The musician’s power of expression is founded upon a prior obedience. To what? To her teacher, perhaps, but this isn’t the main thing—there is such a thing as the self-taught musician. Her obedience rather is to the mechanical realities of her instrument, which in turn answer to certain natural necessities of music that can be expressed mathematically. For example, halving the length of a string under a given tension raises its pitch by an octave. These facts do not arise from the human will, and there is no altering them. The education of the musician sheds light on the basic character of
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