“This is the first of 72 shows,” says Adrian Belew partway through BEAT’s set here, and there’s a little pause in that sentence that tells its own story.

Because, let’s be honest, as experiments go, this is not exactly risk-free. Taking a set built around 1980s King Crimson deep into Japan and South America might not have worked. It might have felt too clever, too niche, too much like four astonishing musicians admiring the architecture of songs that most bands would not dare go near.

Instead, it is thrilling.

Then again, look at who is involved. Belew, now 76, and Tony Levin, who had just turned 80, were both there in King Crimson in the 1980s. They have recruited Steve Vai, who shares Levin’s birthday and had just turned 66, and Tool drummer Danny Carey to join them in this endeavour. That is not so much a band as a summit meeting.

The clue, of course, is in the name. “Beat” was the King Crimson album released in 1982, and this set celebrates that period: the trilogy of “Discipline,” “Beat” and “Three Of A Perfect Pair.” It is a body of work that has sometimes felt overlooked, perhaps because it does not fit neatly into the myth of Crimson as either the Mellotron-led monsters of the early 70s or the heavier beast they later became. Whatever the reason, it is not overlooked here. BEAT shine a light on it for a couple of hours, and what emerges is bewildering, brilliant and frequently astonishing.

“Neurotica” opens things up and immediately asks the obvious question: how does this make sense? The answer is that it probably shouldn’t. It twitches, twists, jerks and darts around like music that has been wired incorrectly, yet somehow lands exactly where it needs to. Vai is incredible from the off, not merely playing the parts but finding his own way inside them, coaxing out sounds that seem to bend the room.

“Neal And Jack And Me” follows, with Belew joking that they like to get the easy ones out of the way. It is a laugh line, but only just. This is not easy music. It is precision-tooled, full of right angles and trapdoors, but it moves with a peculiar grace. “Heartbeat” brings a more obvious 80s pulse, a glimpse of melody peering through the machinery, while “Sartori In Tangier” lets Levin step forward as the master of the low end. There are eastern flavours here, the bass doing things that suggest an entire landscape while Belew simply puts his guitar down and lets him get on with it. Fair enough too.

By the time they reach “Model Man,” the third album in the first half has been represented and the rarities are flowing. It is funky, certainly, but there is something strange and unwelcoming about it too, as if pop music has been rebuilt by men who understood the theory but were far more interested breaking it apart. “Dig Me” and “Man With An Open Heart” keep that unique sound alive: angular, restless, clever without ever feeling smug.

“Industry” is all pulsing keys and dazzling, disorientating shapes, yet there is tongue in cheek in there too. It is serious music made by people who understand that seriousness without wit can become unbearable. Then “Larks’ Tongues In Aspic (Part III)” ends the first set, beginning as something almost straightforward before remembering that straightforwardness was never really the point. There is wizardry here, obviously, but there is also muscle.

After the break, “Waiting Man” arrives on rhythms that feel part drums, part xylophone, part ritual. Carey is immense throughout, not trying to out-Crimson Bill Bruford, because that would be foolish, but instead bringing his own immense physicality and feel to music that demands both control and release.

“The Sheltering Sky” has a moment of technical gremlins for Belew, who jokes, “They don’t need me as a guitar player.” The track drifts and shimmers anyway, with the kind of atmosphere that suggests the whole thing might float off if Levin was not there to anchor it.

“Sleepless” is almost jazz at first, all stunning interplay and restraint, before the bass solo reminds you that Levin can make four strings sound like a structural threat. Then the whole thing crushes. “Frame By Frame” is clearly an audience favourite, and rightly so.

“Matte Kudasai” almost floats away, beautiful and strange, while “Elephant Talk” has all the groove you would expect and ends up funky, fun and utterly irresistible. The title track from “Three Of A Perfect Pair” follows, and by now you can only marvel at how good this is.

“Indiscipline” ends the main set in spoken-word chaos, and perhaps it contains the line that sums the whole thing up: the idea of looking at something again to see if you still liked it. And yes, we did. We all did.

“Red” starts the encore, the only non-80s piece here, dedicated to Fripp and Bill Bruford, and it lands like an anthem. Heavier, more direct, but still unmistakably from the same strange universe.

Then “Thela Hun Ginjeet” ends it all like a snippet from a film, all street-level tension, clipped voices, nervous rhythm and urban paranoia.

What BEAT prove here is simple enough: this music was never museum-piece material. Forty years on, it sounds like the past arguing with itself.

And winning