Edinburgh’s landmark clock tower has been responsible for keeping commuters and travellers on time for more than a century – and yet it is never correct.

Arrive in Edinburgh on any given day and there are certain things you can guarantee. The fairy-tale Gothic of the royal castle, built on an extinct volcanic plug. The medieval riddle of alleys and lanes. The majesty of the churchyards and macabre spires set against a barb of basalt crags, all as if created by a mad god.

Yet there is one other given in the Scottish capital, and it is the hallmark of Princes Street, the city’s main thoroughfare that runs east to west joining Leith to the West End. The time on the turret clock atop The Balmoral Hotel is always wrong. By three minutes, to be exact.

While the clock tower’s story is legendary in Edinburgh, it remains a riddle for many first-timers. To the untrained eye, the 58m-high landmark is simply part of the grand finale when surveyed from Calton Hill, Edinburgh’s go-to city-centre viewpoint. There it sits to the left of the Dugald Stewart Monument, like a giant exclamation mark above the glazed roof of Waverley Train Station.

Likewise, the sandstone baronial tower looks equally glorious when eyed from the commanding northern ramparts of Edinburgh Castle while peering out over the battlements. It is placed at the city’s very centre of gravity, between the Old Town and the New Town, at the confluence of all business and life. Except, of course, that the dial’s big hand and little hand are out of sync with Greenwich Mean Time.

It is a calculated miscalculation that helps keep the city on time

This bold irregularity is, in fact, a historical quirk first introduced in 1902 when the Edwardian-era building opened as the North British Station Hotel. Then, as now, it overlooked the platforms and signal boxes of Waverley Train Station, and just as porters in red jackets met guests off the train, whisking them from the station booking hall to the interconnected reception desk in the hotel’s basement, the North British Railway Company owners wanted to make sure their passengers – and Edinburgh’s hurrying public – wouldn’t miss their trains.

Given an extra three minutes, they reasoned, these travellers would have more time on the clock to collect their tickets, to reach their corridor carriages and to unload their luggage before the stationmaster’s whistle blew. Still today, it is a calculated miscalculation that helps keep the city on time.

The sky was overcast and the air bitingly cold on the day I visited to learn this history, guided by the hotel’s security manager Iain Davidson. After a quick briefing, I followed his echoing footsteps into the dimly lit brickwork turret, a transition from front of house to backstage. In between the sixth floor’s suites, we entered a door that could well have led to a broom cupboard. Above that, beyond the water storage tanks, a black spiral staircase corkscrewed into the tower’s crown through a series of wooden landings. Each step up was a step back in time.

“Visually, this is one of Edinburgh’s most interesting, if secretive, places,” said Davidson, reaching the top as daylight flooded in to reveal a brickwork gallery embellished with four symmetrical clock faces. Around us, the airy attic featured slit windows that afforded views of central Edinburgh’s commercial hodgepodge, raising us to the level of the castle and the chimneys of the Royal Mile. “Everyone always wonders what it’s like up here when they’re on the street below. Isn’t it marvellous?”

Everyone relies on it being wrong

While exploring the nooks and crannies, Davidson explained that the only major change over the past 116 years is the clock was manually wound until the 1970s, when it was electrified. “It means the tower doesn’t get as many visitors as people might think.”

That the clock is wrong every day of the year is not technically true, either. Its time is stretched to accommodate an annual event. On New Year’s Eve, or Hogmanay as Scots call it, the tower welcomes a special one-off house call, when an engineer is dispatched to remedy the timekeeping error. “Plain and simple, the clock needs to be right for the traditional countdown to the midnight bells,” said Davidson, leading our two-man party back down to the hotel’s grand lobby. “Beyond that, everyone relies on it being wrong.”

While the turret clock has remained dependably inaccurate over the past century, the hotel has understandably moved with the times. Following World War Two and the 1948 nationalisation of Britain’s railways, the golden age of steam was over, and so, too, was the era of the railway-owned hotel. Where once stood 112 hotels on the map in 1913, there are now but a handful left. For its part, the North British Station Hotel severed links with the railway in the early 1980s, before being rebranded as The Balmoral in 1990. Two refurbishments totalling £30m and a change of ownership to the Sir Rocco Forte Group followed, and yet the clock’s time was left unaltered.

To learn more, I contacted Smith of Derby, a fifth-generation family-run clockmaker, which has maintained The Balmoral’s turret clock for almost a century through its Broxburn-based subsidiary James Ritchie & Son.

Among the other world-famous clocks under its guardianship are those aloft on St Paul’s Cathedral and the elegant Victorian dial at St Pancras Station in London; and the 64m tower anchoring the Majlis Oman, the parliament in Muscat. Smith of Derby’s greatest achievement, however, is the world’s largest mechanical clock, a 12.8m-diameter, pendulum-operated timepiece that decorates the Harmony Clock Tower in Ganzhou, China.

“We look after 5,000 different clock towers around the world, and to say The Balmoral’s is peculiar is a massive understatement,” the firm’s Tony Charlesworth told me. “It’s hard to believe, but it’s the only one we’re paid to keep wrong.”