Neneh Cherry was born and currently resides in Sweden, and it was there that she was introduced by a mutual friend to fellow Skane resident, saxophonist and The Thing bandleader Mats Gustafsson, who formed the group with Norwegians Ingebrigt Haker Flaten and Paal Nilssen-Love after they performed some of Don Cherry's compositions together at a tribute concert in 2000. The Thing named themselves after a track on Cherry's 1966 long-player Where Is Brooklyn, which featured Pharaoh Sanders on sax.

Now, it's entirely possible that Gustafsson's suggestion that they work together was born of some kind of deferred hero worship; after all, the chaotic, violent noise the band usually creates hardly lends itself to the smooth, honeyed tones of a vocalist like Cherry. Best known for their interpretations of tunes you don't hear the milkman whistling (by artists as diverse as James Blood Ulmer and Lightning Bolt), and collaborations with the avant-rock elite (Thurston Moore, Jim O'Rourke), the trio's music has always focused on the ability of semi-improvised jazz to recreate the brutal catharsis of punk. Here, however, by luck or by design, they've stumbled on something altogether different: by adding Cherry's soulful vocals to the mix, they've created a thing of true, transcendental beauty.

Comprising six covers and an original composition apiece from Cherry and Gustafsson, Cherry Thing's tracklist is as varied as you might expect, but with Ms. Cherry on board the threads tying together these song choices are more apparent. Cherry Sr. is represented, of course, in the form of his own 'Golden Heart' and also 'What Reason Could I Give' from Ornette Coleman's 1971 album Science Fiction (Don contributed pocket trumpet to two of that record's tracks), whilst Neneh's own past is referenced by way of 'Too Tough To Die', a strutting, bluesy number originally recorded by Martina Topley-Bird, former muse of Cherry's Bristol buddy Tricky. There's even a daring nod to the singer's previous flirtations with hip hop in a bizarre reading of Madvillain's 'Accordion', Cherry scatting her way through MF Doom's surreal rap as Madlib's boom-bap beat and melancholy squeezebox hook are reimagined with clattering drums, flatulent double bass and droning woodwind squall.

The album's towering twin highlights, however, are two inspired choices of no apparent significance to either Cherry or The Thing. On the Stooges' 'Dirt', Gustafsson and Haker Flaten double up to offer a steroid-pumped take on Dave Alexander's iconic proto-sludge bass riff as Cherry puts contemporary soul divas like Beth Ditto and Alabama Shakes' Brittany Howard firmly in their place with a performance of such primal, sexual ferocity that even Gustafsson's blistering solo sounds timid in comparison. The quartet's version of Suicide's 'Dream Baby Dream' fares even better: whereas the original had Alan Vega gibbering like a speed freak on the verge of a nervous breakdown over Martin Rev's frantically ticking drum machine, here Cherry turns the fever-dream into a calming mantra, and when – after five hypnotic minutes of that gorgeous, endlessly circling bass hook – Gustafsson finally succumbs to his better instincts and lets rip with a truly glorious sax freak-out, you can't help hoping you never wake up.

Cherry Thing won't be everyone's cup of tea; yes, it's raw, but not in the uncompromising way long-term Thing followers might prefer, and certainly not Like Sushi. Instead, the point in the middle where the two parties meet turns out to be a particularly sweet spot where jazz, punk, soul and even a hint of pop blend together beautifully in a dream come true.