Some songs tell stories and some songs paint pictures.

The strange, slow, beautiful music of Sigur Rós falls firmly into the latter category, which is why it's probably unfair to ask Jónsi – he of the ethereal falsetto and impenetrable 'Hopelandic' lyrics – what the songs on the band's new album, Valtari, might be about. It seems too literal; too exact. But let's do it anyway and see where it gets us.

Not terribly far, it transpires, although between "umms" and "ahhs", the Sigur Rós singer and guitarist does let slip that Dauðalogn, meaning Dead Calm, is "about when you can't sleep or when you wake really early before the day starts". It's an evocative but hardly revelatory answer, and before long he's talking about "soundscapes, drones and textures" as opposed to words, songs and singing. "The lyrics are really quite introverted and abstract," he concludes. "If you want to read a story from it you can, but it's more about throwing around pictures."

Carrying out promotional duties in the not terribly taxing location of the Covent Garden Hotel in London, Jón "Jónsi" Þór Birgisson's excellent English comes with a burring Icelandic accent and a smile. He seems happy, and little wonder. The band's sixth album is their most beautiful yet, a poke in the eye to the hustle and bustle of modern life: 54 minutes of drift and wonder during which, to paraphrase Irish critic Vivian Mercier's infamous review of Waiting For Godot, nothing happens – not twice, in this case, but eight times. And gloriously.

This is music that slows the heartbeat and heightens the senses. The tracks are rooted in stillness, retreating from the more conventional song structures of their last album, Með suð í eyrum við spilum endalaust, towards their more ambient and open-ended earlier work. Having taken their music to the border of somewhere "upbeat and festive" on the two previous Sigur Rós records, Jónsi says that "we're maybe rebelling a bit against that with Valtari. We wanted to take a left turn and do something different to keep it exciting." Half the album is either instrumental or choral, with Jónsi taking a back seat as lead singer. "There is actually more of my voice than we were planning," he says. "Alex [Somers], my boyfriend, who mixed the album, encouraged me to sing more and write more lyrics. I was going to sing less." Why? He shrugs. "It was just the nature of the songs."

There is, he agrees, at least the hint of a band being deliberately contrary by reacting against their growing popularity. "Maybe," he nods. "There might be some kind of mini-rebellion." There are certainly no hit singles on Valtari. It evokes such a slow, serene landscape that every chord change becomes seismic and every shushing sound is transformed into a vast block of ice drifting on the sea. Pictures, not stories.

The album has a complex history which belies its unity and serenity. Indeed, for a long time it looked like a record that was destined never to be made. In the four years since Með suð í eyrum við spilum endalaust, Sigur Rós sent out a series of what can only be described as warning flares. As early as May 2009 they revealed that they had almost completed a new album, only to later announce that the recordings had been scrapped. Meanwhile, Jónsi went off to do his own thing, which included recording his peppy solo album Go and collaborating with Somers on the Riceboy Sleeps project. More recently, he wrote the soundtrack to the Cameron Crowe movie We Bought A Zoo, starring Matt Damon and Scarlett Johansson.

Were the rest of the band relaxed about all these solo excursions? "No, they were gonna fire me ..." he chuckles. "No, they were super-supportive and cool about it. I think. I hope! It's good to do different stuff. Even though you're busy, in some ways it's like a rest. It takes your mind off the daily routine. They were very challenging projects and I learned a lot from them. The solo album was something I wanted to try for a long time. We always write together as a band, so I had a lot of songs I had written by myself. It was fun to play with different musicians and it would be fun to do it again one day."

The scrapped Sigur Rós record and Jónsi's extracurricular work coincided with talk of an "indefinite hiatus" for the band; frankly, it all seemed rather ominous. "There was a phrase that I think came from our managers," he laughs. "It sounded pretty bad! It didn't come from us – we just wanted to have a break after touring, and the guys were having kids. But we have never talked about stopping."

Nevertheless, he admits that Valtari "is kind of a scatterbrain. There were many points where it seemed confusing. Normally we'd meet at rehearsals, write a song and then go into the studio to record it. But this is such a weird album, we didn't do any of that. It was all over the place." Some of the music dates back to a 2003 collaboration with The Sixteen choir at AIR studios in London, which was subsequently shelved. Then they started working on another project, before giving up on that too. "It wasn't until a few months ago that we revisited all these attempts and realised we had some good stuff there," he says. "It was our managers who pushed us to make this album happen. We had these old sessions, which were confusing and all over the place, and we recorded new stuff also."

Jónsi and the rest of the band – Georg Holm (bass), Kjartan "Kjarri" Sveinsson (keyboards) and Orri Páll Dýrason (drums) – all still live in Reykjavik, where they have a rehearsal space cum HQ, but the singer admits "it's different now. People have families and kids and we have to organise our time better."

Shortly after we spoke, Sigur Rós announced that Sveinsson had left the group to pursue other projects. Still, Jónsi is adamant that there is a "long plan" for the band stretching well into 2013, involving lots of touring, film projects and another album. He clearly thrives on making music. "You do it because it gives you some fulfilment in life. It's pretty selfish, in the end. You do it because it makes you feel good."

Following their long lay off, one of the most distinctive and downright ravishing bands around certainly seem to have recaptured some of the wonder of making music together. "We hadn't played for four years and it was funny when we started rehearsing again," says Jónsi. "It was like being 14 again, playing in the garage and trying just to get through one song. But it's like riding as bike – the muscle memory serves you and kicks in. It was such a fun thing meeting up with the guys and being back in the band. It was a relief, like coming home." And off he goes, ready to paint more beautiful pictures.