As guitarists in world-beating rock bands go, Jonny Greenwood takes some pinning down. Yes, for almost 40 years he’s been a ceaselessly inventive, occasionally head-banging member of Radiohead, the group formed at Oxfordshire’s Abingdon School by Greenwood, his bass-playing brother Colin, guitarist Ed O’Brien, drummer Philip Selway and singer Thom Yorke.

But he’s also roamed far and wide from the strictures of mere rock music. We’re meeting to discuss Ranjha, his second album with a group of traditional Indian musicians, the Rajasthan Express, led by Israeli songwriter Shye Ben Tzur.

It’s hardly Greenwood’s only recent voyage down myriad musical avenues. In February the 54-year-old was in contention for Best Original Score at the Academy Awards for the third time, for repeat collaborator Paul Thomas Anderson’s One Battle After Another (he lost). In September, he’ll perform with the London Sinfonietta in a concert titled Steve Reich at 90 at the Royal Festival Hall.

As we speak, he’s almost finished a second collaborative album with Israeli musician Dudu Tassa, a follow-up to 2023’s Jarak Qaribak (“Your neighbour is your friend”), which featured singers from Palestine, Morocco, Egypt, Dubai and Iraq.

As for the meaning of the album title Ranjha, “it derives from a romantic story in Indian mythology,” explains Greenwood as we talk in a no-frills restaurant near where he lives with his family in the Oxfordshire countryside. “It’s a bit like Romeo and Juliet. I think Ranjha is the Romeo character.”

He admits he doesn’t understand Ben Tzur’s lyrics across the album’s 11, magical, Eastern folk-meets-brass-meets-funk compositions. But he knows it’s “all devotional, about the Sufi saints and God and the divine. I’ve stopped asking! Which is really disrespectful,” he acknowledges. But he recognises that being so focused on the sacred “is the last taboo, you could say. There’s not many [Western] bands singing about God with any sincerity. Or if they are, they’re talking about themselves and God. It’s slightly different.”

Amid all this, though, what fellow Radiohead guitarist O’Brien calls the “mothership” is never far away. Last November and December, Radiohead went on tour for the first time in seven years.

A nightly highlight of those ecstatically received 20 European shows was Let Down. The OK Computer (1997) track has become a viral hit with Generation TikTok. Embraced by waves of new, young fans, it’s now the band’s fourth-most streamed song on Spotify (after Creep, No Surprises and Karma Police). Yet it barely made its parent album. “I find [its belated success] especially bizarre,” said Yorke ahead of the tour. “Because I fought tooth and nail for it not to be on the record.”

“Yeah,” nods Greenwood, smiling from beneath his swoopy, career-long fringe, when I point that out. “Well, that’s Thom, isn’t it? He’s got a long history of such…” He tails off. “Yeah, that’s true. But he’s also always been the most enthusiastic about things. And the most energised and the most encouraging when he hears something and he thinks it’s great – more than any of us. So he’s certainly not dour. He’s the opposite when we’re recording. People don’t realise his level of energy and enthusiasm.”

Well, they do if they see him onstage – Yorke, and his singular, antic dancing, was a mesmerising presence during those shows. Greenwood felt the same.

“I was stood on stage, watching and listening to Thom sing and the rest of the band play, thinking: ‘This is amazing.’ Put it this way: I was ill for two shows, and I was so depressed that I was ill, that I couldn’t enjoy every second of it, like I had the rest of the shows. I can’t believe we got another chance to do it, really.”

There must have been relief, too. Having become embroiled in the intense debate around Israel and its military actions in Gaza, had Radiohead braced for protests at the concerts from pro-Palestinian activists?

“Braced? Yeah, I mean, no, we just focused on rehearsing and did the first show and realised it was fine.”

In 2017 the band performed in Tel Aviv, incurring the wrath of the Boycott, Divestment and Sanctions (BDS) campaign. Greenwood, whose wife Sharona is Israeli and has raised their children in the Jewish faith, also played there with Tassa in 2024. Performing a solo show in Melbourne that year, Yorke was heckled for his “silence” on the war in Gaza, causing the singer to angrily confront the audience member before abruptly exiting the stage. Last May, concerts Greenwood and Tassa were due to perform in Bristol and London were cancelled after threats to staff at the venues. In response, Greenwood and Tassa released a statement saying, “Intimidating venues into pulling our shows won’t help achieve the peace and justice everyone in the Middle East deserves.”

Prior to Radiohead’s reunion that same year, the BDS called for more boycotts. “Radiohead continues with its complicit silence, while one band member repeatedly crosses our picket line,” the campaign organisers said.

