Ten years ago, British saxophone legend Courtney Pine painted a sobering picture of life as a modern British jazz musician in an interview with the Guardian. For all the study involved in becoming one, most jazz musicians had no hope of making a living, unless they were one of the clean-cut vocalists content to ring-a-ding-ding their way through the great American songbook to the delight of Michael Parkinson: you could fully expect your weekends to be spent not exploring the outer limits of improvisation, but playing in a wedding band to make ends meet. “An incredible sale in this day and age is 3,000 copies,” he lamented.

Here was evidence of how modern jazz lurks on the very fringes of mainstream public consciousness. You could fill a book with ways jazz has influenced rock and pop – from post-punk’s skronk to the samples of hip-hop and trip-hop – but apart from the aforementioned ring-a-ding-dingers, no serious jazz musician has really crossed over to huge mainstream success since the 1970s, the era of Miles Davis’s Bitches Brew and the Mahavishnu Orchestra, of the super-smooth George Benson and Grover Washington Jr, and of Keith Jarrett’s Köln Concert wafting around in the background of dinner parties.

All of which makes Kamasi Washington faintly extraordinary. His last London gig was not at the intimate Servant Jazz Quarters, but the Roundhouse, a venue at which the audience was clearly not comprised of longstanding jazz buffs. He records for Young Turks – home of the xx, FKA twigs and Sampha – and is reviewed in the kind of places jazz artists seldom get a mention. It all seems to have been achieved without pragmatic compromise. The record that catapulted him from self-releasing CDs in amateurish home-made sleeves, 2015’s The Epic, was a three-hour-long concept album.

Various theories exist as to how Washington has pulled this off, all of which are supported by The Epic’s full-length follow-up, Heaven and Earth (by Washington’s standards, this is a work of economy, clocking in at a mere two-and-a-half hours). One is that the time is simply right: his guest appearances on Kendrick Lamar’s epochal To Pimp a Butterfly didn’t merely elevate his profile, they established him as “the jazz voice of Black Lives Matter”, in a grand tradition of jazz as black protest.

Heaven and Earth frequently appears to be a furious state-of-America address. You can hear portentous anger in everything from its track titles – Street Fighter Mas, Song for the Fallen – to its astonishing opening cover of the theme from 1972 kung fu movie Fists of Fury, which arrives not merely extended to 10 minutes, but with additional lyrics: “Our time as victims is over / We will no longer ask for justice.” Washington’s sound tends to the maximalist – he is not a man afraid of breaking out the orchestra and choir – but on the album’s closing tracks Show Us the Way and Will You Sing it doesn’t feel dense so much as tumultuous, the former heaving and yawing behind a high-drama choral arrangement, the latter calmer, but with its ostensibly positive message of empowerment and change underscored by noticeable darkness. It sounds more like storm clouds gathering than sunlight breaking through.

Another theory is that his sound is audibly rooted in the kind of old jazz texts that non-jazz buffs tend to recognise, the kind of thing that gets collected on hipster-friendly compilations released by Soul Jazz and Strut: the spiritual jazz of John Coltrane and Pharoah Sanders, Sun Ra’s big band Afrofuturism, the political funk of Archie Shepp’s Attica Blues, the synth experiments of Herbie Hancock and Joe Zawinul. They’re all present here, further smoothed with ample references to early 70s soul and funk, not least the ambitious, orchestrated psychedelia of Rotary Connection. But what’s striking about Heaven and Earth is how expansive and ever-changing it is, its musical focus shifting constantly from lavish grandiosity to perspiration-soaked Latin rhythms to concentrated improvisation, from the edge of chaos to the lushly melodic – sometimes within the same track, as on The Invincible Youth. It never lingers in one place long enough for its running time to seem gruelling. Instead, Heaven and Earth feels writhingly alive and passionate, angrily of the moment but inclusive.

If describing Heaven and Earth as “jazz for people who don’t like jazz” sounds pejorative, it isn’t meant to be. Rather, it’s simply to indicate that on Heaven and Earth, Washington continues to explore a sweet spot between artistry and approachability. Whether his success will lead audiences to further explore music that usually exists on the fringes is an interesting question. What is more certain is the quality and accessibility of his own music.

This week Alexis listened to

Chaka Khan – Like Sugar
Major Lazer’s Switch provides Chaka Khan’s first single for a decade – indebted to the Fatback Band’s (Are You Ready) Do the Bus Stop, a fabulous slice of 21st-century funk.