How quickly our ears have become attuned to the pitch, gestures, speeds and textures of the “period” revolution. Even when a young orchestra of such remarkable flexibility as the present Leipzig Gewandhaus perform Bach’s Brandenburgs, we imagine an underlying motivation of reclaiming territory for a famous old Bach house orchestra (often with the Thomanerchor) returning to its roots with its own “restoration” agenda.

This forms, however, only a very small part of the story. There can be no question that these players are comfortable to be performing Bach on modern instruments – and, for that alone, bravissimo – combining an unselfconscious love of the tonal possibilities in their natural environment with the sophisticated and immersed sense of style, balance, scale and nuance one associates with a “period” ensemble. Vibrato is selective or negligible, and thankfully not just the latter.

The best of this happy mélange is heard in a boisterous and suave Concerto No 1, which is ripe, warm and controlled, but the horns still cluck (as Baroque horns do, so charmingly) with personality in the mini-divertissement which is the fourth movement. The oboe and violin in the second movement intersect each other in mellifluous dialogues largely absent in the neo-baroque world of the formal, slightly stiff and glamorous solos of Münchinger, Richter and even Marriner. The contrast is especially strong when one revisits the demoralised-sounding Gewandhaus in their copious Bach recordings of the post-war period.

How much Chailly actually directs these works is a moot point. The Second and Sixth Concertos sound like self-led chamber performances with the conductor choreographing rather than leading. The former is a remarkably lithe affair. Perhaps only the motoric (brilliant if occasionally sharp) trumpet and a pushed tempo – which rather strips the ensemble of its true colour – reveals the more unyielding side of orchestral musicians operating in the Baroque arena.

The Third and Fourth Concertos appear more gripped by Chailly in their careful placement, terraced dynamics and often wearingly detached, light and regulated string articulation. This seems a shame since it’s the joy of playing these pieces naturally and unapologetically on modern instruments which ultimately wins over the listener, not paying lip service to current orthodoxy (or worse still, what it’s thought to be). The Fourth takes time to get going and the outer movements are disappointingly uninflected. This is where, in comparison, the joie de vivre and new-found freedom of the best period bands becomes all too apparent.

The most successful concerto is the Fifth (the Sixth, robust but unsettled) and for all Chailly’s containment, the concertante trio thrive on each other’s filigree, despite a manic harpsichord cadenza from Michael Schönheit in the first movement. The second movement is a gorgeous essay in unalloyed lyricism, one of several isolated moments of abandon in a fascinating but only intermittently satisfying project.