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The Greeks not only made music; they were the first to use reason to understand its production. Early musicians had already observed that the tone produced by a plucked string could be varied by decreasing or increasing its length. In the sixth century B.C., Pythagoras found that when he divided the string by whole numbers, he could produce half the notes of an octave of music. Thus, he demonstrated that intervals had a mathematical, which meant a rational, foundation, and music and physics entwined for the first, but not the last time.

After he discovered the interval's arithmetic basis, Pythagoras proceeded to speculate about celestial music. He proposed that the movements of the planets and stars created vibrations for the gods, and he named this divine harmony, unheard by mortal ears, the Music of the Spheres. To the objection that no mortal had ever enjoyed this music, Pythagoras replied that the sound is present at the moment of our birth, but because there is no silence against which we can compare it, we cannot hear it.

Since the fourth century B.C. the changes in Western music have been so enormous that despite his knowledge and love of music, Pythagoras would be completely bewildered by what we listen to today. Ancient Greek music was monodic. Their word for melody, melos modus, literally meant the "road around," and Greek melody was a single-line theme that meandered through the musical register.3 Though the Greeks understood the textures of harmony, they had little knowledge of the complexities of counterpoint, and all members of a Greek chorus sang the same song in unison. This linearity reflected the ancient Greek outlook in other matters, including a reliance on Euclidean rectilinear axioms and a pictorial linear narrative style in art best exemplified by vase paintings.

When Rome conquered Greece, the Romans usurped Greek music. As they did in art and science, the Romans refined what the Greeks had begun but they made few original contributions to music.

The ascent of Christianity accompanied the disintegration of the classical world beginning around A.D. 400. These contrapuntal forces clashed with such dissonance that they brought about a four-hundred-year-long European intermission in human knowledge that we now call the Dark Ages. The statue of Calliope lay toppled from her pedestal. There was no one to reassemble the pieces in the midst of the mass migrations and almost constant warfare of those difficult times. As the vast Roman Empire fragmented, Latin, its monolithic language, also disintegrated into many different dialects.

The musician, like the artist, sought sanctuary in the Church. Protected and surrounded by the new religion, music served it. In Europe, during this formless lump of centuries, what individual powers the kings could not claim, the Church subsumed. The Red and the Black created a checkerboard on which society could play out its destiny. Artists, authors, and composers did not sign their works; faith rather than reason dominated intellectual debate, and people sang in chorus. The hypnotizing cadences of Gregorian chant, seeking to create a divine vibration that would resonate with the powerful message of the New Testament, became the song that would last a millennium. Scientific inquiry was lulled into a long hibernation.

As this aesthetic ice age began to melt, music suddenly blossomed forth in a most unexpected form. Love songs appeared like primroses after a cold, bleak February. These eleventh- and twelfth- century paeans to courtly love were something new. Passion had been the province of the Church, as in the Passion of Christ, not of sexual attraction. But when troubadours began to sing the praises of Arthurian romantic love, their songs became the musical fashion of their age.
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