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They are the measurements many American women (and not a few American men) know so well: 32A, 34B, 36C.

On they go, the canonical brassiere sizes, up to at least a 50N. They have been around since the 1930s, maddeningly unconventional standards, varying from brand to brand, from demi-cup to strapless — a kaleidoscopic vision, in lace and elastic, of fashion, culture and the enduring power of marketing.

But is anyone ready for measurements like 1-30, 7-36 and 9-42?

Those are three of 55 new sizes that a major American manufacturer has devised to address a lament as old as the bra itself: many don’t fit.

The undergarment industry, eager to sell its wares, has seized on the complaint, offering an ever-growing assortment of sizes and shapes — often at ever-growing prices — to entice women to buy that next bra.

Jockey International, a grand old name in undergarments, has spent eight years developing the new measurement system, which the company says takes into account the shape of a woman’s breasts, not merely bust size. The bras are a mass-market answer to custom fittings that have become increasingly popular in boutiques and high-end department stores.

Whether Jockey’s approach will catch on is uncertain. But the Jockey Bra, formally introduced Thursday, marks another step in the evolution of the modern brassiere. In the 1920s, flappers opted for snug bras that gave them a boyish silhouette. By the 1950s, bras that created a fuller, pointier bust were the rage. The ’70s brought more comfortable, unstructured bras — and then Victoria’s Secret. By the ’90s, the Miracle Bra was battling with the Wonderbra for the title of queen of cleavage. The 2000s brought larger sizes for bigger women.

As the cycle turns again, the industry is talking up the benefits of a better fit. The pitch may appeal to women newly conversant in fashion. “People are becoming more knowledgeable about fashion minutiae, and they’re focusing on things like fit,” said Valerie Steele, director of the Museum at the Fashion Institute of Technology.

It may seem surprising, but the lingerie industry pushes the notion that off-the-shelf bras often don’t fit well. The bra manufacturer Wacoal, for instance, says about eight out of 10 women wear the wrong size. Until now, however, standard sizes have barely changed, although the range has expanded. Cup sizes are based on two measurements: the breast at its fullest point, minus the rib-cage measurement. If it’s a 1-inch difference, it’s an A cup; a 2-inch difference, a B cup; and so forth. That approach, Jockey executives say, doesn’t account for different breast shapes.

Jockey began the project by scanning 800 women, getting “data points about all of the different measurements of a woman’s torso and the breast size,” said Sally Tomkins, a senior vice president. Researchers followed women in their homes as they chose bras and dressed, and heard “complete dissatisfaction about every aspect of the bra-purchasing process, from the inaccuracy to the way you get measured,” said Dustin Cohn, the company’s chief marketing officer.

Jockey came up with 10 cup sizes. “Our bras don’t necessarily get bigger, bigger, bigger, but in different proportions; they get larger, but in different shapes,” Cohn said.

To fit the bras, Jockey uses a kit with 10 plastic cups in varying shapes, along with a measuring tape. Customers are meant to try on the cups and see what works best, and then measure their rib cage. Someone with a 34-inch rib cage and medium-size breasts might wear a 5-34 or a 6-34, for instance.

Charla Welch, who reviewed the fitting process on her blog, found that the plastic cups were a little long and that none fit perfectly. She said she is a size 32H (in more conventional sizing) and would wear a 9-32 in Jockey.

The Jockey Bra confronts several business challenges. First, the sizing kit costs online customers $19.95, although Jockey says it includes a $20 coupon, plus a money-back guarantee on a bra if it does not fit. Other companies that sell difficult-to-fit items, such as Warby Parker with eyeglasses, send customers try-on versions for free.

“Essentially they’re being asked to shell out cash upfront to be part of this experiment,” said Jennifer O’Brien, director of strategic planning at Laird & Partners, an advertising agency, who did not work on the Jockey bra. “At least for the introductory phase, I would think that would be free. You want to remove as many barriers as possible to get people engaged with this, because it is a new world.”

And the bra costs $60, more than many competitors, despite its functional looks and a limited choice of colors: beige, white or black. “It is a high price point,” Tomkins of Jockey conceded. She said the company was selling the bra only online and in its boutiques, rather than in department stores, to try to get women to understand what is behind it.

As for converting women to new ways of sizing, O’Brien pointed to premium denim jeans, where women now shop by waist size.

Tomkins said that had been a concern. “It’s something that worried us all the way through,” she said. “It’s always a risk when you change something that’s been in the market for a very long time, but not only are we changing the fit, we’re changing the whole product.”