“They’re the best,” said Mr. Salcedo, 50, a policy officer in Chile for the United Nations’ Food and Agriculture Organization, who began playing the accordion when he was a child.

“You won’t find them in stores; they have to be made to order,” said Mr. Salcedo, who was combining the visit with a work trip to Rome. “And this is the place to come.”

For some people, the idea of traveling almost 7,500 miles for one purchase may seem extreme.

For accordion makers in Castelfidardo, it is a common occurrence. Ask around and prepare to be regaled with stories of delegations of Frenchmen, Argentines and other aficionados traveling to this town just south of the Adriatic port of Ancona to buy a bit of Italian industrial excellence.

Just after World War II, when entire accordion orchestras were fixtures in the festivities of Italian immigrants to the United States, Castelfidardo churned out its prize product by the tens of thousands.

Now, years after the electric guitar became the instrument of choice in popular music — people here still point to Elvis Presley and the Beatles as their economic nemeses — and the production of basic models largely moved to Asia, Castelfidardo has continued to shift its focus to quality from quantity. That has allowed the town to sustain a key industry, though in a much diminished form.

“Our accordions are like bespoke apparel,” said Francesca Pigini, a top manager for the company her grandfather started in 1946. “For us, it’s a pleasure and an enrichment to work and collaborate with artists and people who make music a big part of their lives.”

Pigini is the largest accordion maker in Castelfidardo, splitting production between instruments tailored to traditional music like polkas, waltzes or easy listening, and a classical repertoire, which grew considerably after Tchaikovsky introduced an accordion part in an 1883 suite — a milestone, accordionists say. The company makes about 60 models, costing from 2,000 to 30,000 euros, or $3,000 to $43,000.

Pigini is one of the few companies in Castelfidardo that still makes almost every component in-house, employing about 40 skilled workers and producing about 1,500 accordions a year.

Mr. Salcedo, incidentally, planned to buy a Pigini, he said later in an e-mail.

Pigini accordions count for a sizable chunk of Castelfidardo’s production, which has been inexorably eroded by changing musical tastes and — more recently — by the global economic crisis.

The story of how a 5,000-year-old Chinese free reed instrument called the sheng metamorphosed into the modern-day accordion passes through Vienna, where the first patent was presented in 1829, and winds through several European cities. But as far as Castelfidardo is concerned, the accordion is a homegrown success story pinned to the ingenuity of Paolo Soprani, who opened his shop in 1863.

Several stories told here romanticize the origins of Mr. Soprani’s inspiration — including improbable references to accordion-playing soldiers who fought at the Battle of Castelfidardo in 1860, one of the definitive skirmishes against papal troops that led to the unification of Italy.

But Beniamino Bugiolacchi, director of the International Accordion Museum in Castelfidardo, dismisses such legends, saying that Mr. Soprani’s major accomplishment was taking an artisanal activity and applying modern industrial strategies to increase the business.

Production in Castelfidardo peaked in 1953, when nearly 200,000 accordions were made in dozens of factories that employed about 10,000 workers. Accordion makers in other Italian towns also did brisk business. Today, only about 27 companies remain, mostly small businesses employing about 300 people, a number that has been stable for the last five years, Mr. Bugiolacchi said. Rising production costs shifted the competitive edge to manufacturers first in Eastern Europe and more recently in South Korea and China.