The Music of Pythagoras (10 page)

According to the tradition, Pythagoras sired children. After introducing his paragraph concerning Pythagoras’ family with the words “It is said,” Porphyry recorded that Pythagoras’ wife was Theano, from Crete, the daughter of Pythenax. Pythagoras and Theano had a daughter named Myia “who took precedence among the maidens in Croton and, when a wife, among married women,” and also a son, Telauges, and perhaps a second son named Arignota. Iamblichus wrote that Pythagoras’ “acknowledged successor,” Aristaeus, married Pythagoras’s widow Theano after Pythagoras died, “carried on the school,” and educated Pythagoras’ children. Among those children Iamblichus mentioned none of the names that Porphyry listed, but spoke only of another son named after Pythagoras’ father, Mnesarchus, who, in turn, took over “the school” when Aristaeus became too old. Iamblichus confused matters still further by mentioning a “Theano” who was the wife of Brontinus of Croton and one of the “most illustrious Pythagorean women.” Did Brontinus die and Pythagoras marry his widow, or was it the other way around? More likely there were two Theanos, mother and daughter. Diogenes Laertius recorded variously that Theano, the wife of Brontinus, was Pythagoras’ pupil, and that Pythagoras’ wife was probably Theano, daughter of Brontinus of Croton.

Theano’s name was preserved on a list thought to have come through Aristoxenus of seventeen “most illustrious Pythagorean women” that also included Mya, the wife of the Olympic wrestler Milo. Women apparently played an active part in the Pythagorean “brotherhood.” Diogenes Laertius said Theano had written books that still existed in his lifetime. Though these, sadly, were almost certainly some of the “pseudo-Pythagorean” books that appeared in antiquity, Diogenes Laertius felt confident enough of his source to quote Theano’s outspoken advice: Asked how soon a woman becomes pure again after
intercourse, she was supposed to have said, “The moment she leaves her own husband she is pure; but she is never pure at all, after she leaves anyone else.” She advised that a woman going to her husband should “put off her modesty with her clothes”—which seems a great waste if these were indeed the words of Pythagoras’ wife and Pythagoras really did entirely abstain from the pleasures of love!

P
YTHAGOREAN LIFE IN
Croton was, it appears, a good life—with the begetting of children who would be new Pythagoreans and could be schooled in a new, wondrous approach to the world and the universe . . . with properly chosen food, whatever it included, appearing on Pythagorean tables . . . with men and women engaging in fascinating studies that also improved their chances in the next life. Within the community, moreover, word got around of some occurrences that were difficult to explain and that indicated their leader was no ordinary man.

Unlike the ancient miracles in the Hebrew Scriptures and the Christian New Testament, the “wonders” attributed to Pythagoras were not associated with any teaching or divine revelation, nor were they examples of Pythagoras’ helping or healing anyone. They were of a more random nature, chance glimpses of existence on a more divine level than that experienced by the men and women around him, a level on which the unity of all being—of all things, places, animals, and gods; of past, present, and future—could easily be seen. Aristotle told of reports that Pythagoras appeared on the same day at the same hour in Croton and in Metapontum, and that on one occasion, getting up from a seat in Olympia, he revealed his thigh, and everyone saw that it was made of gold. In Etruria (Tuscany), a poisonous snake bit him and he bit it back. The snake died; he did not. Several witnesses heard the river Casas greet him by name, and he correctly predicted that a white bear would be sighted in Caulonia. Once, after foretelling serious strife, he disappeared in Croton and appeared in Metapontum. “According to credible historians,” wrote Iamblichus, and “ancient and trustworthy writers,” wrote Porphyry, in each case without naming them, birds and beasts listened to Pythagoras and followed his advice—the same effect that Orpheus had on even the most savage animals.

Countering the miraculous reports were rumors that Pythagoras was a charlatan. Diogenes Laertius repeated a story from Hermippus, the third century
B.C
. native of Samos who had said Mnesarchus was a gem
engraver. Pythagoras disappeared for a time into a set of subterranean rooms while his mother recorded everything that took place, marking the times and dates on tablets that she sent down to him. Eventually Pythagoras emerged, looking like a cadaver, and announced that he had arrived from Hades below. When he told the assembled people in detail all that had happened to them in his absence, they were awestruck, believed he was divine, wept and lamented, and “entrusted to him their wives,” “who took upon themselves the name of ‘Pythagorean women.’” That same story was told by Herodotus (who was skeptical about it himself) of a man who had been Pythagoras’ slave when he lived on Samos, who was supposed to have used this strategy to create an aura of magical power among gullible people in Thrace. In an interesting turnabout, some scholars have suggested that the miraculous stories, as well as the rumors of charlatanism, were all inventions to discredit Pythagoras in an era when people scoffed at the “miraculous” in a way they no longer would in late antiquity.
¹²

Sixth Century
B.C.

T
HE
P
YTHAGOREAN DISCOVERY
that “all things known have number—for without this, nothing could be thought of or known”—was made in music. It is well established, as so few things are about Pythagoras, that the first natural law ever formulated mathematically was the relationship between musical pitch and the length of a vibrating harp string, and that it was formulated by the earliest Pythagoreans. Ancient scholars such as Plato’s pupil Xenocrates thought that Pythagoras himself, not his followers or associates, made the discovery.

Musicians had been tuning stringed instruments for centuries by the time of Pythagoras. Nearly everyone was aware that sometimes a lyre or harp made pleasing sounds, and sometimes it did not. Those with skill knew how to manufacture and tune an instrument so that the result would be pleasing. As with many other discoveries, everyday use and familiarity long preceded any deeper understanding.

