Polite, eternally self-effacing and, at the age of 42, still letting his eyes retreat behind a diffident fringe, Jonny Greenwood is not a man given to extravagances. He is quietly proud, for instance, to drive an 18-year-old car. As a member of Radiohead, the Oxfordshire five-piece that redefined contemporary rock and, latterly, the mechanisms of the music industry, he is regularly voted among the best guitarists in the world, yet he hates the reverence given to the instrument: he owns just three (one of them a touring back up). It is refreshing, then, and more than a little revealing, when he finally owns up to an indulgence.

“I’ve flippantly said in the past, but I meant it, that instead of spending so much money on your hi-fi, you should really go and hire a string quartet,” he says, folding himself into a sofa in his management company’s office in Oxford. “It will be the most affecting thing you could possibly do in your house. I’ve done it once, just as a present for someone, and it was embarrassing for the first 20 minutes because it was only the two of us watching. But it was more memorable than any holiday. Wouldn’t you rather do that, once in a year, when most people spend far more money on technology to play their music?”

In the company of orchestras

Over the last year or so, Greenwood has been spending more time in the company of orchestras, composing for ephemeral performance and it has made him reconsider his relationship to studio music. “I love the impermanence of the music live,” he wrote recently. “It’s played in the room – which is itself infinitely variable from one concert to another – and then it’s gone, soaked into the walls.”

His most recent composition, Water, is a case in point. It will receive its world premiere in Dublin next week, presented by the Australian Chamber Orchestra in a programme that includes Mozart, Haydyn and Tchaikovsky, and there are no plans to record it. Rock musicians rarely cross over to classical composition with as much grace – consider the fates of Paul McCartney and Elvis Costello – and very few ever find themselves in the company of marble busts.

“I like to feel, in my fraudulent way, that I’m joining the orchestra for as long as I’m with them,” Greenwood says of his former residency with the ACO. “I’m kind of bluffing and dissembling wildly. But at the same time, wanting to feel like they’re not just a collection of presets on a keyboard. It’s not just first violin and second violin, it’s a whole bunch of people with their own ideas and that’s what makes it so interesting, I think. How they play and how it sounds is always going to be different from one rehearsal to the next. It’s like trying to catch a liquid.”

Water has been composed for strings, flutes, piano, organ and tambura – an Indian drone instrument that Greenwood discovered during his year off from Radiohead.

"Have you heard one?" he asks, never more animated than when describing a new musical discovery, and quickly retrieves a sample from his iPhone. "It's that sound. It constantly shifts. It never quite repeats itself, and it's just kind of obsessed me. This piece, Water, is orchestral, but the orchestra is meant to come out of the tambura instead of the other way around. It's sort of meant to be a solo for this instrument that doesn't change note or pitch. It's a little perverse, I know."

Restless experimentation

This seems typical of Greenwood's restless experimentation. In Radiohead, his evolving interests have made him a wide-ranging multi-instrumentalist: keyboards, percussion, glockenspiel, analogue synths, software programming, an array of tech. "I'm a good bluffer," he says. "Most instruments I can convincingly play for a few minutes. Any longer than that and people would find me out. It's like being an impressionist in a way." He is, however, one of the world's few adept players of the ondes Martenot, an early electronic instrument that Greenwood discovered via the 20th century French composer Olivier Messiaen, and which he has made an idiosyncratic component of Radiohead's expansive sound.

In his orchestral work, Greenwood has channelled the spirit of Messiaen, Bartók and the Polish avant garde composer Krzysztof Penderecki, most notably on Popcorn Superhet Receiver. A darkly meditative piece, written 10 years ago when he was the BBC Concert Orchestra's composer-in-residence, that composition formed the basis for his film score, There Will Be Blood, for director Paul Thomas Anderson, and has led to several more. In one appreciation of Greenwood's composing, the New Yorker's Alex Ross invoked his classical training, and a music degree thwarted by his band commitments, to argue that Greenwood was best understood as "a composer who has crossed over into rock".

Greenwood is better able to reconcile his parallel careers, which is just as well, because they are about to make him extremely busy. A new score for Anderson's forthcoming Thomas Pynchon adaptation, Inherent Vice, will emerge later this year. "Such a funny film," he smiles, "yet there's some strange emotion in it, neither anger or sadness, which I couldn't really pinpoint. It was a really peculiar tone."

He has also been collaborating with the London Sinfonietta chamber orchestra and premiering genre-melding pieces in gig-like recitals with the London Contemporary Orchestra.

Radiohead reconvene

And now, after their longest ever break and a profusion of solo projects, Radiohead have reconvened this month to begin recording their ninth album.

“I think I was always going to be in a band,” Greenwood reasons, scooping back his hair. “When I was tiny – six or seven or eight – I would be obsessed with the idea of being in a band. It’s only as Radiohead got more successful, and we got the budget to play around with orchestral string groups and write arrangements for Radiohead songs and then do the occasional soundtrack, that it made me remember how I spent my teenage years, which was in the company of recorder groups and string groups.”

Now, he says, whenever he sees someone carrying around a cello, he considers it far more admirable than another wannabe toting an electric guitar. “When someone is playing in an orchestra and devoting all their time to playing and practising and learning, it’s sort of amazing.”

Of his role in Radiohead, Greenwood says: “It’s like being an arranger. How do you put this song across without being retro, and without being offputtingly, wilfully obtuse, but still put the song across really well? A lot of these songs work when Thom [Yorke] just sits and plays them on the piano. It’s tempting to leave it alone sometimes, but it feels like it could go elsewhere, so it usually does.”

Greenwood is uncertain if he could attend the world premiere of Water, which he has not yet heard fully realised ("Until then it's just ink"). It seems unusual for someone who seems happiest when participating, lending guitar or manning the Martenot for his own compositions. "It's the best place to be, in the middle," he says contentedly, "to sit amongst the musicians and hear it like that." It sounds like a purely musical indulgence, as intimate as a private string quartet recital or a composition that exists only for the fleeting moment: in Greenwood's philosophy, you have to be there.

“That’s how it feels,” he says. “It’s just how to get people there, and to decide where ‘there’ is.”

Water, by Jonny Greenwood, receives its world premiere at the National Concert Hall, Dublin on October 2nd as part of the Australian Chamber Orchestra's European Tour