NEW YORK (NYT NEWS SERVICE ).- Poised on a cliff above First Avenue, Tudor City was conceived during the 1920s by the storied developer Fred F. French as a high-rise community for thousands of middle-class residents. A century later, it remains a throwback to the early glamour days of skyscraper living: a dozen brick towers fancifully decorated with half-timbered lobbies, stone crests and other mock-Tudor details.

I gather from “Housing Density,” a timely and thought-provoking show at the Skyscraper Museum in New York, that the density of Tudor City is 463 people an acre.

What does the number mean? The answer gets to the heart of some of the biggest problems facing American cities today.

Density is a concept that may dredge up memories of middle-school science class. In an urban context it is simply a measure for quantifying people or buildings or housing units in a given space. There is no universally accepted methodology for calculating density. “Housing Density” measures the average number of residents in a project like Tudor City divided by the project’s footprint, and also considers how much area the buildings occupy on the site.

However you calculate it, “density” sounds a lot like a synonym for overcrowding and congestion, for too-tall buildings and greedy real estate developers, unwanted neighbors and lost parking spaces. Such associations make the mere mention of the term a Molotov cocktail that opponents of housing initiatives can lob at community board meetings.

This is a big problem. To address the country’s monumental housing crisis and also become less automobile- and carbon-dependent, America needs to densify its job-rich metro areas so that more people can afford to live there and walk, bike and take public transit to work and back. According to a much-cited report by the McKinsey Global Institute, California is 3.5 million houses short. Housing shortages exacerbate home prices and homelessness and cause all sorts of other ripple effects on commute times, economic productivity, health and family life.

But opposition to density has only stiffened as the gulf widens between the 1% and everyone else. Well-to-do NIMBYs, congenitally opposed to new developments, have lately been joined by anti-displacement tenant activists — advocates for poor and working-class residents who might ordinarily want more housing but have come to fear that nearly all development brings gentrification that prices the most vulnerable out of neighborhoods. In cities like New York, San Francisco, Chicago and Boston, this new alliance means that even initiatives promising some subsidized housing have become lines in the sand.

In 2016, for example, activists in Upper Manhattan derailed a proposal to construct a 15-story, 355-unit residence on the site of a derelict garage. The building was to be the first private project under Mayor Bill de Blasio’s Mandatory Inclusionary Housing program, which requires that in new developments on rezoned land, at least 20% of units must be below market rate. Without the rezoning, the developer was free to put up a 14-story building with no affordable apartments.

But in return for the rezoned extra square footage, the developer agreed that half of the units — 178 of them — would be rent-subsidized. Opponents still took to the streets, declaring the construction of any new market-rate housing “an existential threat to our homes and our community.” The developer abandoned the project.

In California, a similar dynamic has threatened pro-densifying legislation like Senate Bill 50, which aims to encourage transit-oriented midrise development, disallow some low-density single-family zoning and extend the rights of homeowners to build backyard accessory units — granny flats, as they’re called. The proposed bill, facing a deadline to pass the State Senate, now includes some targeted protections for existing renters. But a growing coalition of tenant activist groups, including the Housing Rights Committee in San Francisco, opposes it — saying the legislation doesn’t do nearly enough to prevent landlords from harassing vulnerable renters and predicting its passage would “exacerbate real estate speculation, which has already played a key role in displacing low- and moderate-income tenants, immigrants, seniors and families across California.”

SB 50 would also prohibit California towns and cities from downzoning, or lowering density, near job centers and transit infrastructure. Upzoning will give developers “carte blanche to cut down trees,” wreaking environmental havoc, NIMBYs respond. America, of course, has a long, sordid history of downzoning to keep poor and racially diverse populations out of more prosperous, predominantly white neighborhoods.

“Terrifying” was the term one Silicon Valley resident at a community meeting used to characterize the prospect of a seven- or eight-story apartment building rising near the local train station as a consequence of SB 50.

For many New Yorkers, the concept of density conjures taller buildings, although tall buildings are often low density. In particular, New Yorkers tend to picture midcentury-style tower-in-the-park public housing projects. “They equate density with ‘inner city,’” is the way Yonah Freemark, a scholar of urban development, put it the other day. “They perceive public housing as dangerous, failed, not integrated into the surrounding communities. So they think density is the enemy.”

As “Housing Density” points out, that notion gets density almost exactly backward.

The show’s curators, Nicholas Dagen Bloom, a scholar and advocate of public housing, and Matthias Altwicker, a Brooklyn architect, document the 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 an acre, leaving only 13% 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 an acre. Three-quarters of the site remained open space.

“Public housing was designed to ‘take people out of the city,’” 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, 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.

Jane Jacobs preached what “Housing Density” enumerates: New York’s lower-density housing developments failed to achieve the quality of life that high-density neighborhoods provide.

Jacobs wasn’t focused on gentrification, and New York is not Palo Alto is not Barcelona is not Hong Kong: Density is not one size fits all. Urbanism isn’t a mere kit of parts. That said, the implications today are still plain for rezoning legislation like SB 50 and for efforts like de Blasio’s proposal to densify select public housing sites by building new mixed-income private developments on their land.

I suspect some of the community pushback to that idea derives from a lack of collaborative planning and architecture. The added costs and complications of upfront design can help deliver buy-in, better neighborhoods and more affordable housing. People want to feel invested and need to picture improvements. Helping de Blasio dig out of a giant fiscal hole to repair long-neglected, crumbling developments isn’t motivation enough for public housing residents who want to know what densifying looks like.

Solving what ails American cities also requires urbanists and activists to acknowledge that not all real estate development is automatically bad. It demands rethinking some anti-densifying rules and regulations. And it will depend on a shared understanding of what density actually means.

“Housing Density” is not a bad place to start.

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‘Housing Density’: Through Feb. 23 at the Skyscraper Museum; 212-968-1961, skyscraper.org.

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