The National have become one of the pivotal bands of the last 20 years because their songs reflect the chaos, mundanity and existential angst of modern life and serve it up with spellbinding, accessible melody. Like most of us, the Ohioans have had a tough time of it lately, facing a pandemic and frontman Matt Berninger’s depression and writer’s block. Now, though, a creative explosion has produced two albums this year and there are smiles and banter onstage as this stunning two-and-a-half-hour epic becomes a communal catharsis.

With a setlist extending all the way from 2004’s Cherry Tree EP to the title track of latest album, Laugh Track, here making its live debut, the 28 songs range from exquisite melancholy to pulverisingly redemptive. Channelling everything from Americana to post-punk – the latter flowing through Bryan Devendorf’s propulsive drumming – there’s sublime piano balladry and extreme noise. Milestones such as Bloodbuzz Ohio and Terrible Love are turned into anthemic singalongs by a fanbase who know every word.

Although the quintet (with brass players at times here) are at heart an alternative band, they’re willing to subtly take on the requirements of arena rock and push against them. Guitarist brothers Bryce and Aaron Dessner lead audience handclaps and the fluidly playing latter is in some ways an albeit unshowy guitar hero. They play so long they risk a fine for breaking the curfew and Berninger’s livewire edge makes for a compelling spectacle.

With his unkempt black suit and mutinous hair, the frontman looks – as Aaron Dessner teases him – like a “dishevelled professor”. His stage persona veers from man undergoing psychotic episode to someone having the time of his life. He hurls a drink so high it showers over him and on at least one foray to the back of the hall – with the tangled mic lead trailing over the crowd’s heads – you fear he won’t actually make it back. Perhaps most memorable is the sight of Berninger and the front rows almost hysterically yelling the lyrics at each other, faces touching, jointly celebrating an era-defining band at the peak of their powers.

• At Glasgow Hydro, Sunday 24 September, then Alexandra Palace, London, Tuesday 26 and Wednesday 27.