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Notebook, 1993- RELATIONSHIPS

Accoustical Measurements

Pythagoras believed that one could demonstrate order in the universe by expressing all relationships among the parts of things in terms of single whole numbers; he believed that such relationships do exist among the perfect intervals of tones produced by sounding a stretched string. Phythagoras' work with acoustical measurements was presumably the basis of Greek tuning and the six modes or scales, which carried over in the liturgical music of the Middle Ages. Taut strings of different lengths, when related to one another according to simple numerical ratios, produce agreeable sounds or euphony. Harmonic intervals were applied, on occasion, to achitectural design during the Renaissance. Their first imaginative use was made, however, by disciples of Pythagoras in their attempt to explain the position and velocity of the heavenly bodies. They combined astronomical and musical discoveries in the famous doctrine of "the harmony of the spheres."

[Harlan, Calvin. Vision & Invention, An Introduction to Art Fundamentals. Englewood Cliffs, NJ: Prentice-Hall, 1986.]

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