The aim and final end of all music should be none other than the glory of God and the refreshment of the soul. If heed is not paid to this, it is not true music but a diabolical bawling and twanging.
    -J. S. Bach (1685-1750)

Picture to yourself, if you can, a universe in which everything makes sense. A serene order presides over the earth around you, and the heavens above revove in sublime harmony. Everything you can see and hear and know is an aspect of the ultimate truth: the noble simplicity of a geometric theorem, the predictability of the movements of heavenly bodies, the harmonious beauty of a well-proportioned fugue--all are reflections of the essential perfection of the universe. And here on earth, too, no less than in the heavens and in the world of ideas, order prevails: every creature from the oyster to the emperor has its place, preordained and eternal. It is not simply a matter of faith: the best philosophical and scientific minds have proved that it is so.

This is no New Age fantasy but our own world as scientists, philosophers, and artists knew it until the advent of the Industrial Revolution and its companion in the arts, the Romantic movement. [...]

The concepts of the musical universe and the Great Chain of Being originate in the classical bedrock of our culture, flow through the Christian tradition, and remain firmly centered in the Renaissance and the Age of Reason. They are at the core of the culture. It was not until the the nineteenth century that the perspectives shifted decisively to the earthly, the tangible. Materialism and sensuality, qualities that had been deeply mistrusted throughout most of the Western tradition, emerged ascendant.

All art, including music, was a much more serious matter before the self-conscious aestheticism of the late nineteenth century took root. [...]

In the same way, science was deeply involved in the whole ethos of the culture. [...] The history of science is the continuing process of the widening gulf between the ideals and the practice of science. At the birth of Western science in the sixth century B.C., the two were identical. The asking of the question was the intellectual breakthrough, and the answers were as poetic and expansive as the questions, for there existed no data with which they were expected to conform, aside from the perceived order and beauty of creation. "Doing things" was disdained as unworthy of science, whose true purpose was to elucidate the fundamental unities that explain the function and thuis the meaning of the phenomenal world. [...]

Nowadays most scientists would accept the thesis that the cosmos has no underlying logic in the classical sense, but it rather a confluence of accidents, which are governed by laws. However, the laws themselves are irrational and do not arise from any fundamental orderliness.

It is scarcely an overstatement to say that most of what you will read in the first chapters of this history was known to every well-educated person from the earliest days of Greek civilization until the end of the last century. Here is not the place to bemoan the decline of classical education, but it is a fact of modern life that the core of what constituted education and civilization throughout the whole sweep of Western thought is now a scholarly specialty, and a rather exotic one at that. Modern students are able to obtain degrees, even in the humanities, from the country's best colleges having read no more of the classics than translations of the Republic, one of Homer's epics, and the Aeneid. However, in order to make sense of Western music from any period, it is essential to understand its humanistic basis, which is firmly grounded in the classics.

Music and science begin at the same point, where civilization itself begins, and standing at the source is the quasi-mythical figure of Pythagoras. Although most people today know little more about him than the geometrical theorem that bears his name, Pythagoras's contribution to what we call civilization is fundamental. Arthur Koestler used a musical metaphor to describe it:

The sixth century scene evokes the image of an orchestra expectantly tuning up, each player absorbed in his own instrument only, deaf to the caterwaulings of the others. Then there is a dramatic silence, the conductor enters the stage, raps three times with his baton, and harmony emerges from the chaos. The maestro is Pythagoras of Samos, whose influence on the ideas, and thereby on the destiny, of the human race was probably greater than that of any single man before or after him.

[...]

We shall never know exactly to what extent the historical Pythagoras corresponds to the Master of humanist tradition, any more than we shall ever know who actually wrote the Iliad and the Odyssey, or whether all those spiritual utterances in the Gospels were really said by the historical Jesus of Nazareth. Yet for the purposes of the historian it really does not matter, for the doubts themselves are anachronistic: the point is that through the vast span of history in which Pythagorean humanism (and the study of Homer, and Christianity) were vibrant intellectual forces, there was never a shadow of doubt as to the authenticity and veracity of the tradition. You can put quotation marks around "Pythagoras" if that will make you feel more up-to-date, but it will not alter the meaning; the people who pursued Pythagoreanism over the course of thousands of years did believe, implicitly, in the historicity of the Master. The real Jesus may have been a charlatan, but the Jesus worshipped by millions of people changed the course of history; and it would be wrong, regardless of what a thousand copiously annotated doctoral dissertations may say, to attribute the Iliad to Anonymous.

Therefore, let us assert that Pythagoras, in or out of quotation marks, was a figure of fundamental importance to Western thought. The very word "philosophy" was coined by him; his primitive precursors were known as 'sophoi'; the wise, but Pythagoras called himself 'philosophos'; a lover of wisdom. Nonetheless, it may not be quite accurate to characterize Pythagoras as simply a thinker or a philosopher; while he propounded a scientific view of the cosmos he was also a mystic who advocated a way of life. If pundit and guru were words not so much sullied by specious usage in recent years, we might aptly apply them to him. The Pythagorean system was not only the first attempt to answer the great questions-What is the universe? From what was it created? What is man? What is the nature of human knowledge?-it also created an overarching view of the cosmos, and showed man his place in this great scheme. Perhaps of even greater importance in establishing philosophy as a thriving enterprise in the emerging civilization, Pythagoras told his adherents how to live. The language used by his tightly knit band of followers was often ambiguous and even baffling, but it covered every aspect of life. [...]

The Pythagorean philosophy, like Zoroastrianism, Taoism, and every early system of higher thought, is based upon the concept of dualism. Pythagoras constructed a table of opposites from which he was able to derive every concept needed for a philosophy of the phenomenal world. As reconstructed by Aristotle in his Metaphysics, the table contains ten dualities (ten being a particularly important number in the Pythagorean system, as we shall see):

Limited - Unlimited
Odd - Even
One - Many
Right - Left
Male - Female
Rest - Motion
Straight - Curved
Light - Dark
Good - Bad
Square - Oblong

Of these dualities, the first is the most important; all the others may be seen as different aspects of this fundamental dichotomy. To establish a rational and consistent relationship between the limited (man, finite time, and so forth) and the unlimited (the cosmos, eternity, etc.) is not only the aim of Pythagoras's system but the central aim of all Western philosophy.