The Pythagoreans believed that the only true realities existed in the realm of numbers and geometric forms. Therefore, all other aspects of human existence were mutable and susceptible to decay. Accordingly, the perfect geometric forms of triangle, square and circle, visible in the heavenly orbits and in the natural world of crystals, became symbols of the eternal realm beyond matter. Man's only recourse to an understanding of this immutable realm was in the contemplation of the unchanging order of numbers -(i.e. in the observance of the motion of the heavens) (Miller,1976,p.8).
The Pythagoreans are also responsible for discovering that the relation between tones and semi-tones in the musical scale could be expressed as simple numerical ratios. This led them to posit that sounds, as well as the movements of the celestial bodies were governed by numbers, and therefore, the workings of the universe could be subject to a musical interpretation. Cosmic order could be understood as musical harmony (Miller,1986,p.37).
This mystical concept of number and geometric figure was inherited by Plato. Plato's writings on the ordering of the cosmos, in particular, Timaeus, provided Renaissance scholars with philosophical concepts that profoundly impacted the composition and interpretation of dance.
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