Eriugena worked out the problem of the varying pitches of the heavenly bodies in his own way in an elaborate system involving numbers, ratios, and musical intervals, drawing examples from organ pipes and stringed instruments: “Here one must admire the wonderful virtue of Nature; for what anyone can accomplish on a four-stringed lyre is achieved in the eight celestial sounds. But the method by which it is done must be sought out with diligent investigation.”13
He explained some of the results of this investigation in language that he tried to make reader-friendly:
As you see, the sounds do not always relate by the same intervals, but according to the altitude of their orbits. No wonder, then, that the Sun sounds an octave with Saturn when it is running at the greatest distance from it, but when it begins to approach it, it will sound a fifth and when it gets closest, a fourth. Considered in this manner, I think it will not disturb you when we say that Mars is distant from the Sun sometimes by a tone, sometimes by a semitone.14
Eriugena also urged his readers to keep in mind that when comparing the distances of planets, one was talking about the ratios and relationships of the distances between the planets, not the absolute distances in stadia (or, in modern terms, in miles or parsecs).
He had his own take on the agreement between neo-Pythagoreanism/Platonism and Christianity: Everything in creation derived from the One, and the One was the same thing as God. From this One, who was universal, all-containing, infinite, and incomprehensible, emanated the realm of Plato’s Forms. Under the influence of the Holy Spirit, the Forms manifested themselves in created things. All creatures would eventually be drawn back to reunion with the divine level of being from which they had fallen. God was both “the source of all things and the final end of all things.”
For Eriugena, all was “fairest harmony,” including not only the heavenly spheres but “even the sounds that will arise from the punishment of evil, for punishments are good when they are just, and so are rewards when they are more in the nature of gifts than payments for what is earned.” The result of punishment and reward would be a final purification and redemption, even of animals and devils, and reunification into the divine One, with full knowledge of God, seen “face to face,” as St. Paul had written. For Eriugena, the great harmony of creation was a “combination of low, high, and intermediate sounds making a certain symphony between them through their proportions and proportionalities.”15
A younger contemporary of Aurelian and John Scotus Eriugena, Regino of Prüm, referred to the Pythagoreans in the introduction to a book he wrote about the plainsong melodies used in Trier, his native town. Claiming that he got his information from Boethius’ De musica, he offered what he believed was the Pythagorean argument for the existence of heavenly music.*
The Pythagoreans argue the presence of music in the heavenly motions thus: how, they say, could the heavenly apparatus, so rapid in its course, move in silence? Even though it does not reach our ears, it is still quite impossible that such headlong speed should lack sound, especially since the course of the stars are arranged in so convenient and well-adapted a way that nothing so enmeshed and conjoined can be imagined. Some are higher, others lower, yet all are turned with an equal impulse so that their unequal and disparate orbits fall into a determined order. From this it is argued that there is a harmonious arrangement in the heavenly motion.16
The more important issue for Regino was not whether the heavenly motions produced a sound but whether they took place in a “harmonious arrangement.” For him, “harmony” was a beautiful scheme of numbers and number relationships pervading the universe, underlying both music and the arrangement and movements of the planets and stars.
Regino was a musician, not an astronomer, but before moving on from the introduction of his book to its main subject matter—plainsong—he wrote a paragraph that sounded like Archytas’ idea about the connection between pitch and fast and slow motion and the beating of the air, described the connections between the planets and strings or cords on a lyre, and paid tribute to Cicero’s “Dream of Scipio.” To cover all bases, Regino closed his introduction with the words “We would just add that not only the heathen philosophers but also vigorous commenders of the Christian faith give their assent to this heavenly harmony.”17
IN THE ELEVENTH century, a Europe that had been relentlessly tormented for two hundred years by waves of marauding invaders experienced an era of relative peace and optimism. The pace of life quickened, and populations and trade increased, including trade with regions under Islamic rule.