What did “pleasing” mean? When the ancient Greeks thought of “harmony,” were they thinking of it in the way later musicians and music lovers would? Lyres, as far as anyone is able to know at this distance in time, were not strummed like a modern guitar or bowed like a violin.
Whether notes were sung together at the same time is more difficult to say, but music historians think not. It was the combinations of intervals in melodies and scales—how notes sounded when they followed one another—that was either pleasing or unpleasant. However, anyone who has played an instrument on which strings are plucked or struck knows that unless a string is stopped to silence it, it keeps sounding. Though lyre strings may not have been strummed together in a chord, more than one pitch and often several pitches were heard at the same time, the more so if there was an echo. Even when notes are played in succession and “stopped,” human ears and brains have a pitch memory that causes them to recognize harmony or dissonance. In truth, the ancient Greeks, including Pythagoras, heard harmony both ways, between pitches sounding at the same time and between pitches sounding in succession.

The instrument Pythagoras played was probably the seven-stringed lyre. He tuned it with four of the seven strings at fixed intervals. There were no options about what these intervals would be. The lowest- and highest-sounding of the fixed-interval strings were tuned to sound an octave apart. The middle string on the lyre (the fourth of the seven strings) was tuned to sound a fourth above the lowest string, and the one next higher was tuned to sound a fifth above the lowest string.
^*
The intervals of the octave, fourth, and fifth were considered concordant, or harmonious. A Greek musician could adjust the other three strings on the seven-stringed lyre (the second, third, and sixth string), depending on the type of scale desired.

Pressing a string exactly halfway between the two ends produces a tone one octave higher than the open, unpressed string plays. The ratio of those string lengths is 2 to 1, and they always produce an octave. But the octave is not something a musician creates by pressing the string. Plucking an open string without pressing it at all causes it to vibrate as a whole, sounding the “ground note,” but various parts of the string are also vibrating independently to produce “overtones.” Even without the string being pressed at the halfway point to play an octave, the octave is present in the sound coming from the open string. Pressing the string releases tones at
the octave, fifth, fourth, and so on—depending on where you press it—that were always there in the ground note but more difficult to hear.
^*

Tradition credits Pythagoras with inventing the
kanon
, an instrument with one string, and using it to experiment with sound. He would have found that the notes that sounded harmonious with the ground note were produced by dividing the string into equal parts. Dividing it into two equal parts produced a note an octave higher than the open string. Pressed so as to divide it into three equal parts, the string played a note a fifth above that octave; in four equal parts, it played a note a fourth above that. The series goes on to a major third, then a minor third, then smaller and smaller intervals, but there is no indication the Pythagoreans took the process any further than the interval of the fourth.
^†

Looking beyond the task of getting good, practical results from a musical instrument to ask more penetrating questions about what was going on, and whether it could have wider implications, required an unusual turn of mind. Though with hindsight a shift of focus from useful knowledge to recognizing deeper principles can look simple, it is not a trivial change. A lyre sounded pleasant used one way and not another way . . . but
why
? Often, in writings about the Pythagoreans, a clause added to that question has them asking whether there was any meaningful pattern? . . . any orderly structure? but they were not necessarily looking for pattern or order yet, for no precedent would have led them to expect it. Nevertheless, they were about to discover it.

When Pythagoras and his associates saw that certain ratios of string lengths always produced the octave, fifth, and fourth, it dawned on them that there was a hidden pattern behind the beauty they heard in music—a pattern that they were able to understand, but that they had not created or invented and could not change. Surely this pattern must not be an isolated instance. Similar mathematical and geometrical regularities must lie concealed behind all the everyday confusion and complexity of nature. There was order to the universe, and this order was made of numbers. This was the great Pythagorean insight, and it was different from all previous conceptions of nature and the universe. Though the Pythagoreans hardly knew what to do with the treasure they had found—and modern mathematicians and scientists are still learning—it has guided human thinking ever since. Pythagoras and his followers had also discovered that there apparently was a powerful link between human sense perceptions and the numbers that pervaded and governed everything. Nature followed a fundamental, rational, beautiful logic, and human beings were tuned in to it, not only on an intellectual level (they could discover and understand it) but also on the level of the senses (they could hear it in music).

There are other mathematical relationships hidden beneath the experience of music that neither Pythagoras nor others of his era had any way of discovering. The ratios he found represent the rate at which a
string vibrates, but there was no way he could have studied the vibrations. However, after the initial discovery using a
kanon
or a lyre, Pythagoras and/or his early associates may well have begun listening for octaves, fourths, and fifths in other sounds and attempted to discover what could, and what could not, produce the intervals. Perhaps it is the memory of some of their experiments that lies behind several puzzling early stories in which Pythagoras made the discovery of the relationship in ways that he could not possibly, in fact, have made it.

According to one tale Pythagoras was passing a blacksmith’s shop and noticed that the intervals between the pitches the hammers made as they struck were a fourth, a fifth, and an octave. That part of the story is possible, but the next part is not: The only differences between the hammers were their weights, and Pythagoras found that those weights were related in the ratios 2:1, 3:2, and 4:3, presupposing that the vibration and sound of hammers are directly proportional to their weight, which is not the case. Pythagoras then took weights equaling those of the hammers and hung them from strings of equal length. He plucked the taut strings and heard the same intervals—another supposed discovery based on false premises, for the account incorrectly assumes that the frequency of vibration of a string is proportional to the number of units of weight hanging from it. However, it is easy to imagine Pythagoras, or his followers, or both, performing such experiments and considering, with more understanding and skill than those who later ignorantly repeated the tales, what could be learned from the successes and failures. The manner in which these stories came down in history as the way Pythagoras
made
the discovery could be an example of how knowledge is sometimes preserved while the manner of its discovery, and true understanding of it, are lost. Such a loss would be explained if, as some have supposed, the more sophisticated knowledge of Pythagoras was largely forgotten with the breakup of Pythagorean communities after his death.