FLORENCE, Italy — In December 1929, Irving Berlin published a song with an irresistible but notoriously complex rhythmic pattern and lyrics about the custom in Harlem of putting on one’s Sunday finery to parade up and down Lenox Avenue, “Spendin’ every dime/For a wonderful time.”

Issued by Columbia, Victor and the Brunswick record labels (which had a No. 1 hit with it), “Puttin’ on the Ritz” was eventually sung on film by Fred Astaire and Clark Gable; revised by Berlin to replace the lyric’s resplendent black people with rich whites strutting down Park Avenue; and definitively entered pop culture as easy shorthand for dressing to the nines.

To understand how durably Berlin’s tune permeated pop culture, consider the story of Matteo Gioli, a 28-year-old musician from Pisa who played banjo, guitar and double bass in a retro-style swing band until 2010.

Image Hats are part of the fashion look at Pitti Uomo. Credit... Chris Warde-Jones for The New York Times

It was then he went looking for headgear as resplendent as that worn by the Harlemites of eight decades ago. And when Mr. Gioli couldn’t find what he was searching for, he and his girlfriend, Veronica Cornacchini, impulsively decided to go into the hat-making business. First knocking on the doors of what few traditional milliners remain in this Renaissance city, they eventually apprenticed themselves for a year and soon were turning out the first models bearing the label “SuperDuper Hats,” a phrase from the song.