If there was ever an artist that cries out for orchestral arrangements then surely it is Leonard Cohen. The very idea brings to mind the Joni Mitchell Travelogue orchestral reinvention from 2002, songs as familiar as your sitting room lifted again, reinvigorated by the filling out that only the big, big band can provide.

"It's coming to America first, the cradle of the best and the worst." Phelim Drew's plummy voice talks us through 'Democracy' from 92's The Future, the first of the show's frankly magnificent orchestrations rising as the song reaches its apogee. The backing vocals lift Drew's voice for 'Anthem' from the same album. "There's a crack in everything, that's how the light gets in." There isn't a writer alive or dead who wouldn't skin his or her granny for a line even close to that.

The weather can't seem to make up its mind, but it's notable that precisely nobody leaves when a few drops fall. Suzanne Savage steps forward from backing vocals to the spotlight. There's a delicate cinematic rumbling from the players, a French horn in the distance. The "La, La"s of 'Dance Me To The End Of Love' move couples to waltzing. Savage hams it right up - and I mean that in a good way - for the oom-pah qualities inherent in the song, in this arrangement at least.

David Keenan is out, acoustic guitar in hand, for 'So Long, Marianne'. The swoops and trills in his voice, his way with melisma, are the very opposite of Cohen's sensual growl, a voice that could have turned any pop trifle into the deepest blues, but Keenan gets inside it, the poetry of Cohen's lyrics having struck a resonating chord with him years ago. The organ and then the timpani that introduces the last chorus are inspired arrangement choices. For 'Bird On The Wire' Keenan has shed his guitar to concentrate fully on a vocal that brings out the latent soul in the original melody, buoyed up by a rimshot beat. There's a bit of Van Morrison, there's a bit of James Carr, and the guitar solo is pure country soul.

Patrick O'Laoghaire's vibrato drifted a little to close to Tiny Tim territory at times - although, to judge by the reaction, I may have been on my own in thinking this - but 'Famous Blue Raincoat' is hard to damage, and the string and woodwind arrangement carried it. Mick Flannery, brought in, as far as I know, at the last minute to replace a sadly absent Glen Hansard, essays 'The Stranger Song' solo at the keyboard. He takes a while to find the tune but it is worth the search, the crowd very much behind him. 'Who By Fire' seems a much better fit. An evocative guitar intro that combines elements of flamenco and the African desert blues, staccato strings and militaristic drum patterns lift what wouldn't have been my favourite Cohen song and Flannery's gruff delivery suits it perfectly.

Keenan reappears to read some thanks, to Cohen for these "poems, prayers, and songs" and a heartfelt nod to John Reynolds - the man who brought Cohen to Ireland for those downright spiritual series of shows, to which this writer, previously a bit of a Cohen sceptic, was dragged along to and converted forever - for "bringing us all together."

You already know what song has been chosen to finish. Morgan MacIntyre and Gemma Doherty of Saint Sister build 'Hallelujah' carefully. For the first chorus, they drop down the scale slightly, there's a slight harmony by the third. By the fourth, I can feel a chill that's not from the air. The other vocalists retake the stage but, with the greatest respect to them, they're surplus to requirements. The crowd's growing reaction is palpable and when the song ends they move to their feet as one, offering an outpouring of affection for a song so luminous that a thousand fake talent show murderings can not tarnish its lustre.

The larger share of credit is due to the men and women of the orchestra for the arrangements and the playing. This was a magical - and profoundly moving - performance. Leonard Cohen - and John Reynolds - are smiling. In the Tower Of Song.