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With its jaw-dropping sculptures and carvings of bulbous women and half-human animals, the British Museum's Ice Age Art exhibition is a sublime reminder of the fact that the creativity of homo sapiens predates what we tend to think of as the dawn of civilisation. But for me, the most moving object in the show is one of the least obviously beautiful: a long, thin flute made from the wing-bone of a griffon vulture. Found in the Hohle Fels cave in south-west Germany, it could be 40,000 years old, making it one of the oldest instruments ever discovered. What's so striking about this ancient wind instrument is how familiar it looks. It's basically an ice age penny whistle: anyone can see it's a tool for making music, with its five finger-holes and a V-shaped notch at one end, through which a prehistoric musician would have blown.

The sounds it makes are strikingly familiar, too. We know this thanks to Wulf Hein, an "experimental archeologist" who made a replica of the instrument – and can be seen on YouTube, dressed in animal skins, using it to play The Star-Spangled Banner. (You will already be familiar with this fascinating figure if you've seen Werner Herzog's 2010 movie Cave of Forgotten Dreams, about the shockingly contemporary-seeming art found in the Chauvet cave in southern France.) Hein shows that the notes the flute can play form the "pentatonic scale", the same scale that's the basis of so many tunes we know and love today. Hein will be on hand at the British Museum next month, to give a carving talk and demonstration, hopefully wearing his animal skins.

Hearing this little flute, and imagining how it was used by the people who made it and played it, collapses the millennia that separate us from them. And the flute is just the tip of the ice-age iceberg. There would have been countless other – and older – instruments that have not survived, fashioned from reeds, wood, bamboo and skin, materials we still make instruments out of today. So if we can assume the deep past was full of artefacts – carvings, paintings and sculptures – then it must have been just as full of people making music together, singing and playing to one another. Back then, just as it is now, music was an essential social glue. And all the wind instruments in the world, from recorders to flageolets, owe it to little works of wonder like the Hohle Fels flute.

• Wulf Hein's bone flute can be heard on Music Matters, Radio 3, Saturday 16 February at 12.15pm. Hein will be at the British Museum's Ice Age Art exhibition on 2 March.