For now, accompanied by iridescent lighting and a cannon shooting star-shaped confetti, Coldplay are back in a venue they first played in 1999. Actor Simon Pegg, one of Martin’s BFFs, introduces the band, recalling how Martin went out with him to the cashpoint after that 1999 gig muttering: “I don’t know what I’m going to do if it gets any bigger than this.” One hundred million albums later, in lieu of a gospel choir, we have The X Factor star-turned radio presenter Fleur East and the classy LA soul act We Are King joining Coldplay for a new song, Human Heart. Pondering that organ’s frailty, the singers’ four-way harmonies produce a resonant, almost a cappella thrum. On the album, the song title is styled as an emoji, just one of a few Music of the Spheres feints towards a Gen Z demographic. In lieu of Kuti, meanwhile, we get a cameo from Ed Sheeran, the second-most-decent guy in exportable UK culture-content, who sits in on the always-affecting Fix You. Later on, having just played a slew of career-spanning anthems – Viva la Vida, The Scientist and a stripped down version of Yellow – Martin quips that some “really big hits” are nigh. It’s Sheeran’s cue to come back to play his own tunes. The two songwriters share similarities: they are, after all, men whose songs make an incalculable amount of people very happy. They’re even dressed alike tonight, in contrasting colour-on-black togs and not-too-loud statement trainers. But Sheeran’s Shape of You really drives home the differences. A line such as “I’m in love with your body” sits oddly within the Martinsphere, a largely chaste space in which the Coldplay main man expresses his hots for someone in far loftier terms. A fresh hit is a case in point: Higher Power is a punchy 80s-channelling celebration of love’s consolations, one lit by lasers and a dazzling skyful of ceiling projections. According to Martin, we have Pegg’s young daughter Tilly to thank for the direction of Coldplay’s latest record. Released on Friday, Music of the Spheres takes its title from the idea that the movement of the heavens vibrates tonally. “There is geometry in the humming of the strings,” wrote Pythagoras, “there is music in the spacing of the spheres.” Although Martin dedicates The Scientist to her, it seems that Tilly Pegg is less an ardent Pythagorean than she is a massive BTS fan. She sanctioned Coldplay’s recent hook-up with the South Korean boyband, My Universe, another lofty love song that has become a global No 1. Sadly, BTS only appear in the video on the backdrop. (Also sadly, Selena Gomez, another new album duettee, isn’t here either. Her oeuvre is due urgent reconsideration in light of her hypnotic performance in the Disney+ hit Only Murders in the Building.) The science bit is saved for the end. Music of the Spheres is a mixed bag of an album, invoking outer space, glam rock, prog pop and operatic terminology, often a little haphazardly. With BTS on board, Max Martin producing and Coldplay premiering a single via the International Space Station last May, there is a sense of bigness calling reflexively to bigness everywhere in the pile-up of vast synth chords. But there is also something curiously affecting about Coloratura, Coldplay’s 10-minute closer from the new album. Martin warns the audience they can leave before “one of the biggest slices of soft rock you’ve ever heard”. It is more than a little rococo, with Jonny Buckland’s lead guitar suggesting an 80s Pink Floyd. But the lyrics find Martin tenderly invoking space missions, Galileo and Jupiter’s moons. He is still convinced by some sort of human progress, of perspectives where differences can be reconciled, of “the end of death and doubt”.