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He was born on September 8, 1824 in Sant Joan de les Abadesses, a town in the province of Girona, in Catalonia, Spain. Both his parents, Francesc Nunó and Magdalena Roca, died before his ninth birthday. After their death, Nunó was raised by his uncle Bernard, a seller of silks in Barcelona, who financed his musical studies in that city. There he demonstrated his skill as a soloist in the city cathedral, for which he gained a scholarship to study with the composer Saverio Mercadante in Italy. Upon his return to Barcelona, he was named director of the Queen's Regimental Band in 1851 and travelled with them to Cuba where he met and befriended Antonio López de Santa Anna, the former Mexican president.
When Santa Anna returned to Mexico in 1853 to again resume the office of president, he invited Jaime Nunó to lead the Mexican military bands. His arrival coincided with the national call to compose the Mexican National Anthem. Nunó participated, composing music for the lyrics of Mexican poet Francisco González Bocanegra, and was declared the winner on August 12, 1854.
After the overthrow of President Santa Anna, Nunó emigrated to the United States, where he worked as a conductor and opera director. One of the operas he directed toured the Americas in 1864. After a time in Spain, he returned to the U.S. and settled in New York, where he was found by a Mexican journalist in 1901. When this news reached Mexico, the current president, Porfirio Díaz, invited him to return; he did so and received various honors between 1901 and 1904. He died in New York on July 18, 1908. In 1942 the Mexican government ordered that his remains be exhumed and interred in the Rotonda de los Hombres Ilustres (Rotunda of Illustrious Men) in Mexico City, where they remain.