The Symphony and the Stars: How the Mysteries of the Universe and the Mysteries of the Muse Shaped our Mind and our Spirit
Part. 5
Titans of Greece—The Pythagorean Revolution
By the 6th century B.C.E. it was pretty clear the Greeks weren’t just your average civilization. In fact, a revolution was underway. Aristotle said of Thales of Miletus, one of the Seven Sages, that he was the first to look to natural forces rather than gods for causation. Aristotle praises another of the Seven Sages, Solon of Athens, in his History of the Athenian Government. Lost until after the American Revolution, his account of Solon’s unilateral establishment of a balance of power between the upper and lower classes—the philosophical if not literal precursors of the Senate and the House of Representatives—came with the request that he be allowed to leave Athens for ten years and nobody was to come looking for him. As everyone of both classes was enraged for not being granted absolute power over the other, it would seem Solon’s island vacation was a timely booking.
Great advances also came in the sciences, particularly mathematics. The Pythagoreans unlocked the vaults of geometry were opened; the animistic foundations of religion were slowly integrated and replaced with the mysteries of the mathematical relationships of the universe. The four main branches of mathematics were astronomy, geometry, music, and arithmetic, all of which were interrelated according to the Pythagoreans. Unfortunately, there are no extant texts of Pythagorus, but there are second-hand fragments from his successor, Philolaus. Enough has survived to get a taste of how the Pythagoreans adjudged the universe to be bound together by the two qualities known as Number and Harmony.
Unfortunately, with the invention of philosophy came the invention of impenetrable philosophical writing designed to make a philosopher appear intellectually superior to everyone else because nobody could figure out what the hell they are talking about—a tradition carried on by doctoral candidates in all fields to this very day. I will simplify the Pythagorean philosophy as best I can.
Philolaus’ expresses the Pythagorean belief that“...everything that can be known has a Number...”, and the universe could not exist if “harmony” weren't there to organize them. Keep in mind there is a musical and non-musical use of the term “harmony”. He says of harmony that “things which were like and related needed no harmony; but the things which were unlike and unrelated and unequally arranged are necessarily fastened together by such a harmony, through which they are destined to endure in the universe...”
The easiest example, because of its universal familiarity, of the relationship between number and the harmony required for things to exist is the Pythagorean triangle. All the elements have a number.
It is the timeless harmony between the disparate numbers that makes this an eternal quality of the universe. Change a number, and the math doesn’t work.
In that sense the proportional relationships of musical harmony were thought to be another manifestation of the eternal—hence its inclusion in the mathematical arts. The most important of the ratios were those of dividing a string into 2:1 to create an octave, 3:2 for the perfect 5th, and 4:3 for the perfect 4th. Philolaus expounds:
“The content of the Harmony (Octave) is the major fourth and the major fifth; the fifth is greater than the fourth by a whole tone; for from the highest string (lowest note) to the middle is a fourth, and from the middle to the lowest string (highest note) is a fifth. From the lowest to the third string is a fourth, from the third to the highest string is a fifth. Between the middle and third strings is a tone. The major fourth has the ratio 3:4, the fifth 2:3, and the octave 1:2. Thus the Harmony (Octave) consists of five whole tones and two semitones, the fifth consists of three tones and a semitone, and the fourth consists of two tones and a semitone.”
What he has described is a kind of modern scale, although in the most obtuse terms. From the perfect fifth, created by dividing a string into the ratio of 2:3, or as we reckon it today, 3:2 (the same is true of 4:3 etc.). By dividing a string by 3:2, you get a pitch a fifth higher. Divide that string 3:2 and you go up another five notes.
Starting on A, go up a fifth to E and then another to B. Drop it down an octave and you've got your major second. This is where the thought process of the Pythagoreans becomes excited. In fact, it turns out that this ratio is a 9:8—a very lovely and rational result.
The discovery of these fundamental ratios were everything to the Pythagoreans, and the co-evolution of all four mathematical arts led them to create the first true proportional model of the universe. Well, “true” in the sense that it reflects some aspect of what we understand as true today. The sphere was the most perfect of the solids, and therefore the shape of the universe. They believed there was a central fire around which the Earth and sun revolved in perfect circles, although the fire is obviously not the sun. According to Aristotle, the Pythagoreans proposed the “music of the spheres”:
“Some think it necessary that noise should arise when so great bodies are in motion, since sound does arise from bodies among us which are not so large and do not move so swiftly; and from the sun and moon and from the stars in so great number, and of so great size, moving so swiftly, there must necessarily arise a sound inconceivably great. Assuming these things and that the swiftness has the principle of harmony by reason of the intervals, they say that the sound of the stars moving on in a circle becomes musical.”
Hippolytus later expounds:
“And he in his studies of nature mingled astronomy and geometry and music <and arithmetic>. And thus he asserted that god is a monad, and examining the nature of number with especial care, he said that the universe produces melody and is put together with harmony, and he first proved the motion of the seven stars to be rhythm and melody.”
This search for the universal perfection in both music and the cosmos continues to this day. However, as these mystical intellectual idealisms were discovered in Classical Greece, there came with them the great conflict of man and his world: the universe doesn’t care if the numbers work out to our satisfaction.
Even in the time of the Pythagoreans it was known that there were problems in both music and cosmology that were not reconcilable with their dogma; ratios of musical notes differed depending on how they were calculated, and Pythagorean harmony—sadly—didn’t sound very good. In fact, it was awkwardly dissonant. If the moving heavenly bodies were making perfect music, it couldn’t possibly sound like that. A mathematical band-aid applied to improve the situation, a questionable practice at best, simply exposed another injury. Perhaps worst of all, the number ten—the god-like Decon—didn’t seem to have much to do with music.
Concerning the cosmos, the circumference of the circle upon which their model was based was slightly too high for their magic number three. Worse, it wasn't a rational number at all. Although the Decon was the supposedly the ultimate expression of perfection in all systems, a Pythagorean with a spare evening could plainly count the Earth, Sun, Moon, Sky, and five planets as being the nine obvious heavenly bodies. This created the first known example of flat-out religious bullshit: "We can't be wrong because we don't want to be. Therefore, we can make up anything we want to fix it."
A counterearth was proposed, rather, plucked out of the thin air of wishful thinking, to round out the Decon. Conveniently, it orbited in exact opposition to the Earth, and therefore remained eternally unobservable.
As mathematics was advanced to explain universal phenomena, so too would this same math allow advances in musical harmony and vice-versa. It is a tremendously characterizing coincidence of the problem that Pythagorus and Galileo were born exactly 2000 years apart. Almost. As satisfying as a nice round number would have been, the birth of the perfect world and the birth of the brave new world were six years short of universal perfection.