I've even armed myself with a manifesto to fend off the pre-conceptual demons, a carefully scribbled note that I read before setting out, bravely stating that I "shalt not lament the Cult of Cool," because "such a thing will not exist." I get a chance to double check this in a brief moment of quiet as Minotaur Shock take to the stage, before wondering why I'm currently without a girlfriend. As soon as the music starts though, I'm O.K, especially as – I'm thinking – the thunder might already be stolen.

This band's drummer is existing in an alternate universe, behind them on a huge screen, and they're conversing with him over the timing of the first song. They finally get the timing right, and it's ace. But now I see that the drummer out there is the same guy that's playing guitar. Fucking crazy. "Is that a clarinet?" Tremendous. "Or is it not?" I've never seen it played sideways before, like a snake charmer's dobru. Minotaur Shock are playing with my mind like a vintage Godard elliptical, but their sound evokes a movie made by Claude Chabrol in the year 3000. Futuristic-shanty-art-cinematic soundscapes writhing with compositional soul.

Clarinettist Emily is a picture of accessible cool, layering amazingly scopey sounds over her two pals' concise bass and guitar shards, and when they crank it up, boy is it good, raging aural spurts of eloquence that are a natural progression from their earthily atmospheric foundations. Throughout the set the pictures alternate on the big screen background from the phantom drummer to affecting, minimalist black and white images of a swaying, cartoon sea and collaged seagulls, and by the time they're done everyone has made a note of the multi-faceted beauty of Minotaur Shock.

You wouldn't have guessed it, but I'm standing in a closed circle of marijuana smokers, and between this, the shock of the Shock, and the Newcastle Brown, feel like I could float away any time soon, but as Yo La Tengo take to the stage to raging bass and guitar lines, I pique again and resist the temptation to consult my manifesto. There's the singer Ira, with his neatly frizzled hair, and this is it: My meeting with the legends of the Unknown.

Yo La Tengo are pretty popular for the world's most obscure act. But then we're talking in the realms of Pop, in which their gravitational pull is awesome. A decent faction of the hundreds of people here are, like me, complete and innocent strangers to their sound, who've come to the Inevitable Destination via directions from East, West, North and South, like a trip round Birmingham's Spaghetti Junction, only a million times more scenic. This song goes on as long as that last metaphor, but hey, it's not bad, and around the corner I sense a wealth of Pop heroism.

Another track of raucous thrills contradicted by an unmistakeable sensitivity, and here we go: some movement. Ira has ambled over to sit at a piano, head protruding above like a frog on a maple leaf, and, wow, the earthy voice of the drummer Georgia and Ira's low-key backing vocals. This is really something. Dreamy alt pop nuggets like this is what I and, I'm guessing, the other novices here have come for, and if only for the current song it's worth the journey. Now we know what the Tengo are about. And they are fantastic if they do nothing more.

This turns out to be one of a number of moments that define tonight's journey of avant-garde legends, a journey in which the word "legends" can only be used in the most complimentary sense. Sure, we'd like to have more, but the nature of such developed genius is to go off on tangents that will give birth to ever more refined nuggets. The band are affectionate and locally-savvy to the core, introducing Gorky's Zygotic Munki violinist Megan to embellish a few of the heavier, futuristic guitar soundscapes, including a fantastic folk-rock ho-down towards the end, where the set softens a bit.

Ira takes requests from the Welsh Tengo fanatics for an encore, which contains two more disarming and dreamy folk-pop classics, presumably from their back-catalogue, that move through the old church like enchanted spectres, before dedicating a sublime Celtic folk song to the Super Furry Animals, one of whom's guitar is borrowed for tonight, and leaving us with a piercing outro that reminds that barbed beauty is the greatest kind. "Thanks for coming … The audience … The Super Furries … The Gorkies …" Yo La Tengo have all the right Welsh heroes, and tonight Wales has all the right American heroes. This is what I've been missing. Now I'm on the inside.

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Mercury Prize 2009 nominees