The Music of Pythagoras (34 page)

The Brethren of Purity viewed all knowledge as a continuum of revelation taking place in all times and places and among all races and religions. Pythagoras, Plato, Abraham, Jesus, Mohammed, and the imams who succeeded Mohammed were all part of it. The Brethren put together a cosmology of their own having many interlinked levels of being, with “One God” whose holiness lived in all things. The highest destiny of a human was to rejoin his or her inner holiness to this One God. The
Rasa’il
wove together many aspects of the world—music, numbers, medicine, theology, astronomy, and other areas. The interlinking was based in a precise manner on numbers and music and conjured up a “unity,” not as the Pythagoreans had done it but very much in the Pythagorean spirit and with them in mind. Referring to ancient “musician-philosophers” who had drawn a connection between the four elements—fire, air, water, and earth—the Brethren linked these
with human health, the arrangement of the cosmos, and the four strings of an instrument called the
oud
:

This we have expounded in the treatise on arithmetic. In effect, the first string is comparable to the element of fire, and its sonority corresponds to the heat and its intensity. The second string is comparable to the element of air and its sonority corresponds to the softness of air and its gentleness. The third string is comparable to the element of water and its freshness. The fourth string is comparable to the element of earth and its sonority corresponds to the heaviness of earth and its density.
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The link with the human body and physical and mental health, echoing Hunayn, had the sounds of the different strings producing different effects in those who heard them: “The sonority of the first string reinforces the humor of yellow bile, augments its vigor and its effect; it possesses a nature opposed to that of the humor of phlegm,” and so forth.
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Unlike Hunayn, however, the Brethren included specific mathematics. In their arrangement of the cosmos, each of the four elements, plus something called frigidity, predominated in one of a set of nested spheres with the Earth in the center. The size of each sphere, in relation to the next, was in the ratio of 4:3. Beyond the orbit of the Moon there was a “harmonious proportion that exists between the diameters of the spheres in which the planets move and those of earth and air.”
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The Ikhwan al-Safa’ or Brethren of Purity arrangement of the cosmos beneath the orbit of the Moon. This drawing shows the spheres, but not the exact proportions.

The Brethren made connections among the cube, the notes of the strings on the
oud
, and the relationships between the notes: The ancients, they said—continuing their reinterpretation of Pythagorean thinking and working Euclid into it as well—had a preference for the octave, because 8 was the first cube number (2 × 2 × 2). A cube has six sides and 6 is a perfect number.
*
All of a cube’s sides are equal and all of its angles are equal, and

we have said that the more the created thing possesses the property of equality, the greater its eminence. It is for this reason that it was said in Euclid’s last treatise that the form of the earth is probably cubic and that of the celestial sphere probably a dodecahedron defined by twelve pentagons.
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The preference for “equality” calls to mind Archytas.

Also in the tenth century, when the Brethren of Purity were compiling their encyclopedia, a Shiite
katib
(secretary) in Syria wrote a treatise in the same tradition. What seemed most significant to Al-Hasan al-Katib was the Pythagorean insight that numbers and the relationships between them were the key to human understanding of the universe. He reformulated this doctrine and applied it both to the human body and soul and to the cosmos: Three was the number of the simple consonances in music (fourth, fifth, octave) and also the number of the divisions of the soul (rational, sensible or sensitive, and natural or vegetative). Seven was the number of notes in the scale short of the octave and seven was also the number of elements of the rational soul: comprehension, intelligence, memory, deliberation, estimation, syllogism, knowledge. Different modes in music were equivalent to different virtues of the soul: justice—the mode of the index finger on the second string; good understanding—the mode of the open third string; purity—the middle finger on the third string; and so forth. In Al-Hasan’s scheme, the movements and positions of the celestial spheres also had their equivalents in music, and the origin of the zodiac could
be explained in similar terms. He wrote that he was indebted to Nicomachus of Gerasa for these ideas.

