A strange moment, on Friday night. Sitting somewhere quite close to the roof of the O2 Arena, it seems to me as if several thousand people are singing, simultaneously, in a scarcely-audible whisper. Onstage, Leonard Cohen and his extraordinary band are playing “Hey, That’s No Way To Say Goodbye”, with a softness, precision and clarity that I can rarely recall hearing at an arena show.

And everywhere around the venue, it sounds like fans who may have been singing those words privately, to themselves, for decades, are now reciting them en masse in a kind of hushed incantation.

It’s pretty incredible, and also moving, and it really brings home that, with great songs, a great band and a decent sound engineer, a charismatic singer can shrink the most inhospitable of performance spaces and make them intimate – sacred even.

By now, I guess quite a few of you will have witnessed this lengthy, graceful victory lap of Leonard Cohen’s – or at least, like me, will have heard and read about the potency of these shows. Still, though, there’s a tangible shock to experiencing it for yourself – one that’s oddly comparable, maybe, to the Led Zeppelin show at the same venue almost a year ago.

It’s weird to think that either Cohen’s or Led Zep’s songs need to be heard live to validate their visceral (albeit radically different) brilliance. But when Cohen plays a sequence of “Who By Fire”, “Chelsea Hotel #2”, “Hey, That’s No Way To Say Goodbye” and “Anthem” at the end of the first set, it reminds me that while, as a music hack, I might sometimes be a little quick to heap praise on artists, occasionally you hear a passage which emphasises that, well, genius exists.

Apologies for the hyperbole, but really, again, if you’ve seen any of the shows, perhaps you’ll understand where I’m coming from with this one. Allan has already blogged about the Thursday show at the O2, so I’ll try not to repeat too much of what he said. He picked out Javier Mas from the outstanding band (that intro to “Who By Fire”. . .), which is fair enough, but I’d like to draw attention to Neil Larsen’s baroque, bluesy Hammond playing, and not just to the singing of Sharon Robinson and the Webb Sisters, but to how Cohen stands, seemingly transported, when they take their leads (on “Boogie Street” and “If It Be Your Will” respectively).

What’s striking, beyond the brilliance of the songs and the way they’ve been so meticulously arranged and performed, is a certain reinvention of Cohen himself. This ongoing tour, that now looks like it will roll through most of 2009 too, might be a useful financial operation. But it also represents a redefinition of Cohen in the public eye.

To non-fans of Cohen, he’s historically been stereotyped as depressive, gloom-laden and so on, patron saint of lonely people in bedsits or whatever. Now, thanks to his kind of ubiquity over the past few months, a more plausible and accurate image has become wider currency – that of Cohen as droll, urbane and profound; as a poet who can be both playful and spiritual (a remarkable reading of “A Thousand Kisses Deep” being especially powerful here).

From the skipping that Allan noted, there’s a measured lightness of touch throughout that doesn’t detract from the seriousness of some of the content. But as he plays a tiny keyboard solo on “Tower Of Song”, it’s the image of Cohen as wry and self-deprecating that is most enduring. Maybe he’s come out on the other side of something, and while he’s undoubtedly too realistic a thinker to believe in total consolation, at least he’s reached some kind of resolution.

By the encores, the pace ramps up gracefully to an elegaic sway for “So Long, Marianne”, then relatively raucous urgency for “First We Take Manhattan”. Later still, there’s an exquisite slouch through “I Tried To Leave You” that features the band taking jewel-like solos, a pleasure given how grim these bits of a show can often be.

Everything here, in fact, is so perfectly judged, it’s hard to find fault. Even the fact Cohen says virtually the same things every night doesn’t matter – his words are so finely-judged, he probably spent the best part of a year writing them. After so much care, it seems churlish to expect him to abandon them after one use.

By the way, the current issue of Uncut features interviews with Leonard Cohen and his band. For more details, click here.