Jaimie Branch’s untimely and tragic death last year robbed jazz of one of its most singular – and promising – talents. It’s therefore difficult not to approach this posthumous album – recorded four months before her passing and completed by her long-standing Fly or Die band and her sister Kate – with a sense of sadness and trepidation, and also regret for what more might have come.

But that's not quite the case here, because this album is a superb addition to a small but brilliant legacy: as a final statement, they don't come much better than this. It's a glorious listen, rather than the melancholy one I expected. Branch was fond of saying that playing the trumpet was akin to "singing your soul" and that is certainly the case here, as ((world war)) contains some of her best-ever playing: fierce, free, expressive and uniquely Branchian. The writing is her best-ever too.

((world war)) is as electrifying as the group’s first three [two studio, one live] LPs, but comes with a wider sonic palette and heightened ambition. The Taylor-St Louis-Ajemian FoD core unit is there, locked in tighter than ever, but synths, exotic percussion, guest horn players and extra vocalists add real richness to the mix. There's also a much heavier feel than on previous outings and Branch's singing – at times weirdly reminiscent of Patty Waters' – takes the spotlight almost as much as her trumpet.

The nine-minute centerpiece ‘baba louie’ starts out as an eclectic stew of Caribbean carnival rhythm and South African-inflected horns, introduces marimba and flute, morphs into an anthemic trumpet solo section, and finally jumps into a dubby groove. Another nine-minute epic, ‘burning grey’, is an impassioned call for vigilance atop a frantic, steamhammering rhythm; and on ‘the mountain’, Branch and Ajemian create a wonderful two-voices-and-bass take on the Meat Puppets’ country-punk classic ‘Comin’ Down’,

On the closer, ‘world war ((reprise))’, she jangles a 1970s Fisher-Price musical toy (the Happy Apple mentioned in the credits) and entreats in an even, intimate tone: "Publicise, televise, capitalise on revolution’s eyes/What the world could be/If only you could see/Their wings are false flags/On our wings, they all rise". It's a message of hope as much as a warning from an artist (and a band) at the top of her game. A remarkable testament.