Mexican composer, a leading 20th-century exponent of microtonal music (i.e., music using intervals smaller than a halftone, or half step).

Of Indian descent, Carrillo grew up mainly in Mexico City. He showed considerable musical talent very early. Later, in his early 20s, after studying violin and composition in Mexico City, he began to study in Europe. Throughout his life he toured extensively in both western Europe and the United States. From 1905 on, he held many important music positions in Mexico as composer, conductor, teacher, writer on music, and administrator.

Carrillo’s interest in microtonal music was stimulated in 1895 by a class in Mexico on acoustics. He realized that the musical whole tone could be divided not only into two semitones (as it had been for centuries) but also into three third tones, four quarter tones, and so on. In the 1920s he began intensive investigations into the possibilities of composing with these microtonal intervals, through sixteenth tones, which he considered the smallest interval listeners could readily hear. He created a new system of music notation and had special instruments built on which his microtonal works could be performed.

Of Carrillo’s six symphonies, three are microtonal. Two of his five masses are microtonal, as are six of his works for solo instruments with orchestra. He also composed chamber music and music for single instruments in both microtonal and non-microtonal idioms and wrote a number of articles and books.