Our senses were reeling and our brains well and truly wired when, on Sunday night at the Queen Elizabeth Hall, the Emerson String Quartet concluded the epic first leg of their 25th-anniversary recital series. The twilit closing bars of Bartok's Sixth Quartet exhaled like a sigh, not so much of relief – we were all far too captivated for that – but as a sign of wonder that four individuals could survey so much taxing music in a single evening. To play, say, six Haydn quartets at a stretch is a considerable feat of concentration. But the six Bartoks? That's a feat of co-ordination, emotional engagement and physical endurance, not simply concentration.

This was not the first time London audiences had heard the Emersons swallow Bartok whole. A previous QEH cycle added layers of perception to an already impressive recording that the quartet had made for Deutsche Grammophon a few years earlier. Sunday's traversal was better still. It opened to a dreamy fiddle duet led by Eugene Drucker (who alternated the leader's chair with Philip Setzer) then proceeded through intimate asides, lunging monologues, scherzo and fugue, all part of an expansive canvas that was inspired by Bartok's love for the violinist Stefi Geyer. The further we ventured, the surer the playing became, unfolding this auspicious First Quartet as endearing but somewhat over-long.

The Second Quartet marks a huge leap forwards. It's deeper music than the First, rougher-hewn and more concise, with an earthy central scherzo that, before it finishes, switches suddenly from swirling skirts to a lightning coda. This is Bartok in "night music" mode, whereas the tightly bolted Third Quartet takes a handful of motives and works them into a sort of raging novella. Barely 17 minutes in length, the Third is a brainteaser with a wildly pumping heart, and the Emersons held its plot with impressive tenacity.

The Fourth was a little less fortunate, at least in the finale where the ensemble temporarily lost focus. The work had opened with gritty resolve, while the mischievous scherzos that flank its improvisational middle movement – one bowed at speed, the other plucked – elicited a quiet wave of chuckling from the audience. The folk element rings loudest in the Fifth, especially the Bulgarian-style scherzo, which was played almost as if it was jazz. At the point where the finale becomes a mock minuet, the Emersons camped up the humour, though not as much as in the Gypsy-style antics of the Sixth Quartet. And yet the Sixth's laughter has its tragic counterpoint in the many ineffably sad moments, where Bartok weeps for the Hungarian homeland that he is about to leave. We're talking 1939: war was beckoning and the prospect of voluntary exile with it.

In the quartet's finale, at the point where key motives from the first movement waft past like a slow-motion replay, you sense the end is near. The Emersons played this music as if for the first time. And I don't mean to suggest that they were in any way uncertain about how it should go. On the contrary, they seemed as spontaneously stunned by its beauty as we were.

To be broadcast on Radio 3 on 12 Nov at 7pm