The neighbourhood was a jumble of Italian and Jewish immigrants 
originally, David Cossin tells me as he pads 
downstairs and clears space to sit between music stands and bits of drum kit.

We're in the percussionist's basement rehearsal studio – a carpeted den strewn with instruments and recording equipment – in New York's Lower East Side. "Basically whoever got to New York on a boat would come here first then figure out somewhere better to go."

The street of rickety brownstones is tucked between the Manhattan and Williamsburg bridges. Nowadays it's a crossroads between China Town and the bustling East Village, with swish Soho a few blocks north and Williamsburg's hipster apogee just spitting distance across the East River.

If Cossin's band, the blazingly cross-boundary Bang on a Can Allstars, was a neighbourhood, it might well be the Lower East Side.

Then again, the word "Brooklyn" comes up rather a lot. Cossin laughs when I point out that the Edinburgh International Festival brochure promotes the band as Brooklyn-based.

"Our office is over there but that's about it." He's originally from Queens and says that as a musically obsessed teenager it was always "the thing" to escape the outer boroughs and land an apartment in Manhattan.

"I've watched the Brooklyn invasion with arms-length amusement. But I guess that as an international by-word for cool – I mean, how often have you read about the latest Brooklyn-based indie band? – it's probably not that surprising the Allstars are plugged as a Brooklyn outfit."

Essentially the Allstars are about as conscientiously cool as a contemporary classical chamber ensemble gets. They're the performing arm of the multi-faceted Bang on a Can (BOAC) consortium, which for the past 
25 years has embodied a loose strand of accessible American new music.

BOAC was founded by three composers (Julia Wolfe, Michael Gordon and David Lang) who met as Yale students in the 1980s and sensed a common aesthetic leaning towards post-minimalist, pop-infused styles of writing. After graduating, Wolfe and Gordon got married and all three moved to New York; there they encountered a kind of impasse.

"There was a face-off between the formal classical music of places like the Lincoln Center and the avant-garde jazz bars of the West Village," says Cossin. "Academic uptown versus dirty downtown."

On the BOAC website the founders explain that they "started this organisation because we see making new music as a utopian act". For the past quarter of a century their utopia has straddled that uptown/downtown impasse 
with gusto.

Things have moved on since the hard-line 1980s and New York's music factions have opened up and cross-filtered. Rock bands integrate the loop techniques of Steve Reich and Philip Glass, classical composers write for amplified instruments and pinch material from all over the place. It would be misleading to claim BOAC has been solely responsible for the shift, or their work represents all of the new music that comes out of the city. In an age of stylistic free-for-all, Bang on a Can have honed a popularly buoyant, boisterously rock-ish sound and gathered a community of like-minded artists around them.

"Every summer we set up camp at a contemporary art museum in the Berkshire Mountains," says Cossin. "After 10 years with 30-odd people coming to study each year – 
well, soon you have 300 people associated with the thing. A lot of them use it as a stepping stone to move to New York and start collaborations of their own. They're all part of the Bang family."

A family, maybe, but BOAC has never been a school with prescribed doctrines or rules. Artistic decision-making still rests with the founding composers, but what's kept the collective together and distinct is precisely their ability to embrace stylistic breadth.

In 1987 BOAC staged the first of its now-famous annual marathon concerts; five years later the composers founded the Allstars as a house band made with a core amplified line-up of six (piano, bass, guitars, cello, clarinet and percussion). Cossin has been with the group for around 15 years. "I came from a drum set background then studied classical percussion at the Manhattan School of Music. This band couldn't be more perfect for me. I can indulge both sides of my playing and not feel guilty about either."

In Edinburgh the Allstars perform an ongoing project they outed at the Barbican last year (the only brand-new work on the EIF bill, a Laurie Anderson commission, has subsequently been axed). Field Recordings brings together music by 11 composers whose brief was to integrate sound and image footage into short works. Each lasts around five minutes, and together they form a set – "more like a rock band's set than a typical classical concert," is how Cossin puts it. "All of the pieces add up to a kind of meta-piece."

Thematically the commissions were left open and the composers responded accordingly. Julia Wolfe's Reeling features a scratchy recording of traditional Quebecois foot-tapping. Michael Gordon's Gene Takes a Drink uses video footage from a camera that was attached to a cat's head. David Lang's Unused Swan spins winding melodies over the sound of knives being sharpened. Anna Clyne features a Chicago street singer; Tyondai Braxton plays with the sounds of a casino; Mira Calix manipulates images from an airport. There's also a new arrangement of The Cave of Machpelah from Steve Reich's multimedia opera The Cave. As a taster session of the playfully collaborative, cross-genre BOAC house style, Field Recordings is a safe bet.

Within the broader arts-and-technology theme of this year's International Festival, it could hardly make a better fit.

Bang On A Can's Field Recordings are performed at Usher Hall, Edinburgh, on August 23. Visit eif.co.uk/bangonacan.