It's Tuesday night in an uncharacteristically muggy Edinburgh, and in a city centre basement bar sweat-box, a band is about to play their first - and possibly final - gig.

The musical set-up is tried and tested; an all-male indie four piece consisting of vocals, guitar, bass and drums. There's a chemistry among the quartet as they go through the paces of their brief, four-song set, even as they sound rough round the edges and at times appear to be tugging in different directions.

That's nothing new in a pub venue of this size, and equally typical are the two well-refreshed eastern European girls who are getting their picture taken on the lip of the tiny stage the band are playing on. Despite the fact they've never played together before outside of a rehearsal room, the band bluff it enough to make the audience believe everything they're hearing.

I'm With The Band, Welsh writer Tim Price's new play, is part of the Traverse Theatre's Edinburgh Festival Fringe season and is a timely look at the ongoing independence debate in Scotland, which uses the obvious but accessible metaphor of a band made up of members from all four UK nations to make its point.

"It's always quite difficult to put big ideas on the stage," says Price, who unfortunately couldn't be in attendance for The Union's live debut.

"If you're not careful, you can sometimes end up being swamped by those ideas and can forget to entertain. Once I found this way of representing all the four home countries as a band, I felt liberated, and it became easy to work out what the responses of each member of the band might be."

This approach nevertheless somewhat belies what Price sees as a situation in Scotland that is far more complex than advertised.

"To try to condense 300 years of history into a simple yes or no vote, it's more difficult than that," he says. "Part of my frustration comes out of this idea that the debate is just about Scotland and England, but if Scotland does go independent, it will have a huge impact on Wales and Northern Ireland as well, yet there's barely been a mention of that, which I think is really naive.

"The play's quite satirical, but I think there's a serious message about how the debate's being conducted, and the most important point I'm trying to make in the play is that there are four voices, not two.

With new songs provided by Gordon McIntyre of Edinburgh indie band Ballboy, who also scored hit lo-fi musical, Midsummer, one might wonder why such an issue isn't being tackled by a writer based in Scotland.

"Orla [O'Loughlin, the Traverse's artistic director] would've loved a Scottish writer to do something on the independence debate," Price points out, "but no-one pitched anything."

Despite his disclaimers, Price isn't shy of dealing with some pretty meaty stuff. His first appearance at the traverse was with For Once, which looked at teenage deaths in sleepy English towns. This was followed shortly afterwards by Demos, a verbatim show which compared the transcripts of the daily meetings held by the Occupy movement with Prime Minister's Question Time at Westminster.

More than a year on from both plays, and, as well as I'm With The Band, Price's work can be seen in Edinburgh in The Radicalisation of Bradley Manning, which yesterday scooped the inaugural James Tait Black Prize for Drama, which was set up last year by Edinburgh University in partnership with the National Theatre of Scotland and in association with the Traverse Theatre.

Price's site-specific piece looks at the background of the American soldier who was last week found guilty of passing on classified material to the website Wikileaks. It was the contemporary nature of the play that in part persuaded the judges to give Price the £10,000 award.

Presented by National Theatre Wales, Price's play was originally seen in Manning's old school in Wales where he spent some time as a child. In Edinburgh, The Radicalisation of Bradley Manning will also be produced in a school. One crucial element of John E McGrath's production is that, as happened in Wales, it will be streamed simultaneously online, thus enabling a global audience to witness the play in a spirit of open-ness in keeping with Wikileaks.

"It got more than 9000 views in 76 different countries," says Price, "so our play connects up with what Bradley did, and even people in somewhere like Chile can watch it."

We're talking the day that, after a thousand days in prison, Manning's lawyers finally get to pick apart the charges Manning is facing, even as he's already "had his human rights ridden over roughshod," according to Price.

The Radicalisation of Bradley Manning also arrives as former CIA employee Edward Snowden has come under similar scrutiny by the American authorities after leaking details of mass surveillance programmes to the press.

"He's not been charged with anything yet," says Price, "but he's already the most wanted man on the planet."

Despite how Price's sentiments may appear on the page, he comes across as anything but an unreconstructed firebrand, retaining an inquiring intelligence in both works.

"I think art is the best way to look at these ideas," he says. "Political theatre as such doesn't really seem to fit with the sorts of plays I write, and which I think a lot of my generation of writers write.

"What writers are interested in now, I think, isn't politics, but power. Once you look at that, you discover that people who have the power aren't necessarily the politicians, and that its corporations who write policy.

"Once you realise that, it's about finding out how the world works."

I'm With The Band, Traverse Theatre until 25, various times, reviewed opposite; the Radicalisation of Bradley Manning, St Thomas of Aquin's High School, Chalmers Street, until August 20, 7.30pm, and will be streamed simultaneously at nationaltheatrewales.org/bradleymanning