“The first is the belief that the universe is essentially harmonious, and that the source of that concord lies in mathematical proportions which can be directly related to musical harmonies. Pythagoras, in an oft-repeated legend, was said to have meditated on the sound of smiths beating hammers upon anvils, and to have argued that a hammer half as heavy produced a note an octave above its full-sized fellow.3 More important were the experiments with a single string, or monochord, attributed to him by his successors. If a stretched string is divided exactly into two it produces a sound an octave higher than the fundamental pitch (the ratio 2:1), the intervals of the fourth and fifth can similarly be expressed as the ratios 4:3 and 3:2 respectively, and all other intervals can be described in mathematical terms.4 These numerical proportions were then extended to describe the relationships of the planetary spheres, both in their relative distance one from another, and in the speed of their movement. The ideas were given influential (if obscure) expression in Plato’s Timaeus, and endlessly elaborated in succeeding centuries up to the Renaissance. One of the final manifestations of this understanding is provided in the illustration of cosmic harmony from Robert Fludd’s Utriusque cosmi … historia 1”