In one of rock'n'roll's better jokes, a Grateful Dead fan turns up to see his favourite band and finds to his distress that his stash of drugs has run out. "Man, this band really sucks", he announces as the Dead take the stage and he hears them for the first time in sober-minded clarity.

He must have caught them on a bad night. My first Grateful Dead show in 1972 as a teenage hippy neophyte was unforgettable. The group was at the apex of its acid-laced glory and I had no doubt that they were the finest band I had ever seen.

It's true that in my youthful exuberance I had eagerly partaken of the illicit substances that were invariably on offer at Grateful Dead shows back then. But my stash ran out several decades ago and Sunshine Daydream, a newly released recording of a legendary show from 1972, sounds as good in staid middle-aged abstinence as in stoned teenage memory; invigoratingly fresh and full of wonder, combining breathtaking flights of improvisational fantasy with an intuitive craft, a freewheeling trip down the highway of cosmic American music with its own stash of in-built natural highs along the way.

Back in 1972 on the band's first British tour, I couldn't get enough of the Grateful Dead. I saw them on the opening, exploratory night when they transformed the drafty old Empire Pool, Wembley into a north London outpost of the Fillmore West. Then again a month later at a festival in a muddy field at Bickershaw, near Manchester, held optimistically in the first week of May with inevitably cold and damp results, but where they rallied flagging spirits with a courageous five-hour set. And then finally when they returned to London after the European leg of the tour to sign off with a series of triumphant shows at the Lyceum. They were magnificent every time.

The holy grail in the Grateful Dead experience has always been Dark Star, the band's most cosmic and stellar piece of protean, shape-shifting improvisation, on which lead guitarist Jerry Garcia set the controls for inner space on an aural acid trip that on a good night voyaged for half an hour and more before returning to terra firma. Dark Star was not played at every show and no two performances of it were ever the same, which ensured the journey was always special. I can still remember dancing around the Lyceum with a head full of acid as Dark Star filled the ballroom and willing the music never to stop. It was the first time I'd experienced rock music as an act of communal supplication rather than just another gig.

The Dead were on a roll on that tour, as Europe 72, the triple vinyl album released later the same year, proves. But on their return to America, the band played a show on 27 August, 1972 at a fairground near Springfield, Oregon that has since assumed a near-mythical reputation in Grateful Dead folklore and has become the most requested show from the band's vast vault of concert tapes.

Springfield was the hometown of Ken Kesey, author of One Flew Over the Cuckoo's Nest, founder of the Merry Pranksters and instigator of the "acid tests" at which the Dead had played their first mind-bending gigs in San Francisco in the mid-1960s. After serving time for drug offences, Kesey had retreated back to the family farm in Oregon where he was running a creamery. With the business struggling, the Dead agreed to help him out by playing a benefit show.

What transpired was a counter-cultural homecoming, a gathering of the tribes. The original Pranksters – many of whom had followed Kesey to the Oregon backwoods and whose colourful nicknames are immortalised by Tom Wolfe in his book The Electric Kool-Aid Acid Test – were out in force. Tickets were hastily printed on the back of the creamery's yoghurt labels. On what was allegedly the hottest day in Oregon's history, clothing was declared "optional" and the Dead played one of the finest sets of their lives in a belated coda to the original acid tests.

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A total of 20,000 free-spirited Deadheads descended on the fairground and to have been among them would have been a teenage English hippy's sunshine daydream. Alas, I was stranded several thousand miles away, still struggling to escape the drab conformity of lace-curtained 70s suburban Britain. Better late than never, many years later, on a sweltering hot August day in 1999 I made a pilgrimage to visit Kesey on his Oregon farm. Several of the surviving characters from Wolfe's book, including Mountain Girl (Carolyn Garcia) and the Intrepid Traveller (Ken Babbs), showed up to meet me. We hung out in the sunshine, had a barbeque and listened to tapes of the Dead, reliving memories of the day when the band had played perhaps its greatest ever show for Kesey's farm.

What is most striking about the recording from that sun-kissed day is the fluidity with which the Dead absorbed and transmuted every genre of vernacular American music, from blues, folk and gospel to country, R&B and rockabilly, and fed them into some of the most audacious, freewheeling rock'n'roll ever made – past and future, outlaw spirit and hippy idealism fused into a soundtrack for a brave new frontier that birthed an alternative sub-culture which survives to this day.

An epic psychedelic jam around Dark Star full of vaulting, freeform improvisation mutates alchemically into a loping take on Marty Robbins' cowboy ballad El Paso. Merle Haggard's country weepie Sing Me Back Home, delivered hauntingly in Garcia's reedy but expressive voice, gives way to the Dead's surging, feelgood acid anthem Sugar Magnolia, with its irresistible sunshine daydream refrain. Throw in the loose-limbed rhapsody of Chuck Berry's Promised Land, the psyched-up folk-blues racination of I Know You Rider and the group's own storied, myth-making compositions such as Truckin', Casey Jones and Playing in the Band and you have cosmic American music at its most potent and joyous.

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The event was also filmed and the previously unseen footage is included in the package as a DVD documentary. When the greenhorn filmmakers first approached Garcia to ask if they might film the show, in characteristically laidback fashion he replied: "Why? We just stand there.'' When they persisted, he shrugged his agreement. Predictably the Pranksters then dosed the camera crew with LSD and there's an amateurish but life-affirming simplicity to the footage, an hallucinatory celebration of the counterculture dancing in a sunshine daydream, as if the horror of rock'n'roll's darker underbelly unleashed by Altamont and personified by Charlie Manson, was a world away. And for a few hours while the Dead played, in a sense it was.

Sunshine Daydream: Veneta, Oregon, 27 August, 1972 is out now on Rhino Records