Nancarrow was born in Texarkana, Arkansas. He played trumpet in a jazz band in his youth, before studying music first in Cincinnati, Ohio and later in Boston, Massachusetts with Roger Sessions, Walter Piston and Nicolas Slonimsky. Later still, he went to New York City and studied with Henry Cowell, another great iconoclast.
When the Spanish Civil War broke out, Nancarrow went to Spain to fight against Francisco Franco. While there, he joined the Communist party, as a result of which he was refused an American passport after his return. He subsequently moved to Mexico City, which remained his home until his death.
It was in Mexico that he did the work he is best known for today. He had already written some pieces in America, but their extreme technical demands they made on performers meant that satisfactory performances were very difficult to mount. In Mexico, where the contemporary classical music scene was poorly funded, and there were even fewer musicians capable of performing his works, the need to find an alternative way of having his pieces performed became even more pressing. He found the answer in the player piano, with its ability to produce extremely complex rhythmic patterns at a speed far beyond the abilities of humans. Nancarrow has said that if electronic resources were available to him at this time, he would have probably written music for them, but they were not. It is possible that Nancarrow hit upon the idea of using the player piano through Henry Cowell, an acknowledged early influence who wrote about the possibilities of using the player piano in serious music in his book, New Musical Resources (1930).
Nancarrow had a machine custom built to enable him to punch the piano rolls by hand. The machine was an adaptation of one used in the commercial production of rolls, and using it was very hard work, and very slow. He also adapted the player pianos, increasing their dynamic range by tinkering with their mechanism, and covering the hammers with leather or metal so as to produce a more percussive sound.
Nancarrow's first pieces combined the harmonic language and melodic motifs of early jazz pianists like Art Tatum with extraordinarily complicated metrical schemes. The first five rolls he made are called the Boogie-Woogie Suite (later assigned the name Study No. 3 a-e) and are probably the most jazzy of all his works. Later works tend to be more abstract, with no obvious references to any music apart from Nancarrow's.
Many of these later pieces (which on the whole he called studies) are canonss in augmentation or diminution. While most such canons, such as those by Johann Sebastian Bach, have the tempos of the various parts in quite simple ratios, like 2:1, Nancarrow's canons are in far more complicated ratios. The Study No. 40, for example, has its parts in the ratio e:pi, while the Study No. 37 has twelve individual melodic lines, each one moving at a different tempo.
Having spent most of his life in obscurity, Nancarrow became better known in the 1980s, and was lauded as one of the most significant composers of the century. The composer Gyorgy Ligeti called his music "the great discovery since Webern and Ives ... the best of any composer living today." In 1982 he received a MacArthur Award, worth $30,000. This increased interest in his work prompted him to write for more conventional instruments, and he produced several pieces for small ensembles.
Still more recently, Nancarrow's entire output for player piano has been recorded and released on the Wergo label. Many of his studies have also been arranged for musicians to play, and Joanna MacGregor has used multitracking to record several pieces on a normal piano.