“There is no foundational mathematical or physical reason the relationship between Pythagorean and tempered western music should exist. It just does. The rich flexibility of the tempered scale and the … bountiful archives of western music are a testimonial to this wonderful coincidence provided by nature.”

"Handbook of Fourier Analysis and Its Applications" (Oxford University Press, 2009), p. 623, Robert J. Marks II, 2009, 2011-04-29 http://books.google.com/books?id=Sp7O4bocjPAC&printsec=frontcover&dq=Handbook+of+Fourier+Analysis+and+Its+Applications&hl=en&ei=wcm5TaPvJYba0QHYi7nRDw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CDEQ6AEwAA#v=onepage&q&f=false,

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Robert J. Marks II 10
American electrical engineering researcher and intelligent … 1950

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“There is a good deal more to Pythagorean musical theory than celestial harmony.”

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Context: Ancient belief in a cosmos composed of spheres, producing music as angels guided them through the heavens, was still fluorishing in Elizabethan times.... There is a good deal more to Pythagorean musical theory than celestial harmony. Besides the music of the celestial spheres (musica mundana), two other varieties of music were distinguished: the sound of instruments...(musica instrumentalis), and the continuous unheard music that emanated from the human body (musica humana), which arises from a resonance between the body and the soul.... In the medieval world, the status of music is revealed by its position within the Quadrivium—the fourfold curriculum—alongside arithmetic, geometry, and astronomy. Medieval students... believed all forms of harmony to derive from a common source. Before Boethius' studies in the ninth century, the idea of musical harmony was not considered independently of wider matters of celestial or ethical harmony.<!-- Ch. 5, pp. 201-202

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