Always, as the train crawls caterpillar-like on to the Tay Bridge, the urge to start chanting William McGonagall's unforgettably awful poem on the demise of its predecessor becomes overwhelming:

Beautiful railway bridge of the silvery Tay

With your numerous arches and pillars, in so grand array,

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And your centre girders which seem, to the eye

To be almost towering to the sky.

The greatest wonder of the day

And a great beautification to the river Tay;

Most beautiful to be seen

Near by Dundee and the Magdalen Green.

"Shakespeare," noted one of its early readers, "never wrote anything like this." True to form, McGonagall, who, by the by, was not originally from Dundee but Edinburgh (a fact its citizens need no encouragement to suppress), took that as a compliment. Unlike echt Dundonians, McGonagall had what the cultural historian Charles McKean described as "an uncharacteristic myopic arrogance".

"Like most great men," his autobiography audaciously begins, "I was born at a very early period of my existence." It takes a peculiar kind of genius and an insufficiency of self-awareness to write that badly.

That Dundee should be burdened with such an albatross is unfortunate. But of all places it seems to cope well with the slings and arrows of outrageous fortune. The more one talks to Dundonians, it's apparent that they are as outwardly optimistic as they are effortlessly fatalistic. They may pray for better but don't blink an eye when they're rewarded with the worst. Moreover, they have learned to cope with life's inevitable injustices. Instinctively, they know they should get a fairer deal than they do but aren't surprised when they don't. Their equivalent of Mao's Little Red Book is Bill Duncan's Wee Book of Calvinism which is full of such saws as "Hope is the dream o aa foolish men" and "Keep your heid down lest ye meet the Devil's stare".

In Dundee, as Sheena Wellington, the renowned folk singer, says, it never does to get above yourself, for there will always be someone ready to pull you back to earth. Not long after she stole the show at the reconvening of the parliament at Holyrood with her spine-tingling rendition of A Man's A Man For A That, she was accosted in a shop by a woman she didn't know who told her: "I wisnae very keen on your frock. But when you're built like you are Sheena it's difficult to get something to fit."

Far from being affronted, Wellington was cheered. In Dundee, she says, you soon learn to expect nothing less. Hers, she adds proudly, is a city with "nae style, nae flash, nae bling". This is epitomised by DC Thomson, the family-owned publisher, whose effect on the Scottish psyche is incalculable and which provided employment for generations of locals who preferred to seek employment in journalism rather than in the city's two other emblematic industries, jam and jute. Once, recalls Wellington, after her song The Dandy, The Beano And The Sunday Post was played on the radio, she got a call from Thomson's circulation manager. At first, she thought he was going to threaten to sue her, which is always good for publicity, but it transpired he simply wanted to borrow a copy of the record. "They weren't going to dash out and buy it," she says.

Wellington will vote Yes in the forthcoming referendum. Recently, she received by post a leaflet from the UK Government outlining why it's better to retain the Union. "They're just about to get it back with added comments," she says, "in the pre-paid envelope supplied." She has long been a supporter of independence, as are many people who are associated with the folk scene. Nor is she disheartened by the polls, the majority of which continue to suggest that the No camp will prevail. "We will see what we will see," says Wellington.

Sunshine and showers are forecast which, as I emerge mid-morning from Malmaison Hotel, the latest addition to Dundee's cityscape, is what is delivered. Here on the waterfront is the £1 billion project to reimagine the city for the 21st century. Begun in 2001, it has at least another three years to go before it will be completed. At the moment, all there is to see is a building site and an army of men in hard hats. But what is obvious is the scale and ambition of what's envisioned. The plot stretches for almost five miles along the Tay and covers some 600 acres. Eventually, there will be walkways and parks, businesses and apartments, hotels and a swimming pool. By next summer, the new railway station will be unveiled and, a few hectic months later, the £45 million Victoria and Albert will open next to Captain Scott's magnificent, three-master polar expedition ship, RRS Discovery.

Progress, inevitably, has not always been on schedule and on budget. But Dundonians, unlike their counterparts elsewhere, appear sanguine at what is surely the most significant development in their city's history since the building of the Tay Road Bridge in 1966. It is sorely needed. When Paul Theroux, the caustic American travel writer, passed through the city 30 years ago, he found it hard to summon any enthusiasm. Much of old Dundee had been bulldozed and what had been built in its stead was grim. His ire turned on the Swimming and Leisure Centre which "had the look of a Russian interrogation headquarters, a vast drab Lubyanka in rain-streaked concrete".

Theroux was not alone in his loathing of it. The mere mention of it is enough to make many Dundonians recoil. But it has been recently demolished as part of the redevelopment of the waterfront, as has its equally unloved and ugly sister, Tayside House, the former HQ of Tayside Regional Council. Rhoda Miller speaks for the majority when she say she was overjoyed to see such carbuncles reduced to rubble. She has lived in Dundee all her life, going straight from school into DC Thomson where she remained for 40 years until she took early retirement. At her initial interview, she was asked the $64,000 question: what paper do your parents read? As long as the answer was the Courier, you were given a job. In the "heyday of comics", Miller worked on the Bunty and Diana among others. The editor of the former, she recalls, was called Harold Moon. He had lost an eye during the war when he fell drunk off the back of a lorry. As he studied page proofs, "He used to say, 'I can see more with one eye than most folk can with twa.'"

