'The album seems to be resonating with people,' says Kamasi Washington, affirming his happiness with the success of his second studio record Heaven and Earth. 'The message of it was, we each have a stake in this world, we each have the power to make it what we want it to be. We don't have to wait for someone to make the world what you want it to be, you can make it yourself. It's about different sides of reality – how you live on the inside greatly affects the world on the outside.'

This, he says, is the idea of Heaven and Earth; the utopia we carry inside versus the reality of the world around us, and how the former can mould the latter. It also feeds into the album's great physical eccentricity – one disc is named Heaven, one named Earth, and a third named The Choice is sealed inside the package. 'It's understanding that to make the world what you want it to be or to relinquish that power to someone else, that choice can be risky, you know?' he says. '(Cutting the package is) something that you have to decide to do, and you won't really know to what end it will lead until you do it.'

Born in Los Angeles in 1981, Washington has been playing drums since he was three, piano since he was five and clarinet since he was nine. By the age of 12 his saxophonist father had introduced him to the music of Art Blakey and the Jazz Messengers, and saxophonist Wayne Shorter was his favourite player. 'Saxophone's kind of related to clarinet, so I switched over,' he says, speaking on the line from Switzerland.

University educated in ethnomusicology at UCLA, he played for a decade and more within the jazz world – along with the occasional rock session – until mainstream demand for his services suddenly leapt after he appeared on Flying Lotus' You're Dead in 2014. Within a year his first album proper The Epic was out on Brainfeeder, and he rapidly appeared on big releases by Kendrick Lamar, Run the Jewels, Thundercat and St Vincent. Heaven and Earth appeared near the top of many 'best of 2018' lists.

'That's how it works, it doesn't just happen overnight,' says Washington. 'You have to spend time finding out who you are, you know? And it's a matter of timing … the world being ready, where they're searching for what that musician has to bring to them. I've been working on music my whole life, and I guess this is the time when I get to share it.' His arrival coincides with a return for jazz. 'Yeah, I think people are searching for that too – but there's jazz within hip hop, funk, R&B, rock'n'roll. Right now it feels like people are really open to it, the freedoms, the abstract side of it.'

At the moment this avid comic fan's – Alan Moore is his favourite writer – other major creative exploration is a graphic novel he's writing ('It's a pretty complicated story, it's about a village of people who live on a mountain, and a guy who guards the gate, and they worship and also want to be him … I'm still writing it!'). He also expresses a desire to work with Radiohead, but all such dreams are for after this tour.

'We can expect pretty much anything that can happen in that moment,' he says of his upcoming live dates. 'It will reflect the energy of the room, we never play the same way twice. The tempo, the key, the chords, the bassline … we try to really capture the moment that we're in. It's a journey, but it happens when it happens. The best music any of us can make is honest music – to make the music that you want to hear, you have to make it yourself.'

Kamasi Washington plays the Barrowland, Glasgow, Wed 22 May.