Helsinkiläinens have waited four decades for an acoustic worthy of their two brilliant symphony orchestras, and last night they got one. There might be a few months’ more listening to be done before we know just how fine the acoustics of Helsinki’s Musiikkitalo are, but one thing’s for sure: they’re a gargantuan improvement on those of the Finlandia Hall that opened in 1971. The Musiikkitalo sounds a little jumpy, but it has exceptional clarity, presence and brightness.

Twenty years after the idea of a new music centre for the Finnish capital was first mooted, the opening of the ‘Music House’ has proved an abject lesson in that old Finnish virtue – patience. The winning design wasn’t the most groundbreaking, but it has resoundingly proved the most useful. The Finnish Radio Symphony and Helsinki Philharmonic Orchestras have had two months to get used to playing in the building’s 1700-capacity main hall, and at last night’s concert it showed.

Finland’s musical community was out in force for the official opening, and for a country in which musical traditions are of central importance, that means an awful lot of recognisable faces. The Prime Minister Jyrki Katainen spoke from the platform twixt two slices of Sibelius. Sakari Oramo and John Storgårds conducted their respective orchestras and Jukka-Pekka Saraste marshalled a hybrid formed from both. Every second was relayed live on TV and the web courtesy of Finnish state broadcaster YLE, which put up 26% of the 188m Euro bill and filled the building with its journalists and film crews.

Students from the Sibelius Academy – playing and singing everything from a post-Darmstadt choral motet to folk and jazz – seemed equally at home in the building they will share with their illustrious professional colleagues. Classical music sat easily with vernacular music on this prestigious stage, the two feeling like natural bedfellows as they only seem to do in the Nordic countries where each tradition continues to inform the other.

Everyone in Helsinki has had an opinion on the slow rise of the Musiikkitalo from a huge pit in between the city’s parliament building and museum of modern art. Most Finns – true to form – didn’t think it bold or exciting enough.

But that was from the outside. Under its pale green exterior, the audience last night seemed quietly to recognise it as one of the most extraordinary pieces of public architecture of the last half-century. Restaurants, cafés, gallery spaces, four additional auditoria and a CD store will tempt visitors here all day, six days a week. One of the four ‘extra’ halls houses two gargantuan organs – two more, for the two remaining walls, are on the way.

The biggest cheers last night – after that which greeted Oramo’s freight-train Rite of Spring – erupted as architect Marko Kivistö and acoustician Yasuhisa Toyota took to the stage. Together they have conjured an uncannily Helsinki-ish response to the ‘vineyard-gone-crazy’ designs already unveiled in Copenhagen, Hamburg and elsewhere. The Finlandia Hall’s geometric whiteness has been replaced by a forceful, provocative blackness, shot through with daylight from the large windows that surround the tall main auditorium. It’s starkly beautiful, but wryly deceptive too.

Finns are used to buildings of the highest imaginative quality. But it was inspiring to see them so proud last night – proud, at last, to have a concert hall that affords them full enjoyment of the music they love, and does so with such impeccable precision and style.