“Please allow me to introduce myself; I’m a man of wealth and taste.”

So begins the Rolling Stones’ ‘Sympathy for the Devil’, an apparent glorification of the ultimate bad guy. Jagger, giver of hope to camp skinny boys everywhere, snarls exuberantly about the crucifixion of Jesus in the first verse; the Nazis in the second – by the third, he’s onto the murdered Kennedys. For a band who revelled in putting the fear of God – or His opposite number – into America’s ‘Silent Majority’ and Middle England, it’s really not bad going.

The reaction to such a song was predictable, from both detractors and fans. Icon Jean-Luc Godard was so enamoured by its counterculture potential that he made it a film featuring Black Panthers and an extended Marxist voice-over monologue. Indeed, the song held a privileged place on a list of acceptable tracks under the dictatorship of the proletariat (no John Lennon). There’s an interview with Jagger on YouTube in which, in his ever-surprisingly soft-spoken way, he namedrops the songs’ influences; Godard, Baudelaire, Bulgakov’s The Master and the Margarita, essentially scrambling to capitalise on his sudden intellectual significance – and loving it.

The song’s sophisticated ideas – that evil is a human construct, that we “fought for ten decades for the gods we made” – suggest that its more than just a Satanist wind-up, and that the moral panickers simply didn’t get it. Possibly undermining this is footage from 1968’s ‘Rock and Roll circus’ in which Jagger falls to his knees and tears his t-shirt from his back, revealing a massive Satanic tattoo. It fits perfectly into the long, playful tradition of insincerity which burns an anarchic trail through the history of pop music, from Johnny Rotten’s “We mean it, maaann” to Kanye West’s assertions that he is the son of God. Many conflicting moods fight it out in ‘Sympathy for the Devil’ – philosophical, ironic, threatening, and, of course, joyful, what with the best guitar solo of all time (eat your heart out, Stairway). There is no dominant tone.

Mirroring this was the chaos of 1968; turmoil both personal (in Godard’s film, the disintegration of guitarist Brian Jones, who would drown in his swimming pool the next year, is clearly visible) and political (the lyric “the Kennedys” changed from “Kennedy” when Bobby Kennedy was shot during recording). If nothing else, the song stands for the sheer absurdity of middle class, shockingly sexist, culturally appropriative men being seen as revolutionaries when their most subversive quality was being disapproved of by middle class parents.

The epitome of its standing for the madness of the late Sixties is its performance at the notorious Altamont Free Concert. After stopping the band playing, Jagger quips that “We always have something very funny happen when we start that number”, nervously indulging in tongue-in-cheek superstition. But the joke was only necessary because of the palpable rising tension in the audience; the 1970 film ‘Gimme Shelter’ intersperses shots of menacing Hell’s Angels with Jagger’s increasingly desperate pleas for calm: “Hey people, brothers and sisters…cool out.” During the next song, ‘Under My Thumb’, 18-year-old fan Meredith Hunter was stabbed to death.

Why is the song a milestone? Because it ushered in an era of rock bands being oddly interested in Satanic imagery; because it solidified the Stones’ reputation as bogeymen; because it encapsulates the “do they really mean it?” factor. But mainly because it speaks directly to the anxiety of its times. Halfway through the ill-fated Altamont performance, ‘Gimme Shelter’ cuts to a close-up of Jagger, deep in contemplation, looking, frankly, terrified. Who killed the Kennedys? “After all, it was you and me”.