But what would the accompanying music be in the case of his unapologetically modern concrete houses, where glass walls open to sweet-smelling tropical plants, moist warm air and mellifluous birdsong?
You might think of Miles Davis, consider Thelonius Monk, or settle for samba.
"No," the dapper and disarmingly youthful 88-year-old Mendes da Rocha says with a smile. "I would dance with the music outside, to natural sounds -- the ones you hear whether you're composing music, writing a play or designing a building."
His work, stretching back to the late-1950s, when he made his name with the visually daring Paulistano Athletic Club in São Paulo, is, he says, a dialogue, or "dialectical relationship" with nature.
"Of course, it's partly about climate", says Sheila O'Donnell, one of the 2017 RIBA Gold Medal judges, whose Dublin partnership
with John Tuomey won the prestigious award in 2015.
"It's very difficult to build the way Paulo does in Europe, where the climate is against us and where ever-increasing regulations and bureaucracy limit certain architectural freedoms. There's a freedom to build structure in Brazil outside the enclosure of what we think of as a building, and then to inhabit it. It's a far more open way -- and a very public way -- of designing and building."
A lifelong socialist, Mendes da Rocha says: "There is no private space, only degrees of public space. The only private space you can imagine is the private mind."
Even then, he adds, "One could say that even a human being who is apparently alone -- sitting at three o'clock in the morning in a small room, in a cell, before the light of a single burning candle, writing a poem with a goose feather (like Shakespeare) -- is basically a public human being, for his poem may perhaps be read for centuries thereafter."
So, what does he make of London, a city he has rarely visited, with its culture of private homes, where the English are said to hide away from people and noise?
"You see one private house, but then another and another", he says, "and, together, these add up to a city."
Mendes da Rocha's architecture, no matter how grand the project -- like the Brazilian Sculpture Museum sculpture museum of the early nineties, or modest, like the São Pedro Chapel consecrated in 1997 -- is elemental and, when complex, all of a piece.
A single concrete column anchors Saint Peter's Chapel, a concrete building completed in 1987 with two-story glass facades overlooking a mountainous landscape beyond São Paulo. The design is daring, yet nothing about it could be called redundant.
"Unlike many people who are afraid of poverty, I have always been attracted to it, to simple things, without knowing why. Not hardship, but the humility of simple things," he wrote in 2003. "I think everything superfluous is irritating. Everything that is not necessary becomes grotesque, especially in our time."
This creative rigor has its roots in the architect's childhood. It was his engineer father, Mendes da Rocha says, who taught him methodology, technique and structural coherency.
For John McAslan, the British architect and author of the 2017 Royal Gold Medal citation, Mendes da Rocha's "engineering intelligence has always equaled his formal originality."
"His Brazilian Pavilion at Expo '70 in Japan was effectively balanced on a single point," McAslan says, like a ballet dancer en pointe.
Mendes da Rocha's Expo '70 pavilion was realized at a time when the architect was banned from teaching, and only able to build in Brazil through behind-the-scene collaborations with colleagues.
This was during the rule of Brazil's right-wing military junta. Self-proclaimed socialists like Mendes da Rocha were personae non grata. Fellow countrymen, among them Oscar Niemeyer, 1998's RIBA Gold Medalist, left the country until the return of democratic government in 1985.
The Expo '70 Pavilion was demolished after Brazil's military government refused permission for Mendes da Rocha to reconfigure it, as the Japanese had hoped, as a dance school for children.
For the past 30 years, however, Mendes da Rocha has danced to his own architectural tune, shaping the kind of bold, sculptural concrete buildings that make visual and practical sense in Brazil, but which had gone out of fashion in damper countries on the other side of the Atlantic by the mid-1970s.
For McAslan, Mendes da Rocha remains "in the increasingly closely bound worlds of architecture, consumerism and corporatism an architect -- and specifically not a 'starchitect' -- for our times".
"His career has a real strength and continuity to it," says Sheila O'Donnell. "It's been heroic."