nobody went further and nobody did abstraction better than in this piece - including Stockhausen himself!"

Like an early-music specialist approaching a Bach partita, Currie aims to play Stockhausen's score as closely as possible to how the composer imagined it. In many ways he has an easier time than the baroque violinist: unlike Bach, Stockhausen dictated everything in his music, down to what part of the stick he should use to hit the drum.

But Kontakte is still ferociously demanding. "It still gives any percussionist the shivers," says Currie. "Towards the end I have to change sticks so much and so fast that I end up looking like a juggler doing cartoon circles."

And is it demanding for the audience? "It doesn't have to be. Pure instinct is the best way to go. My advice is to just enjoy the ride and you'll be taken to many different places. Sometimes a listener comes out of a performance in ecstasy about the sleigh bells solo in minute 24. That's cool! This piece is vast; everyone will take away something different."

Colin Currie performs Kontakte at The Old Fruitmarket on November 27, part of Glasgow's Piano 2013 series.