Harmony

None of the writings produced by Pythagoras or his contemporaries are extant (see Burkert for a discussion of the authenticity of information about fifth-and sixth-century B.C.E. Pythagoreans), but the impact that the simplicity and exactness of the Pythagorean proportions had on the philosopher Plato (428–348 or 347 B.C.E.) is revealed most clearly in his late dialogue Timaeus, in which Timaeus, a man trained in Pythagorean doctrine, describes the origin and nature of the physical world. Central to this cosmological drama is the Demiurge, a kind of primary arranger, who begins with formless matter in a primitive state of chaos. He proceeds by using a fixed set of numbers to construct the soul of the world as a mixture of metaphysical oppositions (indivisible and divisible existence, indivisible and divisible sameness and difference). Successive lengths of primary material are mixed in the ratios 2:1, 3:2, 4:3, and 9:8, that is, exactly the Pythagorean harmonic ratios (Timaeus 35–36, pp. 64–73). Thus the world's soul is constructed as a harmony of opposites permeated by number in which the formative principles of Platonic cosmology are identical to those of Pythagorean harmonic theory. In a following section, Plato turns to the construction of the physical universe as an "eternal image, moving according to number" (Timaeus 37D, pp. 76–77). The seven celestial bodies—the Moon, Mercury, Venus, the Sun, Mars, Saturn, and Jupiter—are created and placed in orbits about the earth determined by these same harmonic ratios. According to this model, the sun is located at the midpoint of a seven-note scale of revolving bodies; the whole thing is contained within an outer starry sphere that sets the limits of the universe. In his Republic, written some thirty years before the Timaeus, Plato had used striking imagery rather than mathematical relationships to describe his harmonic universe of planetary spheres: "And on the upper surface of each circle is a siren, who goes round with them, hymning a single tone or note. Together they form the concord of a single harmony [musical scale]" ("The Myth of Er," Republic 617B, pp. 502–505).