"I was standing there having to say something," he says, wincing at the memory. "And they were all watching and waiting. Yeah, it's just … wretched." He falls silent. "Being shy is all conceit isn't it?" he ventures. "Because all you're doing is worrying what people think of you and that, in its own way, is a rather self-involved, rather egotistical thing. The mature thing is to not really care." He looks at his folded hands. The room is suddenly very quiet. Jonny Greenwood – only big brother Colin calls him Jonathan – is Radiohead's youngest member, but arguably its most prodigious. Best-known as a guitarist – "an effects-loving wizard whose endlessly mutable style has powered the band's restless travels," as the NME put it – he also plays piano, viola, an eccentric keyboard called the ondes Martenot and just about any instrument he can get his curious hands on. "I bluff and fudge my way with new instruments," he says, anxious to head off any suggestion he's a virtuoso. "I'm very good at pastiche. I can play the drums really well for 30 seconds and make you think I'm a drummer. But if I had to play with a band you'd hear that it's just awful." In 2004, he was appointed composer in residence by the BBC Concert Orchestra and wrote a number of compositions including Popcorn Superhet Receiver.The piece – a "gritty, energetic" string orchestra work inspired by the sound of radio static – became a favourite with forward-looking classical ensembles including the ACO. Greenwood incorporated parts of it into the soundtrack he wrote for director Paul Thomas Anderson's 2007 movie, There Will Be Blood. The film won two Oscars, including best actor for its star, Daniel Day-Lewis, and cemented Greenwood's reputation as an edgy film composer. Since then, he has written scores for Norwegian Wood (an adaptation of Haruki Murakami's novel) and the big screen adaptation of Lionel Shriver's book We Need to Talk About Kevin. He re-united with Anderson to score 2012's The Master and has recently completed work on a third Anderson movie, an adaptation of the Thomas Pynchon novel Inherent Vice. When Radiohead is on hiatus – as it has been since late 2012 when the band's most recent world tour culminated in Melbourne – Greenwood divides his time between composing, performing with ensembles and orchestras and giving solo guitar renditions of avant-garde repertoire such as Steve Reich's Electric Counterpoint. The work he does with Radiohead informs his classical compositions and vice versa. It has been noted that the keyboards on Exit Music (For a Film), a track on Radiohead's OK Computer album, are redolent of Krzysztof Penderecki, the 20th-century Polish composer Greenwood cites as the most important influence on his own writing. Penderecki's often unsettling music has also been used in movies, most notably the scores of two terrifying films, The Exorcist and The Shining.

Greenwood's parents weren't musical – not his father, who served in the army and died when he was very young, nor his mother who reportedly wanted Colin to be a lawyer and dislikes Radiohead's "noisy" music. But Greenwood can still recall his frustration when teachers told him he couldn't start learning the recorder until he was eight. When he finally got his hands on one, he was addicted. He joined a recorder group and played Baroque music until he was in his late teens. "I used to be ashamed of it [playing the recorder], but now I'm, um, proud." He still plays the recorder, using it on several songs on Radiohead's second studio album, The Bends. Greenwood joined Radiohead soon after the band formed in 1985. In those days it was known as On a Friday, a rather limp name inspired by the day of the week Yorke and his mates got together for rehearsals at their boys' school in Abingdon, Oxfordshire. Greenwood contributed harmonica then keyboards, before taking up the electric guitar aged 16. In 1991, he was just three weeks into a music and psychology degree course at Oxford Brookes University when On a Friday (soon to be renamed Radiohead) signed a six-album deal with EMI. His early departure from college is the reason there are large gaps in his knowledge of classical music, he says. While his love of Penderecki, and other 20th-century masters such as Olivier Messiaen, borders on obsession, he is hazy about many of the composers who came before them. "My [classical] training is, um, quite stunted." The residency with the ACO was unprecedented and utterly thrilling. Greenwood, his wife and their children, lived in a rented apartment in Darlinghurst. He fell in love with Sydney's inner-city lifestyle, abandoning any notion of travelling to the outback to seek inspiration from nature. Instead, he spent hours in his room playing the tambura, a string instrument resembling a sitar he'd fallen in love with during a visit to India. Greenwood was determined to work out how to incorporate its distinctive drone into a composition featuring piano, flutes and a string ensemble. "I'm sure it's sacrilegious to say this, but it's [the tambura] quite easy to play," he says. "An Indian friend of mine told me you have to spend a few months learning to tune it. Part of me wants to be reverential and agree with that, the other part of me thinks, 'Well, that's not very punk is it?'" Why is the piece called Water? The ACO's artistic director Richard Tognetti thought it might be a response to Sydney's harbour until Greenwood – avowedly "not a beach guy" – put him straight. The title is inspired by a Philip Larkin poem whose final two lines – "And I should raise in the east a glass of water. Where any-angled light would congregate endlessly" – sat beautifully with the sound of the tambura and the movement of the music. Is he happy with the piece? "Yes," he says. "I do worry that it's too tonal, too gentle and sweet". He looks sheepish. "Again, that's a very childish worry."

Greenwood and Tognetti, a devoted surfer, may not have bonded over outdoor pursuits, but they are clearly kindred spirits when it comes to adventurous music. "The man I met wasn't a rock star," Tognetti says. "He was incredibly modest, but that implies meekness and he's not meek. He's … resolute. To compose, you need to be decisive and he makes incredibly good decisions about sound worlds". Greenwood is equally complimentary about his hosts. "They're the most casual people until they start playing – then they're the most exciting and intense performers," he says. "Just listening to the ACO warming up is exciting. In fact, some of the best moments was hearing them rehearse other people's music. When you're in a small room ... and a group like this is playing, it's so … emotional and exciting. It's … it's overwhelming." I ask him if the passion he evidently feels for live classical music has reduced his enthusiasm for playing heavily amplified rock. His response is interesting. Playing gigs with a band was never the main game, he says; writing and arranging songs is far, far more stimulating. "There's something about bands on stage with guitars. It's not stupid exactly. It's … hackneyed, perhaps? I do feel weird sometimes when I see a band and think this could be the 1960s, so why bother. But I guess it's a good combination of sounds in the way cello and violin is a good combination. I don't see that one is any newer, or cooler than the other. They're all pretty old really. And that's a good thing, a reason to relax and use anything to make the music you want." What's next? Radiohead are about to reconvene at their studio in Oxfordshire to begin work on what may, or may not be a new album. Greenwood can't wait. The 12-month hiatus has been a little too long, he says. He is itching to write new music and play his electric guitar with the band. His phone chirrups: a text message from his wife. He laughs, smiles apologetically and passes me the handset. "How much longer can you talk about yourself?" the message says. "Give it a rest". He makes his apologies and rises to his feet. Life, for Jonny Greenwood, is clearly elsewhere.

The Australian Chamber Orchestra will perform Jonny Greenwood's Water and Tognetti's Beethoven at Hamer Hall, Arts Centre Melbourne, on October 26 and 27, and the Sydney Opera House on November 2 and 3.