Say the word tango and most people picture couples in tuxedos and gowns, cheek to cheek, gliding across a polished floor. Elegant, a little haughty, unmistakably high-class. Its origins were the exact opposite.

At the end of the nineteenth century, Buenos Aires was drowning in immigrants. Italians, Spaniards, Germans, Poles — people who had crossed the ocean looking for work, most of them young single men, packed into cheap tenements near the harbor. Far from home, without families, barely able to make themselves understood, they gathered at night in the only places that would have them: the dockside bars and the brothels.

There, a dozen kinds of music collided. The drum rhythms of candombe, brought over from Afro-Uruguayan Montevideo and taken up by the city's Afro-Argentine population; the fast, two-beat milonga brought in from the Argentine countryside; the springy pulse of the Cuban habanera, a slow-swaying dance rhythm carried in by ship; and the waltzes and polkas the European newcomers had packed in their trunks. All of it fused at the bottom of the port town, and out of that fusion came a new dance. That was tango.

The earliest tango looked nothing like the refined image we hold today. There were no fixed composers and no scores; it passed from ear to ear in the corners of taverns. The dancing was frankly suggestive, and respectable society dismissed it as 'brothel music.' The grandees of Buenos Aires were, if anything, embarrassed that such a thing was catching on in their own city.

One instrument defined the sound of tango: the bandoneon. A cousin of the accordion, worked by pushing and pulling its bellows, it had originally been built in Germany for small congregations that couldn't afford a church organ. By some accident of history it reached Buenos Aires and took the lead role in tango. Its sobbing, breath-like tone matched the loneliness of the uprooted immigrants exactly. An instrument made to praise God had turned, on the far side of the planet, into one that sang of heartbreak and homesickness.

It is worth pausing here on tango's close sibling: the milonga. Older, faster, and more cheerful, the milonga was something like tango's mother. The two rang out in the same bars, were played by the same orchestras, and were often danced on the same night. Long after tango sailed out into the world, the milonga stayed behind as the native pulse of Buenos Aires.

The track below is a signature milonga. Written by the composer Sebastián Piana in 1933, its plain, crisp rhythm still holds the air of the old neighborhood as it was before tango grew up. That lightness was tango's starting point.

What changed the world's opinion of this brothel music was, strangely enough, a trip across the ocean. In the 1910s, wealthy young Argentines went to play in Paris and brought tango with them. Parisian high society, then the very cutting edge of fashion, went wild for the exotic foreign dance. 'It's the rage in Paris' — that single phrase turned the tables back home. A dance that had been an embarrassment in its own country returned to the main stage of Buenos Aires with a European seal of approval.

Then came the man who gave tango a face and a voice: Carlos Gardel. Tango had been largely instrumental; Gardel brought lyrics and singing to it, lifting the 'tango-song' (tango canción) into a national art. His sweet, burnished voice reached across all of Latin America through records and films, and Gardel became far more than a singer — he was a national hero. When he died suddenly in a plane crash in 1935, in his mid-forties, Argentina mourned as a nation.

The track below is 'Por Una Cabeza,' released the year he died. Framed as a horse-race commentary, it sings of the gamble of love; later borrowed by Hollywood, it has become the melody everyone reaches for when they think of tango. Here, the dance from the dockside bar finally found a singer's voice and reached the ears of the world.

But the man who pushed tango up the final step was one the tango world hated for years: Astor Piazzolla.

Given a bandoneon as a child, Piazzolla made his name young in the top orchestras of Buenos Aires. He did not stay there. He went to Paris to study classical composition, and when his teacher told him that his true voice lay in tango, he returned home and poured classical harmony and the improvised feel of jazz boldly into it. Music not to dance to but to sit and listen to — this was 'nuevo tango,' the new tango.

Conservative tango lovers revolted. 'That is not tango,' they charged; he is said to have received threatening letters. The attempt to lift dance-floor music up into the concert hall looked to them like a betrayal, a defilement of tradition. But time proved him right. Piazzolla's works are now performed in concert halls the world over, a modern classic that classical players compete to take up.

Here are two pieces of very different character. 'Adiós Nonino' is the quiet, prayer-like work Piazzolla wrote for his late father. 'Libertango,' by contrast, races on a sharp, driving rhythm, marking the moment tango turned fully into music to be listened to.

A dance that had passed from ear to ear in the brothels of a port town became, a century later, an art performed by tuxedoed players reading from scores. Music once thought shameful became a nation's pride. The story of tango is a rare record of a music that climbed the whole staircase — from bottom to top, from dancing to listening.