As we speak, JPJ, as he's affectionately known, has just finished doing his share of the press for the release of Celebration Day, the film of the band's reunion concert at the 02 in London in 2007.
Unlike some rock stars whose bands have split up and who prefer the talk to steer exclusively towards what they're doing now or, more accurately, themselves, he's happy to acknowledge the importance of Led Zeppelin and what being in the heavy metal giants has done for him.
"It opened a lot of doors and raised my profile," says the man who, before joining Messrs Plant, Page and Bonham had had an invisible but audible presence on thousands of records as a session man. "It was also really good. I'm quite proud of the music we made and apart from anything else, that music was great fun to play – otherwise, what would be the point of doing it?"
Fun also plays a major role in what Jones gets up to these days. Those doors that Zeppelin opened have led to many and varied projects over the past 30 years, ranging from musical settings of 17th-century Spanish poems in the period style for harpist Andrew Lawrence-King and The Harp Consort to Mark Anthony-Turnage's opera about Playboy model-gold digger Anna Nicole Smith, and from bluegrass with Gillian Welch and David Rawlings to the freely improvised sounds he'll be creating with Norwegian experimentalists Supersilent in Glasgow next week.
He says: "Things just kind of speak to me – or not. I know immediately if it's something I'm going to like and the people I tend to like –Seasick Steve's a great example – tend to be a bit sideways, a bit on the periphery of the mainstream music business."
Jones had never encountered Supersilent, whose keyboards, drums and electronics are joined by Arve Henricksen's trumpet, before he was approached by Henricksen at a festival in Norway and asked if he'd like to play on their set.
"I said: What is that you do? And Arve said: We don't talk about it, we don't rehearse, we just play," says Jones in the sort of tone that signals his continuing intrigue and enthusiasm for the idea. "So I just plugged my bass into a big amp and off we went. It's extremely liberating. They're all excellent musicians and really nice people and I get to use all my electronic stuff that I don't get to use with anybody else. We've played together four or five times now and each time has been different. We'll do a soundcheck but that has nothing to do with what we'll play on the gig and while it's very different from Zeppelin, we seem to be getting a few Zeppelin fans along to gigs now, which is good."
Improvisation has played a significant part throughout Jones' career. There were long sections in Led Zeppelin songs onstage where he didn't know what he was going to play next. As a session player in the 1960s, he was continually expected to come up with a suitable idea instantly, whether it be a bass line for Shirley Bassey or a string arrangement for the Rolling Stones. Even before that, though, he says, improvisation coloured his experience as a teenage church organist.
"My playing of Bach cantatas was so bad that what I played before the hymns sounded better if I made it up, and I just got away with it," he says. "But I've always enjoyed going onstage with no rehearsal. Unless it's something that's been composed and has actual charts, like Mark-Anthony Turnage's Anna Nicole, I really enjoy going out there not knowing quite what's going to happen. It keeps me on my toes."
Away from Supersilent, his Minibus Pimps duo with Supersilent's guitarist-electronics whizz Helge Sten, and record production assignments – bluegrass sweethearts Uncle Earle and Nickel Creek's Sara Watkins have benefited from his ears – Jones is hard at work on an opera based on Swedish playwright August Strindberg's The Ghost Sonata that's due to premiere in 2015. He particularly enjoys writing for voices but needs complete seclusion to compose in.
"I turn off the phone, ignore my emails and just immerse myself in composition," he says. "It can get quite intense so it's also good to have something to escape into occasionally, something that just involves playing. Whether it means bass guitar, like these dates with Supersilent, or mandolin, I have no particular preference: I'm just happy to have something that can make a noise hanging round my neck."
John Paul Jones appears with Supersilent at the Arches in Glasgow on Thursday, November 15.