Proms: Richard Goode BBC Symphony Orchestra, Royal Albert Hall London: The last act of an emotional volcano

IT'S A long and winding road down which the final measures of Elgar's Third Symphony - as assembled, elaborated, imagined by Anthony Payne - eventually disappear. There's no knowing where it ends, when it ends, if it ends. It is, and always will be, open-ended. The last music we hear is martial, the weary vestiges of a once-proud Empire advancing and then retreating towards an uncertain future.

Actually, it's not quite the last music we hear: just when you're thinking that the rest might indeed be silence, a fade to black, Payne introduces - as Elgar himself so loved to do - a fleeting recollection, a pale, faded remnant of the symphony's opening motif - a chivalrous motif itself drawing upon the past to reinforce the future. So past and future are briefly reconciled. But the circle doesn't quite close. A hollow tam-tam stroke echoes and re-echoes from somewhere deep in Elgar's subconscious. It is finished, but it doesn't end. One question is answered with another. And so ends Payne's masterly "elaboration". "No one would understand... no one... no one", said Elgar from his death-bed, instructing his friend and confidant W H Reed to burn the "bits and pieces" (130 pages of sketches) which constituted the unfinished symphony. But somebody did understand.

And the depth of Payne's understanding can be gauged from those closing pages. In alluding so poignantly to that terrible unrepeatable thing called childhood (the advancing-retreating march idea comes from the extraordinary movement "The Wagon Passes" from Elgar's Nursery Suite) he has tapped into something very dark and distant in the composer's psyche. The whole symphony sounds and feels like a throwback to it. This is no assemblage, this is a composition. And at the risk of suggesting that Payne had what one might call "a Rosemary Brown experience", there is no question that his total immersion in these sketches and all that preceded them has enabled him to think and feel like Elgar. Yes, even to second-guess him. And even where the seams of "completion" show most (in the first movement, where I'm still not entirely convinced by the development) there is a sense in which this entirely "new" Elgar - sparer, darker, more elliptical - is a departure from all that has gone before.

Hearing Payne's elaboration "in context", as it were, so soon after performances of the other two symphonies (the Second just two days before in a glorious account from Leonard Slatkin and the Philharmonia), served only to intensify that feeling. We are about as far removed from the ethos of the First Symphony (or indeed the Second - as witness the opulent Edwardian splendour, the communal tragedy of its marche funebre) as Mahler's Tenth is from Mahler's First. The Mahler parallel came upon me most forceably watching Tadaaki Otaka conduct the Elgar First a couple of weeks back. The "formality" of his manner concealed a passionate inner-life. Rather like Elgar himself. Outwardly, the fine, upstanding English gentleman; inwardly, an emotional volcano. If he'd been born Austrian, he'd have been called Mahler.

And Mahler stalks the Adagio solenne of the Third. Not so much in manner (though the reach of the very first interval suggests Mahler about to embark upon one of his celebrated adagios) as emotional instability. Elgar wrote that the opening bars of this movement would "open some vast bronze doors into something strangely unfamiliar". It's true, we've never passed this way before; we may never pass this way again. But thanks to Payne's intuition and daring - a daring that honours Elgar's unpredictability - we are close companions on the journey. So close that the public and private Elgar are almost indistinguishable now.

In one of the finale's most dramatic ideas, a full-throated, eminently hummable (and staunchly English) tune is memorably transformed into something darker and more personal than you could ever have imagined possible. If there is any Payne in this moment, I don't hear it. Watching and listening as Andrew Davis and the BBC Symphony threw themselves so wholeheartedly into this Prom premiere over six decades after the BBC first commissioned the symphony, one could not escape the feeling that somehow or other it had been with us all along.