The island of Tagomago basks in the Mediterranean Sea, less than a kilometre off the north-eastern tip of Ibiza. Only a kilometre and a half long, it’s hardly more than an outcrop of rock, the last vestige of an ancient volcanic rim. Even in the early 21st century, there is little more than a handful of luxury hotels scattered around its rocky acreage, connected by a single road; from the air it looks almost deserted, with rocky coastal crags, odd-shaped inlets and a light covering of greenery and parched scrubland. Nowadays Tagomago is owned by a Spanish entrepreneur and is hired out to politicians and celebrities for luxury holidays or business functions. But despite its exclusivity, there is still a wildness about it that no amount of infinity pools or minimalist villas will entirely wipe out. A brother of the Carthaginian commander Hannibal, Mago Barca, who lived in the second century BCE, is believed to have used the island as a bolthole during his many Mediterranean military campaigns. Its name literally means ‘Mago rock’.

The members of Can considered Tago Mago, recorded in the closing months of 1970 and released early the following year, to be its second album. Unlike the previous two releases, which had been compiled from tracks assembled over a longer time frame, Tago Mago was a planned album from the start. From the giant head painted on the gatefold sleeve (which, at a stretch, resembles the outline of the real island), to its sprawl across four vinyl sides of a double LP, including two monumental tracks filling an entire side each, Tago Mago felt big. Taken as a whole, its seven cuts were confident yet exploratory, at times perilously close to collapse. The radical sound it proposed left the group standing as isolated from its peers as Tagomago itself. At last, after several months of bending to this sole task, Can’s energies were focused and intensified, the magnifying glass tilted to just the right angle for the grass to smoke.

“If you study music from all over the world,” Irmin mused to an NME journalist in 1972, “it seems that in lands surrounded by water the music is influenced more by water and air while the more you go into a continent, the more you get into a land mass, the melody of the music becomes less important in comparison with the rhythmic heaviness. It seems water has something to do with melody, while countries like Germany produce music more of earth and fire. At various times Tago Mago is wreathed in all of these elements, the roofless island and the horizonless interior.”

Myths surround Can’s Tago Mago, just as they swirl around the Balearic island itself. One repeated assertion is that the island – and by extension the album – has a connection with the occultist Aleister Crowley. While the group members often referred to magic and occult practices around the time it was made, there is no provable link between Crowley and Tagomago – it just seems to be one of those fanciful legends repeated unquestioningly in print and online. As we’ll see, though, there is a Crowleyan link to one of the album’s most significant cuts.

Several conflicting stories of Can members’ visits to the island circulated at the time too. Even as late as 2014 Holger was spinning this blatantly nonsensical yarn to an American interviewer: “Tago Mago is a magical work. Before Jaki came to Can, he was trying to commit suicide. He was playing with Chet Baker in Barcelona, as a jazz drummer. Then he went to Ibiza. And south of this island is a rock called Tagomago. Mago means magic, and Tago was the name of a magic master who lived there. And Jaki was on that rock and tried to spring down because he thought his life didn’t make any sense. I think he is the one who said we should call it Tago Mago.”

But whether you choose to believe any or none of these unverifiable legends, one way to make sense of Tago Mago’s barrage of aural sensations is to consider the album itself as a magic isle of the mind, the remote site of initiation rites that take the listener – and the musicians themselves – on a hermetic journey from light to darkness and back again. In the course of its seventy-two minutes, it hits peaks of rapture and plunges into the void. In texts that spin forwards and backwards, it entertains visions of bloodflow, disturbing drug experiences, gnomic chants, mass destruction, and winds up pleading to be cleansed. It’s a garden of earthly delights teetering over a hellish, all-consuming abyss.

It was on this album that Can at last learned to harness its extra-sensory faculties. A few years later, Irmin described the events on the record as ‘witchy surprisings’. Michael, in 1974, told Nick Kent: “Tago Mago was our real magic album. Irmin kept making these spells throughout the time it was being recorded, and I was warning him against it. It’s something that you just understand and get into if you read a lot of books about it.” Much later, he added: “We were interested in everything . . . in the universe . . . in nature. Magic is a way to influence nature. That intrigued us. We never tried to commercialise magic. We were also interested in things like astrology . . . because it was an opportunity to explain certain things. Why are people born in the spring . . . different from those born in the autumn . . .? Your environment is your music, and thus we were a German group. If you live in the desert, you’ll make a music that’s different from if you lived in a rainforest. We lived near Cologne, an area with a lot of industrial sounds and beautiful scenery.”

As Can embarked on the choppy voyage towards the edifice of Tago Mago, the group’s make-up, and the powers at their disposal, had altered considerably. Their last appearance of 1970 was supporting Black Sabbath at Essen’s Grugahalle on 16 December. As the new year broke, the West German Sounds magazine – the nation’s equivalent of the NME – voted them second-best German group (after Amon Düül II) and Soundtracks the second-top German album of 1970 (after Düül’s Yeti). Since the spring Can had not only scooped up a new vocalist, they were also supposed to be under the management wing of Abi Ofarim’s PROM organisation. Until now their affairs, bookings and general arrangements had been casually handled collectively by the group; private artist management was not permitted under West German law at the time (all such dealings were supposed to be handled by a state bureau), but the rules were relaxing fast in the new music-business climate.

