Glasgow quartet Mitchell Museum must think festival programmers have something against them.

Last month, at Rockness, they found themselves scheduled to play at the same time as Dizzee Rascal, who then proceeded to suck away all of their audience.

Tomorrow, at T in the Park, their set coincides not only with the Main Stage appearance by a certain Eminem but also, across the fields, The Prodigy, Mumford & Sons and The Stroke’s front man, Julian Casablancas. That’s a shame because it means festival punters risk missing one of Scotland’s best new bands.

Consisting of singer and keyboards player Cammy, his drummer brother Raindeer, guitarist Dougie and bassist Kris, Mitchell Museum eased through the T Break competition stages – I know because, as one of the judges, I witnessed a rare moment of unanimity when we lifted them out of the 1300 entries and placed them among the final 16 invited to Balado.

This year’s T Break entries could be split into three roughly equal camps: the wannabe Biffy Clyros, the wannabe Frightened Rabbits, and everyone else. Mitchell Museum fall into the last category, fusing a Flaming Lips/Animal Collective experimental side with a canny knack for writing big, catchy tunes.

Programming issues aside, the T in the Park slot is a gift for the foursome as their debut album, The Peters Port Memorial Service, is due out on Monday. From its opening notes – imagine if Brian Wilson and the Beach Boys went into the studio dragging an accordion – through its many dense, multi-tracked layers, it’s quite unlike anything currently being made in these parts.

Early reviews have been excellent, and when I meet up with Kris and Dougie a few days shy of this weekend’s festival, they’re still coming to terms with the fact that the outside world is suddenly taking notice of their music. Seeing their name in NME when single Warning Bells was reviewed by Kate Nash, no less, was one giant leap forward. So was one particular visit to London.

“I think the Maida Vale session we did [for Radio 1] was the first thing,” says Dougie. “I sometimes forget that we did that; then I suddenly remember, and think, ‘That was amazing!’”

“It didn’t seem quite right,” adds Kris, “in the way that you have it in your head that you’re still some little band your mates play in. The engineer was talking about how John Peel used to come in and do his shows in the booth that Cammy was singing in, and he’d have the bands playing live during the show. That was one of the things that made us think people might be taking us seriously.”

Over the past year, the band have reworked demos and early live versions of their songs until they were barely recognisable, recording, editing and re-recording them in the studio for the new album. Typically it’s Cammy who first comes to his bandmates with new material.

Dougie explains: “Cammy will usually come up with a demo and bring it to us. Then we’ll all work out a way to play what he’s played, and get a bit more dynamics into it because quite often his demos are quite saturated.”

“Cammy will lay out the basics, write the lyrics,” continues Kris, “and then we’ll scrap whatever he’s done and do what we want to do. There was a lot of stuff we had to revisit after the album was done because it sounded so different from how we used to play it. It is constantly changing.”

The results – particularly standout single Warning Bells – are something to behold: exuberant, clever, textured, infectious, meshing 1960s psychedelia with a 1990s US college vibe, usually all at the same time.

“We don’t really want to be part of the ‘Scottish music scene’ as such,” admits Kris. “I like Frightened Rabbit and all those bands, but I don’t really want to sound like them. It’s nice to hear new Scottish bands, but it’s not that we’re inspired by everything that’s going around at the minute.””

This independent streak encouraged them to set up their own label – Electra French Records. “It’s difficult to be heard just on the basis of buzz,” says Kris, knowing that the industry will pay more attention if you’ve got an album under your belt. “You need to have a solid body of work.”

Even if the timing of their T in the Park slot doesn’t work to their advantage, Mitchell Museum might well have the last laugh. In years to come, , they’ll always be able to say they were Saturday night headliners at the country’s biggest music festival. Over to you, Mr Mathers.

Mitchell Museum play the T Break Stage at T in the Park on Saturday at 10pm. The Peters Port Memorial Service is out on Monday.