I was at the first show on last year’s Radiohead tour, in Madrid, and there were indeed no protests outside or inside the Movistar Arena. Likewise, as far as I could tell, at both the shows I saw at London’s O2. Still, the issue never felt far away, either around or within the band. As Greenwood told The Times in advance of the tour: “The only thing that I’m ashamed of is that I’ve dragged Thom and the others into this mess. But I’m not ashamed of working with Arab and Jewish musicians. I can’t apologise for that.” Yorke, meanwhile, said in the same interview he would never play Israel again, as he “wouldn’t want to be 5,000 miles anywhere near the Netanyahu regime but Jonny has roots there. So I get it”.

Talking to me today about his bandmates, Greenwood says, “I mean, they all like and admire the projects I’m doing” – projects he’s pursuing in defiance of censorship or cancellation. “I’m sure they wish it was simpler. But they’re still supportive. That’s what I meant about it being a mess. It could be more of an easy run.

“It’s interesting,” he continues. “I did an interview with Haaretz, which is the Israeli version of The Guardian, sort of. And the guy wanted to know: ‘Why do you keep doing music with outsiders?’ [He meant] like Shye and Dudu Tassa. And I said: ‘What’s outside about Dudu Tassa?’ He said: ‘Well, they’re singing in Arabic.’ And I said: ‘That’s only shocking if you’re Ashkenazi, because the Sephardic tradition is all about [that].’ That was a really interesting revelation, that he would ask that. It shows you the uphill battle it is, a little bit.”

Music has no barriers, I say. People should have no barriers. That’s the simplistic, reductive ideal, isn’t it?

“Yeah, exactly. It is simplistic, completely. But: good record, good songs, amazing musicians, amazing singers.”

Greenwood, a friendly but brisk to-the-point speaker, pauses, then continues, describing some details of his latest record with Tassa. “This is first time we’re working with these Iranian [musicians]. It’s nuts – they were recording while the missiles were landing. I can’t remember if they were coming from or to Iran. But in the height of all that, they were working and sending us recordings, and we’re sending them back. It just felt like a better thing to be exchanging.”

That, he points out, “isn’t necessarily” something to be highlighted. “It isn’t the point of the record at all. That was just a coincidence… But it’s interesting: we had one person in London who was going to be involved, tangentially, in the recording. And he said: ‘OK, I’ll do it, but only if you leave my name off.’ We were like: ‘All the musicians are leaving their name on there. And they’re from Egypt and Morocco and places where they could be threatened. So why would we let you leave your name off?’ It felt really queasy.”

This person, he clarifies, thought that, by collaborating with Greenwood and Tassa on this ethnicity-agnostic, country-roaming musical project, they would be somehow seen as “tacitly endorsing Netanyahu. That was his fear. It’s gruesome”.

The album nonetheless got finished, with Greenwood now in the mixing stages, although he’s as yet unclear how it will be released – if any record label tried to take it on, “I think it would be BDS’d out of the office”.

Still Ranjha has been a revelation for both parties. Greenwood admires the album’s handling of “God and the divine”, while Tzur, speaking to me over the phone from Jaffa, tells me he learnt “so many things about music from Jonny and [from] opening up” – despite only being familiar with Radiohead’s early hits like Creep when Greenwood first contacted him more than a decade ago.

Ranjha is the belated follow-up to 2015’s Junun, which was recorded in the 15th-century Mehrangarh fort in Jodhpur and produced by Radiohead’s “fifth member” Nigel Godrich. Shortly after that, Greenwood persuaded his bandmates to have the Rajasthan Express support Radiohead on parts of the 2016-18 Moon Shaped Pool world tour. I saw that tour twice but, for shame, didn’t catch the opening act. How did they go down with Radiohead fans?

“We’ve got a very open-minded audience, as you know. Just makes a change from a DJ gently nodding away to his iPad pre-recording or whatever.”

Greenwood has also been having problems with borders and regimes in other ways. At his and his wife’s property in Italy’s Marche region, they grow olives and press their own olive oil. Shufra di Shufra is available online (and from Panzer’s Deli in north London), but they’ve just secured the necessary licences to export to America.

“Finally!” he exclaims with a laugh. “Huge problem! Similar to Brexit, just a whole new layer of legal [problems]. It’s an Italian export. And Trump’s not a fan of European exports. I mean,” he adds, smiling again as he promises to send me a sample, “I appreciate it’s the most middle-class thing I could be doing.”

He could be talking about his artisan foodie ingredient, or his artisan, music-sees-no-country collectives. There are huge hurdles to getting his product, whether olive oil or music, to the people who want to consume it. But for Jonny Greenwood, it’s certainly worth it.

“Yeah,” he nods, quietly, hair flapping. “It’s the curiosity of the next harvest, or the next song, or the next record. That feels very similar to me. Wondering what the quality is going to be like this year, the release, and what people are going to taste. I hope you like the oil. I’ll send you one of the spicy ones.”

Ranjha (World Circuit/BMG) is out now