Sunday, March 27, 2011

musical theory and ancient cosmology

New Universe | If science is conceived of as knowledge and philosophy as love of wisdom, then the invention of musical theory clearly is one of the greatest scientific and philosophical achievements of the ancient world. When, where, and how did it happen?

Assuming that Cro-Magnon man processed sound with the same biology we possess, humans have shared some fifty thousand years of similar auditory experiences. Musical theory as an acoustical science begins with the definition of intervals, the distance between pitches, by ratios of integers, or counting numbers, a discovery traditionally credited to Pythagoras in the sixth century B.C.

Not until the sixteenth century A.D., when Vincenzo Galilei (Galileo's father, an accomplished musician) tried to repeat some of the experiments attributed to Pythagoras, was it learned that they were apocryphal, giving either the wrong answers or none at all. Today, as the gift of modem archaeological and linguistic studies, our awareness of cultures much older than that of Greece has been phenomenally increased; this permits us to set aside the tired inventions about Pythagoras and tell a more likely story, involving anonymous heroes in other lands.

My story is centered in Mesopotamia. It demonstrates how every element of Pythagorean tuning theory was implicit in the mathematics and mythology of that land for at least a thousand years, and perhaps two thousand, before Greek rationalists finally abstracted what we are willing to recognize as science from its long incubation within mythology.

What seems most astounding in ancient Mesopotamia is the total fusion of what we separate into subjects: music, mathematics, art, science, religion, and poetic fantasy. Such a fusion has never been equaled except by Plato, who inherited its forms. Socrates' statement about the general principles of scientific studies in book 7 of Plato's Republic, with the harmonical allegories that follow directly in books 8 and 9, guides my exposition here. The Mesopotamian prototypes to which they lead us fully justify Socrates' treatment of his own tale as an "ancient Muses' jest," inherited from a glorious, lost civilization. Scholars who have become too unmusical to understand mankind's share in divinity, as Plato feared might happen, still can lean on him for understanding, for all of his many writings about harmonics and music have survived. (I must suppress here, for reasons of space, the extensive harmonical allegories of the Jews, whose parallel forms infuse the Bible with related musical implication from the first page of Genesis to the last page of Revelation.)

Music was as important in ancient India, Egypt, and China as it was in Mesopotamia and Greece. All these cultures had similar mythic imagery emphasizing the same numbers, which are so important in defining musical intervals; this raises doubts about whether any people ever "invented" acoustical theory. For instance, in any culture that knows the harp as intimately as it was known in Egypt and Mesopotamia, its visible variety of string lengths and economy of materials (strings require careful and often onerous preparation) encourage builders, as a sheer survival strategy, to notice the correlation between a string's length and its intended pitch.

Similarly, in China, where by 5000 B.C. the leg bones of large birds, equipped with tone holes appropriate for a scale, appear as paired flutes in ritual burials, the importance of suitable materials conditioned pipemakers to be alert to lengths. The basic ratios could have been discovered many times in many places, more likely by loving craftsmen and practitioners than by philosophers. Certainly, the discovery came no later than the fourth millennium B.C., before even the first Egyptian dynasty was founded or the Greeks had reached the Mediterranean shore.


Uglyblackjohn said...

Would there be a musical value for Pi?

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