We have basketball to thank for Edinburgh alt-rock heartbreakers Meursault.

"I was into basketball, and only into basketball, until I was 21," says singer-songwriter Neil Pennycook. "I was as passionate about that as I am about music now. But I hurt my knee and had to take six months off, so I started playing guitar. And that was that."

You wouldn't will an injury on someone. You would not wish to celebrate a wound. But Scottish music would be missing a star if Pennycook had not done his knee in. Signed to Edinburgh DIY empire Song, By Toad, Meursault are a chamber-rock force to behold, and Pennycook also moonlights with alt-rock genius Withered Hand, fellow stellar Toad signee Rob St John, and as one-third of Cold Seeds (with King Creosote and Animal Magic Tricks).

Following 2008's P***ing On Bonfires/Kissing With Tongues and 2010's All Creatures Will Make Merry, the terrific new long-player, Something For The Weakened, is Meursault's most cohesive offering yet.

"This album makes more sense to me, and I think I'm more relaxed this time," nods multi-instrumentalist Pennycook across a pub table on Leith Walk. "I can hear it as a body of work, and it resonates more with me than the other records."

The album grew out of current single and live favourite, Flittin'. "Yeah, Flittin' gave me an idea of what I wanted this album to be about. While the other two are pretty heavily themed, I just wanted this album to reflect what was happening over the course of a year," the frontman offers. "I don't think the lyrics are quite as metaphorical as they've been in the past. They're a bit more direct and that's what I was after. That carried through the instruments as well."

There is a clarity and economy to Pennycook's words which can knock you sideways. Take the new album's heart-stopping laments Dearly Distracted ("You painted yourself into the canvas") and Mamie ("And you watch them dance along the promenade / and you'd lose an arm for some of that"), or the deadpan punch of Settling, whose Anglo-Saxon thrust does not bear repeating in a family newspaper, more is the pity.

There's also a thrilling jolt in Dull Spark, whose title belies its epic fire (its preceding track, Lightning Bolt, is conversely a beatific psalm, and the two are intricately related). "Dull Spark was the last song we wrote for the album," Pennycook offers. "Until then, I was a bit worried that I was writing a downbeat album, because people seem to like the really energetic stuff like [2010's hurricane-force] Crank Resolutions, but I wasn't really feeling it. So it's a case of taking the intensity and putting it elsewhere. It doesn't always have to be 180 beats per minute. You can play a waltz with a piano and a cello and have the same energy."

A gorgeous banjo and string-drawn reworking of Lament For A Teenage Millionaire, which first saw light as a lo-fi electro squall on their debut album, underscores how the Camus-referencing band has evolved and augmented since Meursault's early shows in 2007.

The line-up now comprises Pennycook, Calum MacLeod, Lorcan Doherty, Sam Mallalieu, Ben Fletcher, Kate Miguda, Rob St John and Pete Harvey. Harvey also recorded the album and scored its striking string arrangements.

"With the last two records, I was into that idea of just locking myself in a room for a few weeks and emerging with an album, so it was nice to have everyone getting together this time, bouncing things off each other," says Pennycook.

Pennycook met Harvey in the Stockbridge living room of Matthew Young, Song, By Toad label boss (and celebrated blogger/podcaster), in 2009. "I was a huge fan of Pete through Khaya, Desc and The Leg, and then he came in to do the Cold Seeds album. I told him I really liked his stuff, and he said the same, and he actually asked to join the band. I was quite flattered by that," he recalls. "I got to record with King Creosote that day too – I'd been buying his records since I was at college. That was a good day."

Pennycook spent his early twenties "singing and screaming" in heavy metal outfits ("I bailed out when we got a rapper," he laughs) then in a "scrappy college-rock band" called Felix Lighter. His love for Sebadoh and Dinosaur Jr led him to Daniel Johnston and Sparklehorse, on a musical journey that eventually steered him back across the Atlantic, to the shores of the Forth.

"Coming across Fence was a revelation," he says of the DIY Fife collective whose events he now regularly plays (Meursault will perform on the top secret bill at their upcoming festival, Away Game, on Eigg).

"King Creosote was the first time I'd heard that kind of music sung with a Scottish accent. And the first Arab Strap album – a guy with a gruff Scottish accent crossed with Smog, Bonnie Prince Billy and Slint – that was amazing. But the big one for me, because they weren't a million miles away from what I was doing, was Idlewild. It took me a while to iron out my own American accent though," he laughs.

These days, Pennycook's voice is entirely his own – by turns high-octane and vulnerable – and the band is at the heart of Edinburgh's brilliant grassroots scene, alongside acts like Withered Hand and Eagleowl. "Yeah, you don't really see a lot of bands in competition here, and I like that. I don't want to be competitive. That's why I chose basketball," he says of the team pursuit.

"I think my parents breathed a sigh of relief when I had to give up basketball," he continues, "even if I was going from an unlikely chance of ever making any money from one profession to another. Music seemed like a more viable option in their eyes, so they were actually pleased." He smiles at this tale of a weakened knee with a happy ending. "It's funny how it all worked out."

Meursault play Queen's Hall, Edinburgh, July 7; Fence Collective Away Game, Isle of Eigg, July 20-22; Thistly Fest, Dunbar, July 28. Something For The Weakened is out on July 16