It's appropriate that the worship of the cult of Yo La Tengo took place in one of Wales's best venues. The Point is a converted church tucked in around the corner from the regenerated estate agent-trendy Cardiff Bay.

And, beautifully, the kind of people that live in the Ikea-decorated flats round the corner would probably rather go and see James Morrison at the Millennium Centre across the road tonight. Tough luck to them then. After the electronic tippy-tappy beauty of Minotaur Shock, those who know, and those who want to find out, gather in front of Yo La Tengo's pulpit and get ready to praise.

Georgia Hubley strolls out first and begins to bash away at her drums while Ira Kaplan and James McNew casually stroll out and pick up their instruments. They look like a group of teachers from a liberal progressive school. Lesson number one? Noisy rock. Ace.

Kaplan barely even looks at the audience as the trio thunder through ‘Pass The Hatchet, I Think I’m Goodkind’. The track, the opener on the trio’s latest long-player, I Am Not Afraid of You and I Will Beat Your Ass, is an absolute thumper – as the bouncing stained-glass windows will attest.

Kaplan still hasn’t looked at the crowd after four songs. Then he picks up a familiar-looking acoustic: he’s just decided to have a bit of a sing. The curly-haired veteran tell us it’s borrowed from the Super Furries, to predictable cheers.

YLT then go from noisy rock to the kind of breezy pop they perfected on Summer Sun. Newies ‘The Weakest Part’ and ‘Mister Tough’ are beautiful, the kind of songs that would have soundtracked Charlie Brown’s adolescence had he ever grown up. The latter, sung in an airy falsetto by McNew, is the highlight of the night. They've proved they can do noisy. Now they prove then can do quiet.

Few bands in the world can have the same kind of range as Yo La Tengo. Alright, they're not going from orchestra to big-beat, but few bands could so effortlessly weave between making the kind of noise that saw one gig-goer behind me covering his ears and the kind of folky Americana that gets the parishioners swaying in the aisles. Well, swaying in the space where there used to be aisles.

The night climaxes in an almighty racket as Kaplan swings his wood-brown Fender around the stage by its strings. Its bloody strings. It’s an almighty sound, built up with perfection. They obviously teach Indie Rock Crescendos 401 at La Tengo High.

If you’ve come all the way from Hoboken via Stockholm to play, a small thing like a curfew won’t bother you. So, at quarter past eleven, YLT return to the stage for an encore of such dazzling, delicate beauty that you have to wonder if it’s the same band that just about shaved our eardrums out.

Kaplan tells us that the band went to see sixties loons the Bonzo Dog Doo-Dah Band in the city the night before. They then play their cover of ‘The Readymades’. It is very good. And then they play John Cale’s ‘Andalucia’. It is very good.

It’s odd that a band who can make noisy music as good as any noisy band and folky-pop as great as any folky-pop band can still be so, well, marginal after two decades. It’s a shame, but it makes us all the luckier for seeing them here, even after the seventeenth minute of deafening feedback.

Photograph by James Perou