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Nancarrow was one of the great originals of U.S. music, in a generation that included such others as Harry Partch, whose pursuit of a new tuning system led him to build his own instruments from scrap materials, and John Cage. Like Partch, Nancarrow was frustrated by the limits of traditional music-making; his imagination, though, roved more in the domain of rhythm. A trained musician can easily play seven notes in the time of another musician’s four, but what about fourteen in the time of five? And what about maintaining such relationships clearly against several other parts, all going at different speeds? And then what happens when those speeds are continuously changing? Nancarrow decided he needed a machine to articulate such complexities: he needed a player piano, a piano operated not by fingers on a keyboard but by a punched paper roll, each hole in the paper precisely prescribing the moment when a hammer hits a string. For three and a half decades, from the late 1940s to the early 1980s, he composed all his music that way.

Born in Texarkana, Nancarrow was largely self-taught, apart from a year he spent in Boston in his early 20s, taking lessons with Roger Sessions, Walter Piston, and Nicolas Slonimsky. Jazz, too, was important to him at that time — and was to be remembered, in boogie-woogie rhythms chugging through his music into the 1980s. He was also politically aware, and went to Spain to fight in the civil war. In 1940, soon after his return, he found he was denied a passport because of his brief membership in the Communist Party, and so he moved to Mexico, which he could enter without a passport. He wrote some instrumental pieces, including his first string quartet, but his experiences with performers were dispiriting and he gave up trying. With a legacy he returned to New York in 1947 to acquire a player piano and a roll-punching machine, and once that equipment was installed in his home he began creating works he called simply ‘studies’, these by 1960 numbering 30. He did not return to the U.S. until 1981.

His first study was published in New York in 1952 at the behest of Elliott Carter, but otherwise nothing filtered out from Mexico City until someone at the New York Public Library requested tapes in the late 1950s. A little later Merce Cunningham made dances to some of these, and in 1969 a Columbia record appeared. As interest started to grow, Nancarrow returned to composition, which he had virtually abandoned after the first 30 studies. By the early 1980s he had produced about 20 more.

All the studies have complex rhythmic structures, often extrapolated from the elementary devices of canon (one line follows another) and ostinato (one line keeps repeating a pattern). Punching his rolls, Nancarrow must have spent hours in careful measurement. For his basic material, though, he took what lay around him: scales, major chords, jazz figures. The result is a wonderful combination of the arcane with the naive, the mechanical with the human.

With the limits of virtuosity advancing, some of Nancarrow’s studies have become practicable for human rather than mechanical performance, and in 1998 Thomas Adès arranged two of the earlier ones for duo pianists.

Study No. 6 is an untypically lazy piece, though certainly not without its quirks. The repeating bass line, maintained by the second pianist’s left hand throughout, is squashed and stretched by constant changes of rhythm and tempo, while the melody, whose returns are punctuated by up-down scales, develops bits of counterpoint along the way.

Study No. 7 is bigger and much more complex, with scraps of tune and scales caught on rhythmic and harmonic cycles rotating at several different speeds simultaneously. One rhythmic machine, starting up soon after the beginning, keeps repeating a bar of eighteen irregular pulses (5-4-2-3-4), at first attached to thirds. Another, more continuously present, has a similarly lively rotating pattern but longer (5-5-2-4-3-2-3). The larger form is defined by a near repetition of the opening almost halfway through.

Paul Griffiths is a Welsh music critic, novelist, and librettist.