The opening line of Carmina Burana – “O Fortuna!” – could hardly be more apt. Few composers felt themselves more at the mercy of capricious gods and twists of fate than its composer, Carl Orff. He was never a diehard Nazi; indeed, he looked with disdain on their oafish cultural values. Far from espousing the hounding of “inferior races”, he was fascinated by jazz and by what today we would call world music. Yet he rose to become one of the Third Reich’s top musicians.

According to one of his four wives, he “found it impossible to love” and “despised people”. Yet in Carmina Burana he created the world’s jolliest musical celebration of boozing, feasting and generally enjoying the sins of other people’s flesh.

He turned his back on his own teenage daughter, who adored him. “He didn’t want me in his married life,” she recalls sadly. Yet he was (and, in some quarters, still is) adulated in educational circles for his Schulwerksystem of teaching music to young children through rhythm and gesture – a system he originally intended to flog to the Hitler Youth movement. It is still used around the world, particularly (and paradoxically) to help children with cerebral palsy, who would probably not be alive if Hitler’s Germany had triumphed.

A connoisseur of Greek drama, and a perceptive scholar who edited and performed Monteverdi long before the rest of the world rediscovered the Baroque genius, he talked eloquently about the need for people to express themselves through art if they were to become “complete” human beings. Yet one of his wives says that he himself was full of “demonic forces” and would “wake up screaming at night”. He used people shamelessly. Yet, as another wife puts it, “all his life he wanted forgiveness” for the guilt that consumed him. He was obsessed by the myth of Orpheus, the musician who descended into the Underworld. “Just like Orff himself,” his biographer notes.

All this, and an act of treachery hidden until now, is revealed in an exceptional film by Tony Palmer, fittingly called O Fortuna, that’s just out on DVD and will be broadcast on Sky Arts 2 in late January. The timing is perfect. Next month, a spectacular touring production of Carmina Burana rolls up at the O venue in the former Millennium Dome. For the past four decades this bawdy oratorio has been performed somewhere in the world every day of every year. But this show is likely to eclipse all previous stagings. Besides a chorus and orchestra of 250, it has fireworks, giant puppets, cannon effects, and, according to its producer, Franz Abraham, “erotic scenes with naked girls imitating an orgy”.

For once it can be truthfully said that the composer would have loved it. And the show, which has already played to a million people on its 13-year global journey, is expected to attract huge audiences – upwards of 10,000 on each of its two nights.

I doubt whether many of those 20,000 punters, innocently enjoying this tub-thumping, thigh-slapping medley of pulsating choral numbers (based, incongruously, on a collection of poems by 13th-century monks, discovered in a monastery in Orff’s beloved Bavaria) will be aware that the piece had its premiere, in 1937, at a Nazi Party gathering. Nor that its creator had a dark secret that Palmer’s film highlights for the first time.

Orff had a friend called Kurt Huber, an academic who had helped him with librettos. Huber was also a brave man. During the war he founded the Munich unit of Die Weisse Rose (The White Rose), the German resistance movement. In February 1943 he and other Resistance members were arrested by the Gestapo, tortured and publicly hanged. Orff happened to call at Huber’s house the day after his arrest. Huber’s wife (whom Palmer tracked down for his film) begged Orff to use his influence to help her husband. But Orff’s only thought was for his own position. If his friendship with Huber came out, he told her, he would be “ruined”. Huber’s wife never saw Orff again.

Two years later, after Germany’s surrender, Orff himself was interrogated – by an American intelligence officer who had to establish whether Orff could be “denazi-fied”. That would allow Orff (among other things) to collect the massive royalties from Carmina Burana. The American asked Orff if he could think of a single thing he had done to stand up to Hitler, or to distance himself from the policies of the Third Reich? Orff had done nothing of that kind. So he made up a brazen lie. Knowing that anyone who might contradict him was likely to be dead, he told Jenkins that he had co-founded Die Weisse Rose with his friend, Kurt Huber. He was believed – or at least, not sufficiently disbelieved to have his denazification delayed.

And then, as Palmer’s film reveals, Orff did the most astonishing thing. He sat down and wrote a fictitious letter to his dead friend, in effect apologising for his behaviour. He craved Huber’s forgiveness – even, it seems, from beyond the grave.

In my mind Orff’s tangled career raises two fundamental questions. The first is, how would we have behaved in his circumstances? Before the Nazis endorsed Carmina Burana, he had been penniless. He was seduced by the rank and riches he suddenly acquired – far too seduced to bite the thuggish hands that fed him. And unlike many other German geniuses, he loved Bavaria too much to think of emigrating (even though, with a Jewish grandparent, he was taking a colossal risk of being exposed by staying).

So he acquiesced. He even wrote new incidental music to Shakespeare’s A Midsummer Night’s Dream, so that the famous score by the Jewish composer Mendelssohn could be banished. Then, at the end of the war, he panicked and told a dreadful lie to get himself off the hook. From the comfortable perspective of 60 years’ distance, it’s easy to damn his cowardice and self-preserving mendacity. But millions behave with equal spinelessness in offices round the world every day, when the only danger is losing a coveted promotion or having to shoulder responsibility for some cockup.

The second question is, should any of this affect our appreciation of Carmina Burana, with its proto-minimalist rhythmic energy and its alluring exhortation for us to eat, drink, fornicate and be merry, because tomorrow we die?

After all, if we disqualified from our approval all art commissioned by montrous regimes or nasty patrons, or created by appalling people, there would be very few Old Masters in our galleries, and no Wagner in our opera houses.

“The fact that the Nazis liked Orff’s music is not in itelf proof that Orff was a Nazi, or approved of their methods,” Abraham says. “He simply lived in that generation of Germans when, unfortunately, everybody had a connection of some sort with the Nazis. Even the so-called good guys. Look at Günter Grass. Two years ago he shocked everyone by revealing that he was in the SS.” At least one gets the feeling that Orff, waking up screaming in the night, knew exactly how badly he had behaved.

The final irony in his twisted and compromised life? When he died in 1982 this most unsaintly of men ended up, as he wished, buried in a monastery – just like the scurrilous medieval poems that brought him such fame.

O Fortuna is available on DVD at www.voiceprint.co.uk or www.tonypalmerdvd.com. Carmina Burana is at the O2 Arena, London SE10 (www. theO2.co.uk; 0844 8560202), on Jan 17, 18

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