Julián Carrillo was a Mexican composer, conductor, violinist and music theorist, famous for developing a theory of microtonal music which he dubbed "The Thirteenth Sound" (Sonido 13).
Having not completed primary studies, he was ignorant of the acoustic basis of music—so he was fascinated when Ortega discussed laws governing generation of fundamental intervals in music. For example, when a violin string is depressed (stopped) at its midpoint, it produces a pitch twice the frequency of (an octave above) the open string. When a string is stopped at one-third, the remaining two-thirds vibrates a perfect fifth higher than the open string (almost exactly equivalent to 5/8 of an octave). Carrillo explored these relationships in experiments. For a while he tried, but couldn't divide the string further than into eight equal parts. Then he left the traditional way of dividing the string into two, three, four, five, six, seven and eight equal parts, and, using a razor to stop the string, divided the fourth string of his violin between G and A into sixteen parts. He could produce sixteen clearly different sounds within a whole tone.
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