It’s a Sunday morning, and as the Royal Albert Hall darkens and the stage is suddenly back-lit, spotlighting a charismatic figure speaking sibilantly at its centre, you’d almost swear you’d wandered into an American megachurch. But the gospel preached by maverick clarinettist-conductor Martin Fröst is altogether more ancient and more primal: dance. What could be more fundamental, not just to music but life itself, he argues. And with the ferociously dynamic Swedish Chamber Orchestra helping him make his case, it’s hard to disagree.

Wagner famously declared Beethoven’s Seventh Symphony “the apotheosis of the dance”, and the SCO’s DNA project (“Dance Now Always”) transforms his description into a concert that drills down to the rhythmic essence of the symphony, seizing those cells and pulses that are its heartbeat and amplifying them into an ear-bending, time-warping sequence that suspends the work at the centre of its own musical genealogy – past and future.

So while the symphony stands alone after the interval, we approach it via a continuous first-half drawing together works by Bach and Rameau, contemporary composers Jacob Mühlrad, Shai Wosner and both Fröst and his brother Göran, into a constantly evolving commentary and dialogue.

The fluid arabesques of Fröst’s solo Cradle Song (nobody makes the instrument sing in so many different voices) stretched imperceptibly into Mühlrad’s Helix – a specially commissioned introduction that demands principal cello Anna Garde set aside her instrument and turn dancer, mirroring and melting into Fröst as jazz, klezmer and the concert-hall dissolve into a haunting miniature. Drift for even a second and you’ll have missed the arrival of a Gigue from Rameau’s Dardanus – arrangements by Hans Ek smudging the edges of the baroque works into the new until we lose stylistic landmarks and it’s all just pulse and energy and sensation.

But the real test of the programme was the symphony itself. Suspense built irresistibly through the opening before the Vivace released a performance that was pure impulsion. The silvery spareness of the SCO sound sketched a swift, architectural account, the gorgeous woodwind solos the only embellishment. Fröst stripped performing conventions away to reveal the work’s sharp corners and discontinuities – the motoric finale not just a dance but the original wild rumpus.

• Available on BBC Sounds until 16 September. The Proms continue until 12 September.