As for the new vocalist, his lines could be as meaningful – or meaningless – as the other instruments. Unlike Malcolm, whose enunciation was usually piercingly clear, Damo forced listeners to strain to hear what he was singing about. Today there are many websites devoted to reproducing lyrics, but Can’s texts – especially those from the Damo era – are notably inconsistent, vainly transcribed by fans with cans, littered with apologetic question marks and disclaimers. Can songs are neither arguments, logical statements nor message-carriers; they’re certainly not the expressions of sentiment modern ears have been trained to receive since the origins of opera and the birth of the Romantic song in the age of Schubert and Wolf.

“I like Jim Morrison, but I’m not a Jim Morrison so I don’t have to sing like Jim Morrison,” Damo said. “I’m not a protest singer, I’m not interested about politics really. I’m just not so much interested about anything. That’s why I’m singing nothing – It’s how myself is.”

“I was captured when I realised that he was a loud whisperer,” recalled Michael. “He yelled only occasionally; usually he simply whispered loudly. I thought that was ideal . . . Naturally, the sound of the band altered, from a group that had a screaming singer to one that had a whispering singer.”

“He couldn’t really speak English,” adds the writer Duncan Fallowell, who got to know the group around this time. “He’d been busking on the streets and he’d invented this pseudo-language of sounds, which is very original – something Johnny Rotten later tried to do with PiL, but it didn’t go very far – but Damo brought terrific range and invention into something that’s actually gobbledegook. In order to register these songs [with a publisher], they had to have lyrics, because in fact Damo was using his voice like an instrument. The titles came later – I gave them some, they gave some. And there occasionally the odd phrase would appear. But in a lot of them, the so-called lyric you’re hearing is actually just sound, it’s not language. So I actually invented lyrics that approximated to the sound, to satisfy some legal requirement. I felt like Leonardo da Vinci, who was trying to put an enamelled surface of exactitude over a violent sketch underneath, just to satisfy the demands of the emperor!”

For a heart-stopping moment, they nearly lost Damo. Back in May 1969, before he met Can, he had been picked up by the police while busking in Hamburg, where it was found that he didn’t have the required residence permit. A visiting Japanese citizen was not technically allowed to earn money in West Germany, even as a busker, without the proper paperwork. The case finally caught up with Damo in 1971 and he was re-arrested. A friend of Irmin’s who worked in the police force happened to notice Damo in custody and reported back to Irmin that he was being threatened with immediate deportation. Can’s damage limitation mechanisms went into overdrive: they obtained references from various distinguished individuals, including the writer Paul Schallück, Cologne’s cultural councillor Dr Kurt Hackenberg, and Stockhausen himself, who wrote open letters in support of Damo in the national press.

Letter from Karl-Heinz Stockhausen to the Immigration department of the City of Cologne:

Dear Director,

My name is Karl-Heinz Stockhausen; I am the head of the WDR Studios for Electronic Music, composer, and a Cologner by birth. My former student Holger Czukay, a member of the beat group the Can, has explained to me that their singer Kenyi Suzuki [sic] has been arrested by the police and will probably be expelled from the country, and that he was certain that the group could not function artistically without him (I hear that he had been playing guitar on the high street and accepted money). In case my opinion means anything to you, I would now like to urgently request that you do not lump such artists alongside criminals and parasites. Society dearly needs birds like these. Perhaps you do not care for beat music or pop music, but maybe your children do. This group is the nest in Germany at the moment.

‘Where would we be . . .’ you must be thinking.

Now, you must judge musicians like these differently and put aside your prejudices, and you should not allow these people to be deprived or simply chased away, even if they have broken a public law. Do not clean out the stables on account of any inbred German ‘love of regulations’, as if it was 30 years ago. And please do not destroy such a sensitive soul in custody, etc.

Please take heed of this.

Yours

Stockhausen

At last Irmin thought of the well-connected current head of WDR, Werner Höfer, who was already favourably impressed with Can. (He liked Irmin’s interview responses on the steps of Schloss Nörvenich, and invited the group to perform at a televised music awards ceremony. They delivered a monotonous pounding beat, dissonance and extreme volume, pressing on for several minutes after they were asked to turn off. Höfer loved this even more.) On the day that Damo was being driven to the airport to be deported, Irmin pulled out all the stops, begging for Höfer’s help before putting on his smartest suit and, in a bid to try and hold up the plane, presenting himself at the foreign ministry, where he was treated somewhat snootily. Höfer telephoned a close friend – no less a personage than Walter Scheel, the German foreign minister at the time. Half an hour after the call was put through, Damo was granted permission to stay in the country. Irmin returned to the ministry in his scruffiest hippy attire, and relished being bowed and scraped to when the staff realised his request had been sanctioned by one of the highest-ranking politicians in West Germany.

All Gates Open: The Story Of Can is published by Faber on 3 May. Launch events will take place in Manchester (3 May), London (4), Dublin (6), and Bristol (7). It's available to buy from The Wire's online bookshop.