THE MUSIC OF THE SPHERES, OR THE METAPHYSICS OF MUSIC . . . According to tradition, the harmonic structure of music was discovered by Pythagoras about the fifth century B.C. Pythagoras experimented with a stretched piece of cord. When plucked, the cord sounded a certain note. When halved in length and plucked again, the cord sounded a higher note completely consonant with the first. In fact, it was the same note at a higher pitch. Pythagoras had discovered the ration 2:1, of the octave. Further experiments, plucking the strings two-thirds of its original length produced a perfect fifth in the...