Teaching and study in Europe during the centuries of upheaval had never come to a halt, and monks had gone on preserving ancient writings and copying and illuminating manuscripts. However, in the eleventh century new centers of learning started to appear not in the monasteries but in the cathedral precincts and in the larger medieval cities.18 At first, these amounted to no more than one or a few learned men with a huddle of students gathered around them, and most of the teaching was oral. In the twelfth and thirteenth centuries, these groups became formalized, with better defined roles and obligations for students and teachers, better established relations with local populations and governments (often a touchy matter), and student lodgings resembling the colleges of Cambridge and Oxford. Universities on this model were an authentically European development.
Among the earlier gatherings of teachers and scholars, and later in the universities, a critical and discursive (“combative,” Thomas Kuhn called it) tradition emerged that became known as scholasticism. Many giants of medieval thought who engaged in these combats are still familiar names today—Thomas Aquinas, Peter Abelard, Anselm of Canterbury, to name only a few. A primary goal of scholasticism was to integrate classical Greek ideas and learning with Christian belief. With the reintroduction to Latin Europe of the works of Aristotle, translated into Latin in the twelfth century but not immediately available to all scholars, this became a much greater and more complicated undertaking. Scripture was given a more metaphorical, less literal reading, and Aristotle came to be considered, after Scripture, the supreme authority. Scholars revered him not just as a philosopher, but as “the Philosopher,” no other identification required.
The groundwork for the rediscovery of classical literature had been laid in the tenth century, when Christian knights gradually began to take over what is now Spain and Portugal from the Muslims who had ruled there for more than three hundred years. The culture of the Iberian peninsula was one of the highest on Earth, the best of both Jewish and Muslim. Because the population of Christian Europe—from which the conquering knights came—was, on the whole, much rougher and less civilized and literate, the situation somewhat resembled the Roman conquest of the Greeks many centuries before. This newer “conquest” was glacially slow, allowing time for a remarkable intermingling of the three different faiths and cultures. Eventually, in 1492, the Christians would drive the Muslims out of Spain, but for centuries before that the Christians who came there found themselves in the presence of, and mingling with, a long-established, intellectually confident, highly cultivated Muslim and Jewish society.
Clergy who accompanied or followed the knights were awed by the beauty of the cities, the architecture and gardens, the peace in which minority communities coexisted, and the level of learned discussion and scholarship—but most of all by the libraries of Cordoba, Toledo, Segovia, and Lisbon. As long as any cleric in Latin Europe could remember, there had been rumors that priceless manuscripts and books, containing the lost knowledge of the ancients, still existed somewhere in the Muslim countries. The old rumors turned out to be true to a degree beyond their dreams. Here in Spain was the fabled material—much of it translated into Arabic—that had been in the repositories of Christian scholars before the Muslims had taken over most of the former Roman Empire in the seventh century. Since then, Muslim and Jewish translators and scholars had treasured and preserved these works.
By 1100, Christians controlled Toledo and Lisbon. Archbishop R
aymund of Toledo invited the cream of the scholarly world to join in an effort to translate a vast collection of ancient writings into Latin. The first translators were representatives of the three faiths, Christian, Jewish, and Muslim, who were already living in Spain, but soon scholars joined them from all over—Christian clergy from Latin Europe and England, Jews and Muslims, Latin, Greek, and Slavic scholars—to work with no censorship, no banning of any book, no rewording to give a Christian spin to pagan words. Some of the translators were not just bilingual but multilingual. Michael Scot, from England, knew some Arabic and was fluent in Latin, Greek, Hebrew, Syriac, Chaldean, and several other languages. When not enough men could be found who had mastered both Arabic and Latin, two translators with a common language worked together. The effort continued for years. One particularly prolific translator, Gerard of Cremona, translated seventy or eighty books in all, including Ptolemy’s Almagest and Euclid’s Elements.19
Similar work was going on in Palermo, Sicily, under the patronage of the Norman King Roger. Known for an opulent court befitting an Eastern potentate, Roger considered it essential to surround himself with intellectuals, and he was patron to a number of them—Roman Catholic, Byzantine Christian, Jewish and Muslim alike. The translation in Palermo was more often directly from ancient Greek manuscripts into Latin, rather than via Arabic translations, for Sicily in the time of Pythagoras had been a Greek colony and had retained the Greek language through the Roman and Byzantine eras. Roger’s retinue included a number of Greek-speaking scholars. Plato’s Meno and Phaedo were, fittingly, first translated into Latin there on the island where one of the earliest Pythagorean communities had existed and where Plato himself had dabbled in court politics and almost lost his life.
