The music of the spheres in Pythagorean philosophy is the harmony produced by the movement of the heavenly bodies in their orbits (Google). Pythagoras believed that the movements of the stars were governed by fixed laws which could be expressed in numbers according to the numbers which give the harmony of sounds. This is the theory Shakespeare alludes to in The Merchant of Venice, Act V, Scene I, ô...such harmony is in immortal souls, but we cannot hear it.ö
Pythagoras taught not only the magic of numbers but also the healing power of music (Music). He taught of the ôMusic of the Spheresö and how the movement of the heavenly bodies could be perceived and reflected in the intervals of plucked strings.
The Pythagoreans built up an elaborate number lore, but the numbers that impressed them most were those found in musical ratios (Calter). In the frontispiece from a 1492 book on music theory, there is a picture of Jubal, from the Old Testament, and 6 men beating an anvil with hammers numbered 4, 6, 8, 9, 12, and 16. The frames show Pythagoras hitting bells, plucking strings under different tensions, tapping glasses filled to different levels, and all are marked 4, 6, 8, 9, 12, 16. In each frame he sounds the ones marked 8 and 16, an interval of 1:2, which represents an octave, or diapason. In a different part of the frame, Philolaos blows pipes of lengths 8 and 16, again an octave apart, and Pythagoras holds pipes, 9 and 12, giving the ratio 3:4, called the fourth or diatesseron, while Philolaos holds 4 and 6, giving the ration 2:3, called the fifth or diapente.
These three intervals, the octave (diapason), fifth (diapente) and the fourth (diatesseron) were the only intervals considered harmonious by the Greeks (Calter). Pythagoras is believed to have found them by experimenting with a single string with a moveable bridge, and found these pleasant intervals could be expressed as the ratio of whole numbers: 8:16, 4...