Brazil is, almost entirely, an approximation, an amiable muddle. There are two exceptions, and both are to do with aeroplanes. The first is the remarkable Embraer enterprise, building regional jets that are the envy of the world. The second is a capital city born in the jet age, and planned in the shape of an aircraft.
Half a century ago, Brasilia took over from Rio as seat of government. Foreign diplomats found themselves transported to the middle of nowhere. The city new city, with no geographic or economic raison d'etre, offended every tenet of human geography.
Brazil is a nation whose soul resides on the beach, and whose people – or at least the vast majority – reside close to the coast. But in the 1950s, President Juscelino Kubitschek declared that the country's capital should shift west. The move was seen as opening up a brave new Brazil, a vast land of endless promise, unified around a newly created metropolis.
Every president wants a legacy, but few have the clout or cash to move a nation's political centre of gravity. Yet by 1960, Brasilia was ready to wrest Rio's title – and locals started getting used to the 12-hour bus ride from Belo Horizonte.
Fifty years on, is it worth the long overnight haul? Definitely, to satisfy your curiosity about what the human spirit can conceive. While the British were content building Crawley, the Brazilian architect Oscar Niemeyer decanted a whole new city, with all the trappings of state, into the strangest of shapes. The bus drops you off at the aft end of the "plane". The nose of the aircraft is pointing to the middle of the Paranoa lake. Most homes and officers are contained in the swept-back wings. The fuselage is more ceremonial than commercial, though with cultural attributes such as the cathedral (a bolder concrete wigwam than Liverpool's) and the National Museum.
To tune in to Niemeyer's dream, stay in something that resembles a 1970s office block, such as the Aristus (00 55 61 3328 8675; aristushotel.com.br; £70 double, without breakfast.
Feast at Porcao, a restaurant that serves magnificent meat in unlimited quantities for the equivalent of £30. And to walk it off? The capital's own national park is right on the doorstep.
Five nights in Brasília costs from £1,260 through Journey Latin America (020-8622 8479; journeylatinamerica.co.uk), including flights from London, transfers and accommodation with breakfast
Candomblé, capoeira and Carnival – just a hint of what Brazil's first capital has to offer. Founded by the Portuguese in 1549, Salvador presides over Todos os Santos Bay, so vast that it bestowed its saintly name upon the state of which it is capital: Bahia.
This hot, steamy city comprises boho beachy suburbs where the streets pulsate with the raucous carnival; high-rise apartments where cable cars and funiculars siphon moneyed residents down to private bathing jetties; a pastel-painted colonial heart; and a rough-and-ready port. All this is imbued with an African spirit endowed by the 300-year legacy of the slave trade. Through struggle and triumph it has made Salvador the Afro-Brazilian capital – and it touches on everything from music (samba-reggae and drumming) to food (liberal use of chilli and coconut), religion (Candomblé, the worship of "orixa" spirits) and culture (capoeira).
The city germinated from the Pelourinho district, where colonial buildings overlook the docks that were the hub of the 16th-century tobacco and sugar trade. For a taste of the high life, stay at the Pestana Convento do Carmo, an elegantly restored friary dating back to 1586 (00 55 71 3327 8400; pestana.com; B&B from US$366/£244).
Fast forward to 1968 and another political struggle was taking place. Against the backdrop of a military dictatorship, Salvador-born musicians Gilberto Gil and Caetano Velosa helped to spawn the Tropicalia movement, which saw samba infused with the electric sound of Hendrix and anti-political sentiment.
Salvador's musical diversity is best experienced during carnival, with the drum-based afro blocos troupes and huge sound systems of the trios electricos.
Five nights' B&B in Salvador costs from £961 with Steamond Travel (020-7730 9639; steamondtravel.com), with flights from London.
Rio de Janeiro
When a Portuguese expedition sailed into Guanabara Bay on the first day of 1502, it was mistaken for a river. The name, "River of January", stuck. The self-styled "Marvellous City" took the title of Brazil's capital from Salvador in 1763 when it held sway as the nation's main gold-exporting port.
Rio trails along the emerald Atlantic and then tucks up into Guanabara Bay, all the while slithering almost impossibly around forested peaks and fizzling into carpets of creamy sand. Its high-altitude icons – Sugarloaf Mountain, Christ the Redeemer-crested Corcovado and the favela-draped hills – lift the city skywards while the beaches of Ipanema, Copacabana and Leblon embody its Atlantic appeal lower down. Everything else exists in pockets in between.
Life revolves around the beach, where balletic displays of futevolei play out next to dazzling displays of posing (Ipanema, spiritual home of bossa nova, is the place to be).
Quainter charms are found on the cobbled streets of artsy Santa Teresa, home to gracious colonial houses, such as the recently opened Hotel Santa Teresa (00 55 21 3380 0200; santa-teresa-hotel.com; doubles from R870/£324) in a renovated coffee plantation mansion. Close by is Rio's Montmartre – Lapa – which has regained its belle époque bohemian feel after years of decline.
Presiding over it all is Tijuca, the mountainous rainforest iced with the emblematic statue of Christ the Redeemer, which majestically embraces the city below. SL
Seven nights at the InterContinental in Rio cost from £1,354 with BA Holidays (0844 493 0758; ba.com/riodejaneiro), with BA flights from Heathrow.
Festival Brazil Rio de Thames
From today until 5 September, Brazil takes over the UK's busiest tourist hub, London's South Bank, to enliven summer in the city; see southbankcentre.co.uk/brazil.
The organisers say that the aim of Festival Brazil is to celebrate "a nation that has moved from despair to hope in 20 years". The musician Gilberto Gil performs at the Queen Elizabeth Hall (21 July); sculptor Ernesto Neto takes over the Hayward Gallery (throughout the summer); and singer Maria Bethania performs at the Royal Festival Hall (19 July). These are augmented by free performances.