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叠箩枚谤办 is at it again. Ever eclectic, her latest album is inspired by science and there鈥檚 a suite of apps through which to experience it. David Robson met the Icelandic singer to find out more, and enjoyed a sweet music lesson to boot

JUMPING from her seat, plunges her hand into a dish of sugar cubes, scattering its contents across the coffee table. She arranges the cubes in alternating blocks of brown and white, mirroring the keys of a keyboard. To her surprise, she has the perfect combination to make an octave.

鈥淲ow, I can鈥檛 believe it,鈥� she says. 鈥淚 took exactly the right number. We鈥檙e lucky!鈥� She begins to run her fingers over the different 鈥渒eys鈥� of her makeshift piano, singing the notes as she does so, and tries to teach me the differences between Japanese, African and Arabian scales.

We are together to talk about , 叠箩枚谤办鈥檚 new album and suite of smartphone apps that will combine science-themed songs with computer games that aim to teach music theory to the uninitiated, like me. 鈥淢usic education鈥檚 not as hard as people make it out to be, but it鈥檚 been put on this pedestal for a chosen few,鈥� she says. It is for this reason that, like a modern-day Maria von Trapp, 叠箩枚谤办 is giving me an impromptu music lesson.

It鈥檚 not quite what I鈥檇 expected from the avant-garde pop singer, who has been a polarising presence in music for the last 20 years. She鈥檚 sold more than 20 million copies of her six studio albums, garnering numerous awards and fans as diverse as Madonna, Radiohead鈥檚 Thom Yorke and the classical composer John Tavener. But she鈥檚 attracted critics too, who baulk at her unconventional vocals and idiosyncratic lyrics.

Biophilia, her most experimental project to date, looks set to divide opinion yet further. Its name 鈥� inspired by neurologist Oliver Sacks鈥榮 book Musicophilia 鈥� evokes humankind鈥檚 empathy with nature, which 叠箩枚谤办 has borne out with songs about genetics, crystallisation, plate tectonics and dark matter. The accompanying apps will be released in place of music videos, while the live shows have so far included a recorded voice-over by British naturalist David Attenborough, a live Tesla coil and four 鈥済ravity harps鈥� suspended on 3-metre pendulums.

Science and nature aren鈥檛 typical fodder for a pop singer, but 叠箩枚谤办 assures me that they have been life-long interests for her: 鈥淚 was always a bit of a nerd.鈥� As a child in Iceland watching TV at her grandparents鈥� house, she was captivated by the BBC鈥檚 natural history programmes. 鈥淚 just thought David Attenborough was everything,鈥� she says. At school, she always preferred mathematics and science. At age 16, she chose to concentrate on physics. 鈥淣ot just because I was interested in physics 鈥� which I was 鈥� but because it had the most maths in it. So I was doing all these maths courses 鈥� the only girl 鈥� and I really loved it.鈥� Just don鈥檛 ask her to solve a mathematics problem these days, she says.

鈥淪cience and nature are not typical fodder for a pop singer鈥�

Her musical talent would send her shooting along an entirely different path, however. On her 40-minute journey to school, she would sing as she walked, composing new tunes along the way. 鈥淕oing down the hill, that would be the verse, and then up the hill, that would be the chorus鈥� my accompaniment was nature.鈥� After being discovered by a local radio station, she released her first album aged 12, and in her teens she joined various punk, goth and jazz-fusion bands.

By the mid-80s, one of these had morphed into The Sugarcubes, which gathered a cult following across the world. The band split in 1992, and she set about recording her first adult solo album, Debut, which she released in 1993 to widespread acclaim. Five albums later, she started work on the follow-up to 2007鈥檚 Volta. After numerous false starts, she settled on Biophilia in its current form.

But why write an album about science? For one thing, she says, it offered a gentle departure from the confrontational nature of her previous album. 鈥�Volta, for me, was about pointing your finger and criticising things and asking for justice.鈥� After 18 months of touring for that album, she鈥檇 had enough. Natural phenomenon can also offer some fitting visual metaphors to translate the music theory, she says. The jagged shape of lightning for instance, mirrors the rise and fall of pitch in arpeggios. 鈥淭hat鈥檚 really a no-brainer.鈥� She put this to use in a track called Thunderbolt, which uses a bass line of arpeggios recorded from a discharging Tesla coil.

At other times, the subject matter just seemed to click with the sounds she was creating. While working on one particular track, for example, she became obsessed with a DVD documentary about cosmology that showed the distribution of galaxies and dark matter in the universe. 鈥淪uddenly, you鈥檙e actually seeing the whole universe for the first time,鈥� she says, her eyes wide open. 鈥淚 was just like, wow, and I really felt, emotionally, a feeling of isolation.鈥� The feeling seemed to match the emotion of the piece she was writing, so she called it Dark Matter. Since the piece is atonal (it is not written in any particular musical key), she felt like it would be the good basis for an app on musical scales.

鈥淪uddenly, you鈥檙e actually seeing the whole universe for the first time 鈥� wow鈥�

Crystalline, the album鈥檚 first single, has a similar story. 鈥淗earing it, I just felt like someone had a chisel and was chopping into crystals, it was so relentless,鈥� she says. 鈥淎nd emotionally, it had to be about anxiety, because it has that relentlessness.鈥� Whatever the subject matter, some kind of emotional connection to the music and lyrics is crucial, she says.

Many of the songs came about unconventionally 鈥� they were written on music software that responds to a touch screen and a Nintendo video game controller with a joystick. Using the touchscreen, 鈥淚 could draw the bass line with my finger,鈥� 叠箩枚谤办 says. The joystick offered an easy way to juggle the chords and bass line of the music while she sang and improvised.

This liberated her song-writing, she says. Ever since those long journeys to school, she had composed much of her music by singing on long countryside walks, which, she believes, led to 鈥渓inear鈥� songs in which the chords don鈥檛 change for a long time. 鈥淚鈥檝e never really worked it out before, but it鈥檚 probably because I鈥檓 walking at just one speed.鈥� She proceeds with a synaesthetic analogy: 鈥淚鈥檝e always experienced rock music as if it鈥檚 shaped like a cross, it鈥檚 very square.鈥� She makes the shape with her hands. 鈥淏ut with this [technology] I can go into shapes that are in nature, like triangles or octagons.鈥�

The result is one of the most innovative albums this year 鈥� another curve ball from an artist who continues to push the boundaries of the pop song. Her inventive use of apps as a medium to release an album might even suggest new ways to save the beleaguered music industry. 鈥淲ell, it works for me,鈥� she says, but is keen to point out that there will be many other possible solutions too. 鈥淏ut you鈥檇 be surprised how the people at Apple, and Android 鈥� and whatever other systems 鈥� are all gagging for us to comment and collaborate with them.鈥�

Whether the album will convince 叠箩枚谤办鈥檚 critics is anyone鈥檚 guess, though Biophilia鈥榮 debut shows, at the Manchester International Festival in July in the UK, met with almost universal acclaim from the music press.

叠箩枚谤办, at least, feels that the project has been blessed with good omens. As we finish our conversation and her PR person walks in to usher me from the room, he raises his eyebrows at the sugar cubes on the table. 叠箩枚谤办 explains the narrow chance of pulling out exactly the right number to make a scale. 鈥淲e were lucky鈥� but that鈥檚 just what the whole of this project has been like.鈥�

叠箩枚谤办鈥檚 Biophilia album will be out in early October