What is Harmony of the Spheres?

(b. c. 580 BC, Samos, Ionia--d. c. 500, Metapontum, Lucania)

Greek philosopher, mathematician, and founder of the Pythagorean brotherhood that, although religious in nature, formulated principles that influenced the thought of Plato and Aristotle and contributed to the development of mathematics and Western rational philosophy (Pythagoreanism). Pythagoras migrated to southern Italy about 532 BC, apparently to escape Samos' tyrannical rule, and established his ethico-political academy at Croton (now Crotona).

It is difficult to distinguish Pythagoras' teachings from those of his disciples.  None of his writings has survived, and Pythagoreans invariably supported their doctrines by indiscriminately citing their master's authority.  Pythagoras, however, is generally credited with the theory of the functional significance of  numbers in the objective world and in music.  Other discoveries often attributed to him (e.g., the incommensurability of the side and diagonal of a square, and the Pythagorean theorem for right triangles) were probably developed only later by the Pythagorean school.  More probably the bulk of the intellectual tradition originating with Pythagoras himself belongs to mystical wisdom rather than to scientific scholarship.
Encyclopaedia Britannica 97

Harmony of the Spheres

The astronomy of the Pythagoreans marked an important advance in ancient scientific thought, for they were the first to consider the earth as a globe revolving with the other planets around a central fire.  They explained the harmonious arrangement of things as that of bodies in a single, all-inclusive sphere of reality, moving according to a numerical scheme.  Because the Pythagoreans thought that the heavenly bodies are separated from one another by intervals corresponding to the harmonic lengths of strings, they held that the movement of the spheres gives rise to a musical sound-the "harmony of the spheres."
Microsoft Encarta Encyclopedia 2000

The harmony of the cosmos

The sacred decad in particular has a cosmic significance in Pythagoreanism: its mystical name, tetraktys (meaning approximately "fourness"), implies 1 + 2 + 3 + 4 = 10; but it can also be thought of as a "perfect triangle," as in the Figure.

Speculation on number and proportion led to an intuitive feeling of the  harmonia ("fitting together") of the kosmos ("the beautiful order of things"); and the application of the tetraktys to the theory of  music revealed a hidden order in the range of sound.  Pythagoras may have referred, vaguely, to the "music of the heavens," which he alone seemed able to hear; and later Pythagoreans seem to have assumed that the distances of the heavenly bodies from the Earth somehow correspond to musical intervals--a theory that, under the influence of  Platonic conceptions, resulted in the famous idea of the "harmony of the spheres."  Though number to the early Pythagoreans was still a kind of cosmic matter, like the water or air proposed by the Ionians, their stress upon numerical proportions, harmony, and order comprised a decisive step toward a metaphysic in which form is the basic reality.

In reviewing the accounts of music that have characterized musical and intellectual history, it is clear that the Pythagoreans are reborn from age to age. The German astronomer Johannes Kepler (1571-1630) perpetuated, in effect, the idea of the harmony of the spheres, attempting to relate music to planetary movement. René Descartes (1596-1650), too, saw the basis of music as mathematical. He was a faithful Platonist in his prescription of temperate rhythms and simple melodies so that music would not produce imaginative, exciting, and hence immoral, effects. For another philosopher-mathematician, the German Gottfried von Leibniz (1646-1716), music reflected a universal rhythm and mirrored a reality that was fundamentally mathematical, to be experienced in the mind as a subconscious apprehension of numerical relationships.
Encyclopaedia Britannica 97

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Background Illustration Courtesy of KIRA YUKO