I am thinking the notes and divisions of western music has to do with the development of the organ with its fixed pipe lengths, and of the clock with the regular time scale. Thus the desire to regularize the music to a system where it can be reproduced more easily from place to place.
Somewhere around the mid 13th century air driven pipe organs replaced the water type from ancient Greece. And at the same time in the development of science, the idea of a regular time measured with a pendulum or a clock mechanism drove the music world to a more structured way to annotate and reproduce music.
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