With no printing presses yet in existence, copyists devoted long hours to reproducing the translations. The dissemination of the new books was slow, but for the first time in many centuries, scholars in Latin Europe were reading the ancient Greeks, and in the universities Aristotle joined Plato.
The basic medieval curriculum had begun as none other than the Pythagorean quadrivium of Archytas, and students also had to master dialectic, as Plato had required. But when Aristotle’s works began to influence university education, they became the foundation of philosophical and theological studies in a “trivium” that followed after the quadrivium. The seven subjects of the combined quadrivium and trivium—arithmetic, geometry, music, astronomy, grammar, rhetoric, and dialectic—became known as the Seven Liberal Arts.20
The standard arithmetic text was the old, familiar Introduction to Arithmetic by Nicomachus, the second-century neo-Pythagorean who had clung doggedly to “Pythagorean mathematics” and identified himself as a Pythagorean. Boethius’ slightly reworked Latin version of his book had been in the libraries of Latin Europe for centuries. Now, thanks to the translation projects in Spain and Palermo, scholars and students were able to circumvent Boethius’ rewrite and read Nicomachus in direct translation from the original. Whichever version they read—Boethius’ De institutione arithmetic from the early sixth century, or Nicomachus’ original Introduction to Arithmetic from the second—they encountered Pythagoras before they encountered any arithmetic, for the opening passages lauded him. Medieval students thus learned their arithmetic in the neo-Pythagorean form, which they took to be the form; and almost entirely through this one book, the Pythagorean faith in the power of numbers to unlock the secrets of nature and the universe was conveyed to the Middle Ages and beyond. It was a tremendously significant channeling of thought. The image of Pythagoras as the creator of Greek mathematics became entrenched.
In the twelfth century, in many universities, the geometry section of the quadrivium was taught from a much better book, Euclid’s Elements. Though translated into Latin earlier, it had never caught on or become widely available. Now there were fresh translations from the Arabic by Gerard of Cremona and Abelard of Bath, another of Archbishop Raymund’s translators. Early in the century, Abelard had journeyed the whole length of the Mediterranean collecting ancient texts.
In the third section of the quadrivium, music, Boethius’ De institutione musica was the text. Through Boethius’ music books, again probably taken originally from Nicomachus, the “Scale of Timaeus” had already become a significant part of medieval music theory. There is good evidence that this scale did not, in fact, originate with Plato but was used by Philolaus and perhaps earlier, so medieval scholars were dealing with something of impressively ancient origin.21 They accepted Boethius’ divisions of music into musica mundana (harmony of the spheres), humana (relationship of music to the human soul), and instrumentalis (what we normally think of as music), and most agreed that all three were essential parts of their subject.
In spite of a few doubters such as the Florentine Coluccio Salutati, who insisted that the motions of the heavenly bodies could not possibly produce sound, the idea of musica mundana was still favored in the fifteenth and sixteenth centuries in Italy, when Franchino Gaffurio, the most important music theorist of his time, made every attempt to be a true Pythagorean. He refused to consider any but the intervals approved by Boethius as consonant intervals, which made him something of a throwback. Boethius had not regarded major thirds and sixths as consonant, and musicians among Gaffurio’s contemporaries certainly did. Tradition had it that only Pythagoras himself could hear the music of the spheres, but Gaffurio amended that slightly to insist that only men of significantly great virtue could hear it.
