I'm in Amsterdam searching for greatness. Giant-felling, allconquering musical mastery. An international panel of critics last year voted the city's Royal Concertgebouw the world's greatest orchestra, seeing off competition from the august Vienna Philharmonic and the mighty Berlin Philharmonic which, under a series of stellar chief conductors, had unofficially ruled the orchestral standings for as long as anyone could remember. This weekend, the Concertgebouw comes to the Barbican for two concerts with their former chief conductor Bernard Haitink. It's just a taster of a more substantial Barbican residency that the orchestra will take up in 2011. At that time, alongside traditional concerts, the orchestra will be forced to get down with the kids in outreach and community projects in the run-up to the Olympics.

So are they worth the investment? I watch the orchestra file into their dapper 19th-century hall for rehearsals, looking out for the brilliance that will soon grace our own streets. Theirs is a charisma that, says James Inverne, the editor of Gramophone magazine, which conducted the poll, makes them the Michael Gambon of orchestras. “They seem to be able to switch character so deftly to serve the composer they're playing,” he explains, “so you get a dramatic experience whatever the size or type of piece.”

This sort of greatness surely shows. I imagine it lurking in their eyes, in their posture. The Berlin Philharmonic always look as though they own the world - which, musically, they did.

Five minutes in and I'm not getting much feedback. They chatter, mess about and slouch. Is this the B-team? Then, suddenly, out of nowhere, musical greatness spins in. A fanfare from a trumpeter, a reflexive rumble from the principal timpanist, a flutter from the violins and the scrabbly pre-rehearsal noise starts to coalesce into the most handsome, monumental sound one could imagine. They're playing Happy Birthday for one of the second violinists. It's conductorless, ad-libbed, inconsequential. And it blows me away.

Gustavo Gimeno, the 32-year-old principal percussionist, explains why the world is going crazy for that Concertgebouw sound. “Orchestras are looking more and more like each other,” he says. “At the Concertgebouw, however, the traditions are old and the culture strong. We've retained our original colour.”

He tries to pin down this famous orchestral timbre, meandering enthusiastically through a dozen adjectives. “It's warm, especially well balanced, refined, unforced, noble, elegant, characteristic, round, beautiful ...” He pauses. “Mooi.” He's excited about this one. “We use it all the time. I feel it's in our minds when we play.”

Mooi is a Dutch word that sort of means beautiful, but not quite. Less elusive is the source of mooi. One can pin it down to two things: tradition and acoustics. “The hall defines our way of playing,” Gimeno says. Indeed, Haitink once called the hall the best instrument in the orchestra it houses. Aside from the beauty of its neoclassical dimensions, it has an echo time of 2.2 seconds - the Holy Grail of echoes, perfect for the supple, long-lined works of the late Romantics, of Mahler and Bruckner, that so many of the orchestra's conductors have championed. “It often doesn't feel like you're listening to music at all,” Gimeno says . “It feels like you're dreaming.”

As a result, everyone who's anyone has conducted them since the orchestra's foundation in 1888 - Mahler, Debussy, Bartók, Schoenberg, Stravinsky. This legacy has gone hand in hand with a continuity of style - pupils and teachers from the Amsterdam Conservatoire replacing each other in the orchestra over two or three generations - that reaches back half a century. “I hear recordings from the 1950s and I think that's the sound of this morning's rehearsal,” Gimeno says. “It's a little scary.”

These are keepers of a precious flame, and they take their mission to protect the traditions of the orchestra seriously. “It is my duty to preserve this culture,” Gimeno says. “I couldn't do anything else. I belong to this family.” In the heart of the gang there is remarkable tranquility, even before they go onstage. If greatness is calm under pressure then the Concertgebouw has it in spades. Ten minutes to go and they loll around drinking herbal tea. Second violinist Anna de Veij Mestdagh is at the smokers' table, having a fag and a coffee. She can't remember the last time she was nervous before a performance: “Is that bad?”

As the five-minute bell clamours, her husband, the principal bassoonist Gustavo Nunez, walks past, hands in pockets, chilled. “You have to be,” he says, “otherwise you ...” He tenses his muscles, screws up his face and pretends to fall backwards. It's an impression of stress that doesn't convince me that he's ever encountered it.

Confident, composed, stress-free, evangelically wedded to their jobs - it can mean only one thing: hefty salaries. Wrong. The pay at the Concertgebouw is notoriously lousy. It was as low as £1,300 a month for a rank-and-file member until a few years ago, when the chief conductor Mariss Jansons lobbied the management for a 16 per cent increase. What kept them going? Tradition, according to Gimeno. “I don't check my salary at all,” he says.

This seriousness of purpose has claimed a victim: the community project. Children's concerts, outreach, local engagement, things London orchestras love to throw money at, the Concertgebouw shuns. The Barbican might have trouble convincing them to hang with the kids in their London residency. “You have to make a choice,” says the head of public relations, Sjoerd van den Berg. “We focus on our first task: music. It may be a little elitist, yes. But other orchestras in Amsterdam are covering the educational side of things. We don't need to.”

Bernard Haitink, the conductor laureate to the Concertgebouw and chief conductor to the Chicago Symphony, is diplomatic about the primacy of his Dutch colleagues. “After a rehearsal with the Concertgebouw the other day, I told them: ‘Yes, you really are the best orchestra in the world ... together with the Chicago Symphony'.” He thinks we should take lists such as this with a pinch of salt: “We aren't the Olympic Games.”

He does, however, think that the orchestra has got better under Jansons. “He's done a wonderful job,” he says, “and I have the luxury of coming back to the orchestra, now that the technical flaws have disappeared, to make music in my own way.”

One technical flaw that still dogs the orchestra, Gimeno says, is ensemble. Remarkably, the greatest orchestra in the world isn't always that great at, well, playing together. “It's difficult for us to hear each other on stage,” he explains - the acoustics resonate nicely for the audience but create a black hole for the performers. So they often let a curtain hang in the tenth row for rehearsals. “Still,” he adds, “even when we don't play together, it's still mooi.”

Concertgebouw Orchestra, Barbican, London EC2 (020-7638 8891), tomorrow and Sun

ARE THESE THE TOP 20 ORCHESTRAS IN THE WORLD?

1 Royal Concertgebouw Orchestra

2 Berlin Philharmonic Orchestra

3 Vienna Philharmonic Orchestra

4 London Symphony Orchestra

5 Chicago Symphony Orchestra

6 Bavarian Radio Symphony

7 Cleveland Orchestra

8 Los Angeles Philharmonic

9 Budapest Festival Orchestra

10 Dresden Staatskapelle

11 Boston Symphony Orchestra

12 New York Philharmonic

13 San Francisco Symphony

14 Mariinsky Theatre Orchestra

15 Russian National Orchestra

16 Leningrad Philharmonic

17 Leipzig Gewandhaus Orchestra

18 Metropolitan Opera Orchestra

19 Saito Kinen Symphony Orchestra

20 Czech Philharmonic

Gramophone magazine compiled its list after asking 11 critics worldwide to rank their 20 favourite orchestras

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