There are several reasons why Young Fathers currently feel like the most exciting live band in Britain, but for now let’s concentrate on effect rather than cause. The Edinburgh trio have somehow managed to dispense with all the froth and blather of concert-making – gratuitous chat; choreographed audience interaction; the fat and gristle – to deliver a show that is all attack. Every minute is a prime lean cut, direct and thrilling.

They don’t mess about during the first of two sold-out Glasgow shows, but then brevity appears to be a kind of manifesto. The new album, Heavy Heavy, their fourth and not quite their best, lasts barely 30 minutes. Tonight, they perform 17 songs in an hour. The set is similarly minimalist. A huge white curtain hangs crookedly at the back of the stage, against which the musicians cast looming shadows as they whirl around.

There is something of the old-school soul revue about the way Young Fathers assemble. Think a post-apocalyptic Temptations. The three members – Alloysious Massaquoi, Kayus Bankole and Graham ‘G’ Hastings – line up at the front of the stage, alongside two female singers. Behind them is a drummer. Stage right, support act Callum Easter plays keyboards and guitar. Stage left is a contraption that looks like some kind of 19th-century Hebridean loom.

From this they make a hugely exhilarating noise, an ugly-beautiful blend of beats, entwined vocals, melody and meaning. It’s never entirely clear where all the music is coming from. Apart from bashing an occasional drum, Massaquoi, Bankole and Hastings just sing, their blend of voices ranging from Tom Waits rasp to high, honeyed tones. The styles are fluid, a quick-changing mash-up of gospel, soul, rap, R&B and indie. The tonal shifts are extreme but never jarring. ‘Get Up’, ‘In My View’, ‘Rain Or Shine’ – with its woozy ‘Ghost Town’ keyboards – and ‘I Heard’ are all exemplary pop songs.

They don’t say much but their energy is propulsive. Towards the end the intensity levels spiral higher and the songs stretch out. ‘I Saw’ is a loping glam stomp, epic and kinetic. ‘Geronimo’ evokes Massive Attack; heavy, clicking, ominous. ‘Shame’ has a joyous Motown simplicity. ‘Toy’ builds to a frenzied coda and ends in a scream of sirens and shouts. No encore. No need. An hour of feelgood fury felt like a cleansing. Angry yet joyous.

Ivor Cutler would surely have loved the fact that a tribute to his uniquely sweet-and-sharp sensibility is taking place in the Dissection Room in Summerhall, formerly the royal veterinary school. More prime cuts. This year marks the centenary of the birth of the Scottish humourist, poet, philosopher and surrealist, beloved of everyone from John Peel to Robert Wyatt, and a guest star in the Beatles’ Magical Mystery Tour.

Cutler died in 2006. In 2020, drummer Matt Brennan, guitarist Malcolm Benzie and saxophonist Raymond MacDonald compiled a tribute album, Return to Y’Hup, which they performed that year at Celtic Connections. Tonight they perform it again, with guest musicians including vocalists Emma Pollock of the Delgados, and Rick Anthony from the late, lamented Phantom Band.

Cutler’s presence is palpable throughout. The star of the show, plum centre stage, is a suitably battered old harmonium that once belonged to the man himself, played with all the reverence usually afforded a holy relic. Now and then, his taped voice is stitched into the songs.

The septet make a woolly, appealingly ragged kind of alternative rock comprised of conventional instruments alongside bells, chimes and things that whirr and clang. Their music is as much an act of invention as reclamation, adding structural heft to Cutler’s often threadbare songs. Benzie is particularly impressive, marrying the minimalist originals to a series of twisty hooks and riffs, bringing to mind early R.E.M. on ‘Size Nine and a Half’.

Lead vocals are shared around. ‘I Got No Common Sense’ is deployed as a Greek chorus, hollered out by the ensemble every 20 minutes or so. The songs are often comically short, and retain Cutler’s signature blend of lemony humour, Celtic melancholy and Zen-like acuity. Sung beautifully by Pollock, ‘Walking To A Farm’ epitomises his gift for shimmering simplicity: ‘The sky is blue, the sun is yellow.’

Elsewhere, there are songs about green rain, vitamin P, the boo-boo bird, dentistry and pickling your knees with cheese. In the second set we get some Cutler ‘classics’, including ‘Jam’, ‘I’m Going in a Field’ – Paul McCartney’s favourite – and Anthony’s lovely rendition of ‘Yellow Fly’. It’s all slightly disjointed and homespun, which seems an entirely fitting way to meander through the twists and turns of Cutler’s singular vision.