As for the fourth part of the quadrivium, astronomy, the stationary-Earth-centered systems of Aristotle and Ptolemy prevailed unchallenged and unquestioned until one tentatively raised hand in the fourteenth century. It belonged to a Parisian, Nicole d’Oresme, who went only so far as to argue that Aristotle had fallen short of proving Earth does not move. Otherwise, no one anywhere in the Middle Ages and until the fifteenth century took seriously the Pythagorean suggestion mentioned by Philolaus that the Earth does not stand still, or even that it rotates. When a more aggressive challenge eventually came, in the fifteenth century, it would be from a man with a decidedly Pythagorean cast of mind: Nicholas of Cusa.
THE INFLUENCE OF Pythagoras and the Pythagoreans was not confined to the universities during the Middle Ages.22 Freemasons included Pythagoras among their ars geometriae. Gerbert of Aurillac, who became Pope Sylvester II, in the tenth century referred to Pythagoras in his geometry. Gobar numerals—direct ancestors of modern Arabic numerals—were widely believed to have been the invention of Pythagoras.* A work supposedly (though not really) by Boethius included a method called mensa Pythagorea for calculating with these numbers on an abacus.23* In truth they were originally Hindu and were transmitted to the West through Islamic countries and Spain, with Arabic numerals first appearing in a Latin manuscript in 976.24 For Nicomachus, the neo-Pythagorean numerology in his book had been even more significant than the arithmetic, and this numerology too continued to be important in the Middle Ages, for had not even St. Augustine himself taken enthusiastically to the Pythagorean-like idea of the allegorical interpretation of numbers in the Bible? Like Philo of Alexandria, Augustine had written about the six days of creation in the Genesis account and pointed out that six was a perfect number.
Whoever chose what to celebrate in the sculptures adorning the doors of the cathedral at Chartres, one of the architectural wonders of the Middle Ages, decided to include a series of statues representing the Seven Liberal Arts and selected Pythagoras to symbolize music. The sculptor made him long-haired and bearded, hands and face middle-aged at least, seated and clothed in a beautifully adorned robe as he bent intensely over his work. At the cathedral school in Chartres, in the twelfth century, the scholastic movement’s long endeavor to bring together Platonic and scriptural narratives and concepts, including giving the Genesis account of creation a more Greek (in modern terms “scientific”) interpretation, reached its zenith. John of Salisbury called Bernard of Chartres, head of the Chartres school in the first part of the century
, “the finest Platonist of his time.” The Platonism of Bernard and his fellows was based mainly on Augustine and other early Christian scholars, the writings of Boethius, Macrobius’ commentary on Cicero’s “Dream of Scipio,” and Plato’s Timaeus in a translation by Chalcidius. The Chartres scholars saw Timaeus as an explication of Genesis. Bernard had Pythagoras and Plato in mind when he praised the ancients in words usually attributed to Isaac Newton five centuries later:
We are dwarfs perched on the shoulders of giants. Although we may see more and further than they, it is not because our sight is keener or our stature greater, but because they bear us up and add their gigantic stature to our height.25*
Pythagoras depicted in a frieze of the Seven Liberal Arts on the western front of the Cathédrale Notre-Dame de Chartres
The scholars of the Chartres school were addressing an old question: What is the best guide on the journey toward God, or (if one wished to use more Pythagorean/Platonic language) toward reunion with the divine? Was it “reason” or “faith”? Is it not best that the two work together? Boethius had written, “As far as you are able, join faith to reason,” and that was the goal of the scholastics. The hope at Chartres was to stake out intellectual and spiritual ground where one could accept what God had revealed but still strive for more comprehensive knowledge of truth. Faithful to their Platonism, and also to their Christianity (St. Paul had said that humans could only see “through a glass, darkly”), these scholars accepted that full knowledge could not be had in this life. Nevertheless, they thought it essential, insofar as humanly possible, not only to believe but also to understand what one was believing. Plato’s Timaeus seemed a splendid example of this effort and this understanding, albeit from a pagan philosopher. Not surprisingly, these ideas offended some who accused the Chartres scholars of under-valuing religious revelation and mocking simple faith.26
The Music of Pythagoras Page 24
