"It's my way of learning from Bach," says Dan Tepfer of his Goldberg Variations/Variations – an extraordinary project in which the American jazz pianist interpolates his own improvised variations into Bach's original set.

It's not such a far-flung notion. As Tepfer points out, the way Bach strips the Aria's melody but uses its harmony to express new ideas in the variations is akin to contemporary jazz improv. Plus in Bach's day improvising during a performance was par for the course.

Still, there aren't many pianists who could pull this off quite so well. Tepfer has the dexterity to give a persuasive enough account of Bach's score unadorned, and the stamina to cope with a good extra half hour of music. He didn't meddle much with the original notes but his delivery was his own: the Aria was unapologetically sentimental, oozing rubato and pedal, and the variations were jazzed-up with spiky articulation and off-beat emphases. It was all playfully done; Tepfer's job title "jazz pianist" allows him a kind freedom that many a "classical pianist" would struggle to achieve.

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The improvisations themselves were brief and bold, each reflecting on the preceding variation, each culminating in a careful denouement. Often Tepfer's left hand extended Bach's figurations while his right hand went off exploring – the language was angular and boisterous, and had the effect not of making Bach's originals sound sober but of highlighting their own inventiveness. And that is precisely the point. Tepfer's Goldberg project is not an exercise in self-aggrandisement; it's the fondest form of respect. His final improvisation opened up a vast and peaceful space that made the returning Aria sound both timeless and utterly transformed.