The sphere of the Zodiac is divided into twelve parts which represent the houses of the Zodiac. We believe that this division was established [or defined] thus because the number 12 is divisible into halves, thirds, and quarters. These are the elements which are found in the division of the complete system, because the last note of the octave is half the first (2:1), the note of the fifth is in the ratio of one and a half to it (3:2), the note of the fourth is in the ratio of one and a third to it (4:3).
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I
N THE PARTS
of Europe not under Islamic rule, populations in different areas spoke a great variety of vernacular languages and dialects, but Latin was the lingua franca that united scholars, who were almost without exception the only people who could read. As Boethius had feared, Greek had disappeared almost entirely. Little remained in Europe to be read in Greek anyway, since Greek manuscripts that at first had been preserved by Christians were now nearly all far away in Islamic lands.

However, Latin Europe did not languish in total intellectual darkness. Even in the ninth and tenth centuries, when Viking, Magyar, and Saracen invasions repeatedly wreaked havoc, scholars were carrying forward Pythagorean/Platonic ideas about numbers and music. Taking them in a different direction from their Islamic contemporaries, they explored the links between music and astronomy and inventively manipulated the numbers and mathematics of music and the cosmos.

Aurelian of Réôme (now Moutiers-Saint-Jean) was a contemporary of Hunayn; most of his writing dates from the decade 840 to 850.
¹⁰
The earliest medieval music treatise that has survived was his
Musica disciplina
, based in part on Boethius. Aurelian did know Greek and some astronomy and was knowledgeable about the movements of the planets and their periods.
*
He observed that the eight musical modes seemed to copy eight kinds of celestial motion. He wrote of instances when angelic music was audible on Earth, and about the Muses and the zodiac, though he had to be inventive to link eight musical modes with nine Muses. Aurelian followed the Pythagorean lead in more ways than his
interest in the harmony of the spheres: He knew of the quadrivium that Plato learned from Archytas, and he was convinced that the truth of the universe lay in numbers.

The motions of the stars are eight, seven of the planets and one of that which is called the Zodiac [the sphere of fixed stars], which all say make the sweetest harmony of song; that is, consonance. Even the Lord, in the reply that he made out of the whirlwind to Holy Job, called this the harmony of heaven.[
*
]

There are other things that writers about this art have discovered. They say that the whole theory of the art of music consists of numbers.

The natural discipline is given over to four sciences, namely, arithmetic, geometry, music, and astronomy. In these, numbers, the measurements of the earth, sounds, and the positions of the stars are examined; but their essence and their whole origin is in mathematics.
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John Scotus Eriugena also lived in the ninth century, at about the same time as Hunayn and Aurelian.
¹²
Nothing is known about his early life, though his name must indicate he was from Ireland (“Eriugena” can be translated as “Erin born”), which escaped the barbarian invasions overrunning most of Europe until the Danes arrived later in the century. Eriugena may have started out as a scholar connected with one of the great Irish monasteries, but when he was in his thirties, Charles the Bald invited him to France to be head of his court school. He is also thought to have traveled to Greece and Italy, studied Greek, Arabic, and Chaldean, later moved to Oxford at the invitation of Alfred the Great of England, and finally taught at the Abbey of Malmesbury. Eriugena was the scholar who translated the works of “pseudo-Dionysius” into Latin.

The idiosyncratic cosmological scheme that Eriugena developed made him one of the most remarkable scholars of his era—in fact, of all who predated Latin Europe’s tenth–twelfth century rediscovery of the classical literature. In his cosmos, the stars, Moon, Sun, and Saturn orbited the Earth, but Mercury, Venus, Mars, and Jupiter orbited the
Sun. This arrangement was not at all harebrained; in fact, it was an insightful step in the direction of Copernican astronomy. However, it presented a challenge to the harmony of the spheres. In Eriugena’s cosmos, the four planets with Sun-centered orbits were of course continually changing their distances from Earth. A change of distance meant a change in the musical pitch of a planet, and so a theory of cosmic harmony had to allow for varying pitch. That was an idea that no one but Eriugena would explore until Giorgio Anselmi in the early fifteenth century and Johannes Kepler in the late sixteenth and early seventeenth—Kepler, at last, with a correct understanding of the solar system and much more fruitful results.

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.”
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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.
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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.
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