For this programme with the Berliner Philharmoniker, Semyon Bychkov chose two works in E flat major, the traditional key of heroism. But it’s hardly possible to imagine two more different treatments of that favourite musical mode.

Shostakovich’s First Cello Concerto is often described as presenting an anti-hero, a fruitless struggle against insuperable forces in which we nonetheless see glimpses of defiant humanity. The grandiloquent surface of Strauss’ Ein Heldenleben, by contrast, suggests an image of conceited triumphalism. But it’s always worth remembering that it was composed as a companion piece to Don Quixote: the avowedly unheroic Strauss was arguably also channelling Cervantes’ self-delusional knight-errant in this, his own ‘Eroica’.

Certainly both works raise important and fascinating questions about how best to map composers’ biographies and personalities onto their works, as well as about the dangers of looking at those works with the benefit of hindsight. To describe them both, as the programme here did, as giving us an insight into two different musical personalities of the 20th century is not inaccurate, but it rather underplays the time that elapsed between the works (the Strauss from 1898, the Shostakovich from 1959), not to mention the catastrophic events that had shaken the world during that period.

Much of that history reverbarates through Shostakovich’s works. But if the First Cello Concerto might be anti-heroic, it nevertheless calls for heroism from a soloist. Gautier Capuçon delivered it in spades, in a performance of fierce concentration and taut virtuosity. His broad tonal palette was on display right from the start and ran the whole gamut. In the opening Allegretto there was a dulled numbness one moment, steely defiance or sinewy strength the next.

The central elegy of the Moderato was sung out, like all the work's fleeting snippets of lyrical consolation, with moving tenderness. The massive cadenza became a suitably titanic struggle: man against his demons; cellist, in defiant isolation, apparently both with and against his instrument. The finale was a dash both gripping and properly unfulfilling, in line with a description (by Bernd Feuchtner) quoted in the programme, which sees the soloist as being trapped in a hamster wheel, working furiously but ultimately going nowhere.

Capuçon’s performance was a mighty feat, and he was matched by often stunning playing from the orchestra (Stefan Dohr rightly got a bow for his playing of the many horn solos). Under Bychkov, their performance was disciplined in its unstinting precision, but full of biting high-spirits and caustic wit. It was an overwhelming performance, but Capuçon could hardly have chosen a more welcome encore. He offered a beautifully hushed account of Pablo Casals’ Song of the Birds, in which he was exquisitely accompanied by the orchestra’s cello section. It was an appropriate encore, too, given that Casals often played the piece, an arrangement of a Catalan folk song, as a protest against Franco’s regime.

The second half featured similarly breathtaking virtuosity, but here it was the whole orchestra, swelled to magnificent proportions, who were the heroes in Strauss’ great tone poem. Bychkov’s conducting didn’t seek out anything revelatory or revolutionary. It charted, rather, an ideal course through the score’s 45-minute span, balancing descriptive specifics with a totally coherent symphonic overview, linking together thrilling individual moments into a compelling whole.

But what ultimately made this such a fine performance, perhaps, was the fact that beneath Bychkov's benign guiding hand the orchestra seemed to play as much for themselves and one another as for their conductor or audience. It’s a score they evidently love, and they brought an almost chamber-like sense of internal communication. Those inner workings, though, were communicated into the Philharmonie’s acoustic as a big, bright and exciting sound of astonishing power and clarity, with balance perfectly maintained even in the most heavily scored passages.

Dohr and all his horn colleagues excelled themselves, while Noah Bendix-Balgley’s violin solos were a marvel of sweet flexible tone and musical characterisation (his final duet with the solo horn was meltingly done). You’ll rarely hear the critics’ snarky interjections more clearly communicated, or the memory-lane tapestry of the ‘Works of Peace’ more seamlessly woven together – however much the E flat clarinet’s brilliantly irreverent Till Eulenspiegel-esque interjections attempted to upset things.

Where Strauss himself really is in this work remains open to debate, but this was a performance that got directly, powerfully and excitingly to its core. Pure Straussian joy.