Franz Ferdinand, Princes Street Gardens, Edinburgh

Franz Ferdinand's lead singer is referring to the band's planned appearance at Edinburgh's annual Hogmanay party of New Year 2003-04, a date that was cancelled amid torrential rain; the band ended up playing in a friend's living room instead. That was when only a handful of Scottish scenesters and music industry trendspotters knew who they were. Should they try that these days, five thousand people would be ringing the buzzer.

A matter of weeks after that night their second single, "Take Me Out", had broken them as a national Top 3 charting band, and the rest - like their namesake Archduke Ferdinand himself - is history. So it's fitting, perhaps, that they finally get to play Princes Street Gardens as the first stage of the next chapter in their meteoric career.

Whoever has guided Franz Ferdinand's hand so far has an uncanny knack for timing, milking the eponymous first album just so much that it became familiar but not boring. So the forthcoming You Could Have It So Much Better... With Franz Ferdinand is a big deal to those who believe that music has every right to hark back to a perceived golden era when personality, longevity and real, honest excitement mattered more than thinly-veiled commercial imperatives.

The Franz camp has already fired one warning shot. Yet the placing of the comeback single "Do You Want To" amid this striking return to the live arena signalled a clear statement of intent. Two-thirds of the way through the show the band's definitive anthem "Take Me Out" was played, and everyone thronging the grassy hill before the stage - and probably those listening in from Princes Street - went crazy. Then, without a word from Kapranos, came "Do You Want Me" - the frenzied reaction to this hit spoke volumes.

Elsewhere, the band - for the first time adding a live video backdrop, in artful monochrome - seem to have taken their Germanic influences one step further. Not only do the shirted, suited quartet now look even more like Hamburg-era Beatles, but "What You Meant" is a more angular ringer for the sound. It's not all about reinvention, however. The insistent pulse of "I'm Your Villain" sits alongside the now-familiar "Michael", "Darts of Pleasure" and "This Fire" as an update of New Wave classicism. Just like Talking Heads, Gang of Four, the Fire Engines... but refreshingly different in its modernist updating of the genre.

For the band that were once meant to change our lives, the second round begins here. And, by not straying too far from their roots, the all-new Franz Ferdinand are already winning on points.