One reason Western music has had such a powerful impact on the world and why it is so sophisticated an achievement is that in it the function of music – whether used for ritual or dance or worship or pleasure – gradually became an aspect of style, not its defining force. Dance music could stand independent of dance; church music independent of the church, art music independent of patron – because the internal world of each composition was sufficiently coherent to stand on its own. It had no need to remain tethered to the world that gave it birth. Once music is detached from function, once it becomes a repertory art, it explicitly strives to define itself, out of itself, to become “mathematical” – that is to say, to begin from premises and proceed to conclusions by interpreting its own universe, finding its own laws. Systems of harmony and counterpoint become tools for elaborate musical explorations. A great deal of Western music is as much a manifestation of idealism as is mathematics.
– from Emblems of Mind: The Inner Life of Music and Mathematics by Edward Rothstein.