That Isabelle Faust and the Akademie für Alte Musik Berlin have let this Bach violin concertos album run to nearly 2 hours of music suggests a relish of their task that is mirrored triumphantly in the resultant music-making. Their choice of repertoire, too, feels driven by a desire to celebrate Bach’s life with the violin rather than document it. If they had wanted to be pedantically completist about it, we would have the Fifth Brandenburg and the Triple Concerto; instead we get the three known violin concertos plus the three most convincing reconstructions from harpsichord concertos, supplemented by a reconstruction of the putative early violin version of the B minor Flute Suite, and all neatly interspersed with arrangements of two of the organ sonatas and a clutch of cantata sinfonias (including the rarely heard, trumpet-and-drum-laden BWV1045, a violin concerto movement of some flashiness).

Everything here is energy, though the exuberance is of the grounded kind that never gets out of hand. Tempos are brisk; but while there’s certainly not much risk of listeners thinking any of them too slow, neither does any one of them sound too fast, at least not the way they are performed here. Faust’s playing is technically brilliant, yet always at the service of the music, and everywhere enlivened by a richly varied repertoire of interpretative details, from spontaneous twiddle-ornaments to little tempo-tugs or deftly elongated notes within a phrase. From her 1658 Stainer she produces a sound that is period-instrument clean (even at times a little wiry), but can summon warmth of tone and tonal strength when she wants. And together she and this superb orchestra show exemplary contrapuntal clarity while also outlining the music’s architecture through glinting dynamic changes or compelling long-range crescendos and diminuendos. A word should go, too, to Xenia Löffler, whose liquid-gold oboe-playing is a perfect foil for Faust’s busy violin in BWV1060 and a perfect match for its aching beauty of the Sinfonia from Cantata No 21. In short, without being tempted to eccentricity, these performances reveal keen musical minds constantly at work.

The deeper delight of it all is that you can encounter subtle new aspects in the familiar works – the E major Concerto intimate, even a little withdrawn, the slow movement of the A minor given a lightly pulsing, march-like momentum – and real revelations in the lesser-known ones. I’m not sure I’ve ever heard the reconstructed concertos sound so convincing (especially the D minor), the trio sonatas go at a thrilling lick that surely no organ could keep up with and the sinfonias simply gleam. This is a hugely enjoyable celebration of Bach – himself a violinist – which conjures not so much the strict contrapuntal and formal genius as the joyous spirit of the living man.