As the sun sets on another too-long summer festival season, let us take a moment to reflect on the Festival Song.

This is the one tune by a band that even the most reluctant festival attendee will know. It is the song producers stick on the TV highlights package for bored insomniacs surfing the red button. It can save a set, turn grey skies blue and get old bones shaking. The Festival Song survives the artist’s critical nadir; it is the musical cockroach that emerges unscathed from a commercial apocalypse. It is the cast-iron guarantee to every festival booker in the land that an act can still bring something to the party.

Not every artist has a Festival Song, but those who have been around the block and back again will, and they treasure it as they would a winning lotto ticket. As they should. It is the four-minute wonder that can sustain a career for decades.

Connect, now in its second year on the fringes of Edinburgh, is a relaxed late-summer three-day event which marries the new and the old. Boygenius stole Sunday night with a generational love-in. They’re fresh enough right now not to need a Festival Song, which is probably just as well.

On the opening Friday night, however, two bands illustrated the strategic importance of the Festival Song. Headliners Primal Scream, arriving on stage to the sight of an audience significantly under capacity, hit the emergency button and opened with ‘Movin’ on Up’, an ‘old Scottish gospel song’ guaranteed to coax people from the bars and burger stalls down to the front. They ended with ‘Rocks’, a stellar Stones pastiche which sent everyone home believing that they’d had a little more fun than perhaps they really had.

In between, Primal Scream played the entirety of their 1991 album Screamadelica, a beautiful record but not one designed to rouse the masses. Its drifting instrumental passages and wasted 4 a.m. vibes sat slightly at odds to a traditional headlining set. Even frontman Bobby Gillespie acknowledged that the record ‘is very down’, so we needn’t have felt guilty for chatting among ourselves as the band noodled away on ‘Inner Flight’ and ‘I’m Comin’ Down’.

Gillespie was a curious focal point. Not much of a singer, or a talker, or a dancer, he nonetheless exuded the aura of a dishevelled yet somehow courtly ringleader whose role was to unify the whole shebang. He sang the lovely ‘Damaged’ very well, but ‘Higher Than the Sun’ was flatter than a fritter. ‘Remember, kiddies, don’t take drugs,’ he said. ‘Look at the state of us.’ The five-piece gospel choir earned their fee, that’s for sure.

A short while earlier, Franz Ferdinand performed a punchy, professional, more evenly satisfying set which would have struggled to achieve altitude were it not for the expert placement of ‘Take Me Out’ and ‘Do You Want To’ – two killer Festival Songs. I’ve heard this pair of rabble-rousers deliver in enough locations, from arenas to art schools, to declare them infallible. They have endless reserves of propulsion, spring-loaded with a bouncy joie de vivre that energises any crowd. Without them, an hour with Franz Ferdinand would still be fun but much less exciting.

Selling tickets under one’s own name, rather than as part of a multi-act bill, gives an artist greater licence to test their fan base. Playing the same site a few days later, Paolo Nutini illustrated the art of deconstructing mainstream popularity. Nutini has Festival Songs aplenty, but either didn’t play them or turned them upside down and shook the loose change from their pockets. Sometimes it worked, sometimes not, but it almost didn’t matter. He is such a remarkable and versatile vocalist, everything held the attention, and it was fun to play games of Spot the Singer. Look, that’s Robert Plant on ‘Afterneath’! And Bon Scott on ‘Lose It’! And there’s Otis Redding on ‘Coming Up Easy’!

In the case of the lilting ‘Candy’, the alterations in rhythm and melody were not an improvement. ‘New Shoes’ traded its youthful pop bounce for New Wave crunch. ‘Pencil Full of Lead’ travelled from its original Cab Calloway zip to anthemic rock. It seemed a wilful, almost cussed way for Nutini – who arrived in the mid-2000s as a young, pretty singer-songwriter – to over-emphasise his artistic independence. Unnecessary, too. His newest crop of songs – ‘Acid Eyes’, ‘Through the Echoes’, ‘Shine a Light’ – are good enough for him to be gentle with the old stuff. One day he might just need those Festival Songs to behave themselves.