Miller loses no opportunity to hymn Dundee. For her, the development of the waterfront is long overdue and could spur the city into an era of prosperity. "In the main," she says, "Dundee has had a bad press for a long time." That, she feels, may well be about to change. She is likewise keen on the prospect of independence. "I'm a huge, huge Yes supporter." Having said that, she acknowledges she has several friends who are either determined to vote No or who are swithering. "I'm working on them. It might be scary and it might risky but let's go for it."

From the banks of the Tay to Dundee's town centre is a few minutes' walk. It's just after lunch and City Square is bathed in sunshine. Unlike the nearby Wellgate mall, however, it's pretty much deserted, testimony to our aversion to fresh air. There are more than a few pasty-faced young people wandering around in that jerky manner which suggests they may have ingested a banned substance. They are a reminder that for all the city's recent successes, including the local universities' world-ranking life sciences teams and its emergence as a centre for digital media and computer gaming, it is still struggling to cope with its post-industrial heritage. It's estimated that in the past decade around 3500 jobs have been created in computing and related businesses in the city and its hinterland. But, as the historian Christopher Whatley has noted, "this was less than some single jute manufacturing companies employed in the 19th century".

Charged with overseeing Dundee's transformation is Mike Galloway, director of city development at the city council. On Galloway's desk in his office in the council's new HQ, a converted mill, are the plans and promotional brochure for the waterfront. On paper, it looks impressive. Key is the V&A, which seems to float on the firth like a gigantic, beached ocean-going liner. Galloway hopes it will do for Dundee what the Guggenheim did for Bilbao. Half a million visitors are expected to visit it each year, which will be a remarkable number if it's realised. No less of an achievement was persuading the V&A's then director, Mark Jones, to choose Dundee as the site for its first franchise. There was no open competition, no tendering, no petitioning. It was simply a matter of happenstance and personal connections. "The V&A," says Galloway, "is not putting any money into the building." What it is doing is lending its name and giving its Dundee satellite the opportunity to put on exhibitions shown first in London.

Has the forthcoming referendum made life more difficult? "There is currently uncertainty," says Galloway, adding that a few investors are awaiting the outcome of the September vote before making their decisions. "Does it make a big difference once the outcome is known? I don't think so. But if it's close or a No vote - that raises interesting prospects for the future."

In a previous incarnation Galloway was involved in the development of the Merchant City in Glasgow. Thus he is accustomed to taking a long view. He is also keenly aware that what appears to work in theory won't necessarily do so in practice. Inherently, urban planning is a costly game of hit and miss. Public taste is fickle and human behaviour quixotic. What makes one scheme successful and another fail dismally can often be to do with factors outside planners' control. Galloway mentions Jane Jacobs' influential study, The Death And Life Of Great American Cities, and in particular her thoughts on parks such as those in Philadelphia, some of which were well-used by a cross-section of society while others were neglected and adopted by down-and-outs, drug addicts, pushers, alcoholics and vandals. It is a reminder of the risk Dundee is running.

Its bus station is not a place which invites lingering. To kill time I read the evening paper. One man has been fined for stealing gift cards from Boots and for being in possession of heroin. Another can expect a custodial sentence for seizing his partner by the throat and threatening her with a knife. Away from the courts, an appeal is made to Angus residents to look out for red kites. In nearby Kirriemuir, meanwhile, 78 per cent of people have said they are against the erection of a statue to Bon Scott, "the former AC/DC frontman … who lived there as a child". I hop aboard the bus to Perth, expecting the 20 or so miles to take no more than half an hour. In fact, I spend nearly an hour and a half on board, as it follows the ever silvery Tay by way of a necklace of villages: Invergowrie, Kingoodie, Errol, Glendoick and Glencarse.

Perth is one of those towns which seems to exude Scottishness. Where better to purchase a pair of brogues and tartan trews? According to my paper, it had 97,000 visitors in 2013, compared to Dundee's 61,000. In the modest hotel in which I overnight I bump at breakfast into the actor Bill Paterson who has spent a week in Tibbermore church on the outskirts of Perth filming the US TV sci-fi drama Outlander, dubbed "Scotland's answer to Game Of Thrones". Given the weekend off, he's heading for Pitlochry and its theatre to rendezvous with friends who are appearing in a Liz Lochhead play. Among the other guests are a party from China and three elderly natives, one of whom I overhear telling his companions: "My room was hotter than a sauna. Not that I've ever been in a sauna, of course."

It's Saturday morning and Perth is en fete. There is a charity market, children learning to cycle on an improvised track outside the concert hall, and bagpipers around whom tourists flock like clansmen to a gathering. Perth, it seems at least on the surface, has a lot going for it. Compared to other towns it has relatively few charity shops and boarded frontages. If not booming, it appears to have weathered the economic storm. Both the No and Yes camps are touting for business but finding it difficult to distract attention away from the zip wire that's carrying youngsters from one end of the high street to the other.

Vicki Unite, who runs Perth's chamber of commerce, says it has the highest rate of population growth in the country. Born and bred in the town, she returned to it after sojourns in Amsterdam and London. Regarding the referendum, she says that what concerns her members most is the uncertainty. What she herself hopes for is a decisive vote. "It does polarise people," she says. But in Perth what divides them even more is the fate of City Hall, which lies unused in the town centre. Built in the first decade of the last century, it occupies an entire block. Eight years ago, it was proposed to turn it into a shopping mall but that came to nothing. Since then it has been threatened with demolition. Most recently, says Unite, Perth and Kinross Council backed plans to convert it into a hotel only for them to be rejected by Historic Scotland. Now a decision on the building's future is unlikely to be taken until 2015 which, like that in September, is sure to be contentious whichever way it goes. Says Unite with feeling: "We just want something to happen." n