The show’s curators, Nicholas Dagen Bloom, a scholar and advocate of public housing, and Matthias Altwicker, a Brooklyn architect, document the various ways midcentury public housing reformers replaced slum tenements mostly with far less dense forms of urbanism. All those high-rise slab buildings and H-, Y- and T-shaped housing complexes were designed to provide tenants with more light, air and open space. They were about replacing slum tenements with quasi-suburban developments. The same approach defined middle-class projects like Co-op City in the Bronx. Low density was the point of building towers in the park.

So while the notorious Lower East Side tenements described by Jacob Riis in “How the Other Half Lives” packed in some 1,100 people per acre, leaving only 13 percent of the tenement blocks as open space, Queensbridge Houses in Queens, from 1939 — one of the largest public housing complexes in North America — was built for 245 people per acre. Three-quarters of the site remained open space.

“Public housing was designed to ‘take people out of the city,’” Mr. Freemark said, but “denser urban neighborhoods are where people with choice have almost always preferred to live.”

He cited Chicago, where the densest neighborhoods are mostly on the wealthier North Side. In New York, the largely well-to-do Upper West Side is one of the densest neighborhoods in the city; underserved East New York, in Brooklyn, is one of the least dense. Few buildings in New York are more densely populated than London Terrace, in Chelsea. Designed around the same time as Tudor City, it’s a 22-story behemoth with some 1,600 apartments. To build it, Henry Mandel, French’s rival, demolished rowhouses along West 23rd Street between Ninth and 10th Avenues.

While Mandel imagined working-class tenants occupying London Terrace, over the years John O’Hara, Nicole Kidman and Debbie Harry moved into the building. In 2013, the television producer David Chase bought Susan Sontag’s penthouse at London Terrace for $9.65 million.

London Terrace was built to house 931 people per acre. It’s nearly four times as densely populated as Queensbridge, 18 times as dense as Co-op City, closer to the density of city centers in Paris and Barcelona.