The bandoneon, which is sometimes called the button accordion, is a peculiar instrument–and I’m being charitable. A conventional accordion has that small piano-style keyboard for the right hand and a rack of chord buttons for the left. The bandoneon has no keyboard, and each of its buttons plays only a single note at a time; but since there are 76 buttons, the bandoneon has a range that nearly matches that of a piano. What makes the bandoneon “a diabolic invention,” in the words of Astor Piazzolla–its signal virtuoso, who has played the instrument for 60 years–is that each of its buttons actually plays two notes–one when the bellows are being closed, and another when they are being opened.

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The bandoneon was invented in Germany in 1854 as an inexpensive substitute for the harmonium (reed organ) for churches too poor to afford a decent keyboard instrument. During the next 75 years, they were manufactured only in Germany, culminating with the custom production of 25,000 instruments in 1930 for the Argentine market. (Production ceased as Germany went to war, and virtually no bandoneons–at least none of old-world quality–are produced today.)

In the 1880s, these immigrants had begun fusing their native musical traditions with the rhythms and passion of their new land. The bastard child that resulted was called tango. “I would say that 99 percent of the tango musicians were Italian immigrants,” explains Piazzolla, who is himself of pure Italian heritage; “that’s why it’s so sad, so dramatic.” As the Argentine-born music critic Fernando Gonzalez writes: “[Tango] grew up in the muddy fringes of Buenos Aires, in brothels, in a world of orilleros . . . men of fast knives and half-smoked cigarettes permanently dangling from a corner of their mouths.” When the bandoneon’s dark, lachrymose sound was brought to Argentina, the bastard tango had found its voice.

In fact, Piazzolla’s infamy as a revolutionary is exceeded only by his renown as a composer. The new tango, lauded in Europe and America, was no hit in Argentina, where most people resented Piazzolla’s experiments; he was accused of pretension, of cultural heresy, of trying to dress the old whore in society gowns. Tango fans reviled him, and older tango musicians, steadfast in their approach to the idiom, threatened him with beatings and worse; Piazzolla, who is combative and nonconciliatory by nature, did nothing to ease the tension (“I wasn’t strangled to death because I learned growing up on the streets of New York to defend myself”). Just last month, Piazzolla, says, an Argentine taxicab driver railed at him, calling him a communist when he recognized the master of new tango in his cab. Understandably, for most of the last three decades, Piazzolla has lived outside of Argentina.