London has a curious lack of nerve when it comes to making new cultural buildings - particularly for music. We have had the protracted saga of the rebuilding of the Royal Opera House, and the slightly less protracted saga of the refurbishment of the Coliseum for English National Opera. Patches of various kinds are still being applied to the Barbican concert hall. And now the £71m gutting of the Royal Festival Hall is about to begin, in an attempt to put right that lovable old venue's acoustic deficiencies. In the meantime other cities, other nations have been building afresh. Go to Copenhagen, for instance, and you will find a sumptuous new opera house built in its equivalent of docklands.

Copenhagen, Porto - and closer to home Cardiff with its Wales Millennium Centre (an opera house in all but name) and Gateshead with its bulbous Norman Foster-designed Sage Music Centre - all these places have their quirks and deficiencies. But an authoritative big music venue somehow completes a city. Bristol's harbour area still feels keenly the lack of its axed Gunter Behnisch-designed concert hall. But at least there are other museums and visitor attractions in the Bristol docks. What have London's docklands got to show, culturally?

Copenhagen shows what we could have had. Its new opera house, by veteran architect Henning Larsen, is a formidable moated stronghold of a building, balancing Scandinavian reticence with touches of flamboyance in its semicircular glazed lobby and the baseball-cap of its show-off roof, projecting 35 metres. For all that, in plan it is not so very different from a competition-winning country opera house Larsen designed for Compton Verney in Warwickshire back in 1989. That Glyndebourne of the Midlands was never built. In Copenhagen, the Møller family, owners of the Maersk shipping and airline business, just donated the £230m cost of the new opera house. All of it.

Shame they didn't also cough up for a shuttle-ferry for the short hop across the harbour. It's a nightmare of circuitous roads or infrequent waterbuses to get to the opera house. Unusually for the Danes, they haven't sorted out the public transport. The chattering classes in Copenhagen are inclined to grumble about this gift horse and say it blocks the view from the royal palace. If only we had that kind of problem. We have the public transport in our docklands. We just don't have much that's interesting to visit there.

While interesting, the Copenhagen Opera is too unambitious to be great. Porto's Casa da Musica concert hall, however, has an aura of greatness about it. I'm not the biggest fan of Koolhaas - as a theoretician he is inclined to talk, and write, the most preposterous drivel - but as an architect he is now world-class. His massively in-demand firm, the Office of Metropolitan Architecture or OMA, has long been a university for new talent. Both Zaha Hadid and the equally avant-garde Foreign Office Architects started off there. But Koolhaas himself has an uneasy relationship with architecture. For years, it was as if he was trying to avoid it, to be an anti-architect. He likes ugliness, is mesmerised by unplanned urban sprawl, prefers diagrams to fine detail, is in all things contrarian. His favourite word is "provocation". Koolhaas takes architecture out for a walk and then hides behind a tree and watches it panic. But Porto marks a new maturity for a man who is now 60 and has a big international firm to run. This building is insane. It is also brilliant.

Back in 1999, I wrote in these pages that the Porto concert hall would prove that Koolhaas was, after all, only an architect, obsessed with form as all architects are. Now that the project is finally complete, I wouldn't change that view. This is indeed a case of the Emperor's Old Clothes rather than those regrettable new theory-driven ones. Koolhaas, his colleagues at OMA and his long-time collaborator, Arup's poetical structural engineer Cecil Balmond, have combined to produce a thing of power and - for all Rem's love of the ugly - grace. A relatively conventional shoebox of an auditorium is set high in an improbable chiselled sculpture (in fact precision-moulded white concrete) of a building. The auditorium has huge rippling glass walls, front and back. Through the filters of these walls, it is visually open to the sky and to the city. I don't know if this is a good thing or not. Maybe there's a sound reason for most auditoria to be hermetic spaces. Such as a desire not to be distracted from the music. But this too becomes, in the world of Koolhaas, curiously irrelevant. Because like Garnier's 19th century opera house in Paris, even this auditorium is less of an event than the processional public spaces around it.

The Opera Garnier has its wonderful stairs but mostly works horizontally. In contrast, the Casa da Musica works vertically. It has no lobby to speak of. Instead, you mount external steps, enter through a horizontal slash in the wall, and find yourself at the foot of a dizzying, Piranesian angular space, disappearing to a point high above. Through this winds the ultimate fantasy staircase, its polished aluminium steps taking you up to and around the main and secondary auditoria. Your route is not obvious, you get lost, but it's great. Though anyone in a wheelchair is going to miss out badly. Lifts just aren't the same.

Why is it the shape it is? Because this design was originally for a small house elsewhere, that never got built. Koolhaas liked the shape, inflated it vastly, and what would have been the living-room became the main auditorium. Its name - the House of Music - is thus a very true one. Houses, of course, have windows. This may be the only reason the auditorium has windows.

You find other Koolhaas provocations as you wander around. The room that is clad throughout in strongly geometric tiles. The other room clad in ironic pale-blue tiles with religious themes - commonly found on Portuguese churches. The padded lime-green room. The rough plywood walls to the auditorium, with an applied gold-leaf pattern that turns out to be an enlargement of the grain of the plywood itself. The high-tech canopy over the orchestra, clad in inflated transparent foil. The fake glass-fibre baroque organ case. The bar set high on a bridge between the two layers of glass wall behind the auditorium. Beneath Koolhaas's serious, even doleful, external demeanour there lurks a merry prankster. Just don't let him start to intellectualise it.

I can see every reason to hate the Casa da Musica. It is swaggeringly egotistical. Its very shape wants to topple over, requiring below-ground structural heroics to keep it upright. It is daft. It is also wonderful. To understand it, you must experience it. Then you will be glad, because what you will experience is the pure rush of raw, cask-strength architecture, undiluted, at its best.

And look at it this way: if Porto can do this - and stump up the £51m to build it - then what are we doing in London fannying around with the Royal Festival Hall at a cost of £71m? True, the RFH is bigger. But once the work is done, it will still be the RFH. Heretical to say it, I know: but maybe there's more to the concert hall experience than the puritanical quest for improved acoustics. There's room for a sublime madness as well.

www.oma.nl - the Office of Metropolitan Architecture
www.hlt.dk - Henning Larsen website