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The Music of the Heavens
Kepler's Harmonic Astronomy
By Bruce Stephenson
PRINCETON UNIVERSITY PRESSCopyright © 1994 Princeton University Press
All rights reserved.
For as long as people have contemplated the heavens, they have perceived music in the stately cycles of the motions overhead. Attempts to link the organized knowledge of astronomy and of music go back at least as far as Plato—as far as Pythagoras, if we heed the indistinct but nearly unanimous voice of tradition. Certainly Plato's account of the creation of the world was drenched in the language and symbolism of musical harmony. Music theorists of the Hellenistic world and encyclopedists of the Roman world expounded the subject, and through their writings it passed into the common knowledge of the learned in the middle ages. This tradition went well beyond a vague claim that the heavens seemed "harmonious" (in the sense of fitting together well) to make associations that were explicitly musical, and indeed rather technical, according to the best musical theories of the time. Often described poetically, the music of the heavenly spheres was also loosely integrated into the scientific view of the world as late as the seventeenth century. It was silenced, probably, by the increased precision with which astronomers measured the heavens, and probably also by the dissolution of the belief that Creation was specially arranged for the benefit and edification of humanity.
The last serious attempt, and perhaps the most earnest, to find musical harmony in the motions of the heavens was that of Johannes Kepler. Better known today for the laws of planetary motion he discovered, Kepler was a polymath who worked near the boundaries of contemporary knowledge in astronomy, mathematics, optics, physics, astrology, music theory, meteorology, and historical chronology. In most of these fields he searched more or less explicitly for the harmony that he was sure could be found in the world.
Harmony was for Kepler an ideal that was expressed in many ways, all based ultimately on the eternal relationships of geometry. The most important expressions of harmony were literally the biggest: the harmonies in the large-scale structure of the world and in the motions of its parts. His study of these celestial harmonies was closely related to his profound and original work as an astronomer. He believed that the heavens had been created, and the planets set into motion, as an embodiment of rational and harmonic principles. Kepler believed from an early age, before he acquired competence as an astronomer, that harmonic principles could be found in the heavens. His first book, the Mysterium cosmographicum of 1596, displayed to the world his discovery that the five "Platonic" solids were the key to the number and spacing of the planetary spheres. This insight into the world was geometric, and not specifically musical. While pursuing it as an assistant to Tycho Brahe, Kepler developed rather quickly into an astronomer of the first rank. Meanwhile, he did not neglect musical forms of celestial harmony. In 1599, he sent one of his correspondents a set of proportions that were harmonic and also, he thought, in remarkably close agreement with the best available sizes for the planetary orbits.
Over the next few years Kepler evidently drafted a substantial work on the harmony of the world, which he did not publish at that time. Finally in 1618, as the initial convulsions of the Thirty Years' War threw central Europe into turmoil around him, he discovered the relation between the sizes and periods of planetary orbits, a relation known today as his third, or harmonic, law of planetary motion. Working almost in a trance, as Max Caspar has suggested, he incorporated it into his harmonic theories, extending their scope greatly. The following year he published the work that he probably considered his greatest contribution to human knowledge.
Harmonices mundi libri v
The Five Books of the Harmony of the World, which he published in 1619, treated harmony in its mathematical, musical, astrological, and astronomical aspects, culminating in an analysis of the harmonies in the motions of the planets. Treating all these diverse fields of knowledge under the single concept of "harmony" was not only permissible but necessary, in Kepler's opinion, for all these forms of harmony had the same mathematical basis. That basis was to be found in geometrical relations between physical quantities rather than in the purely numerical relations between integers on which Pythagorean harmonic theory was based. For a relation to be harmonic, Kepler thought, its beauty had to be perceived by a soul, which might be human or otherwise. The planetary system, as revealed by Copernicus, expressed a harmony that was designed to be perceived at its center, by a soul in the Sun. Astronomy thus became the most precise and objective field for harmonic discovery. Many things on Earth were far removed from the hand of the Creator, but God alone had created the heavens: harmonies found there were inarguably divine.
In the prooemium, or preface, to book 5 of the Harmonice mundi, Kepler recalled his early conviction that the construction of the heavens was best understood from both geometric and harmonic principles. Before he had ever seen Ptolemy's Harmonics, he had convinced himself that the heavens had been built from a harmonic plan. Upon finally reading that book, in 1607, he had found, "beyond expectation and with astonishment, that almost all of [Ptolemy's] third book was devoted to this same contemplation of the Harmony of the heavens, fifteen hundred years ago." Ptolemy's detailed account of these harmonies, based as it was on geocentric astronomy, and not much of that, was essentially useless to Kepler. This could hardly have been otherwise, he recognized. Ptolemy, ignorant of the heliocentric arrangement of the heavens, and equally ignorant of the theories of polyphonic harmony developed by Gioseffo Zarlino, Vincenzo Galilei, and others in the sixteenth century, could not possibly have understood the intricate cosmic harmonies. Kepler believed, in fact, that he was probably the first person in a position to grasp, in all its detail, the harmonic structure whose presence Ptolemy had faintly perceived in the heavens. His own work on astronomical harmony thus brought to fruition what Ptolemy had been unable to accomplish. The belief that he shared his inspiration with so great a scientist strengthened Kepler's determination to do correctly what the Alexandrine astronomer had been unable to complete.
The first two books of the Harmonice mundi dealt with the geometrical symmetries that gave rise, in Kepler's opinion, to all manifestations of harmony. J. V. Field has analyzed these difficult books admirably, highlighting the parts of this material that were mathematically original and pointing out the relevance of all the seemingly pure mathematics to Kepler's real concern, which was to use harmonic principles as an aid in understanding the natural world. The material, in fact, was not really pure mathematics but rather, in Field's words, "applicable mathematics." It was all intended as an aid in comprehending the harmonies found in nature.
Book 3 of the Harmonice mundi dealt with specifically musical harmony, a subject about which Kepler knew a good deal more than is commonly realized. Kepler ranked the recent development of polyphonic theories of harmony alongside his own astronomical discoveries as a reason why it had not been possible in antiquity to give a true account of the harmonies in the sky. Although music theory is not a primary concern of ours, we will necessarily examine Kepler's concepts of consonantia and concinna intervals; of durus and mollis, concepts similar to but not quite the same as our major and minor; of genus and modus and tonus and all the attributes of "modern" sixteenth-century polyphony. Kepler found that all these things were included in the design of the heavens, and we cannot begin to appreciate that design as he did without learning to recognize them.
In his book 4, Kepler turned to astrology. He rejected a good part of traditional astrology but firmly believed in its fundamental principles. These he derived from the same harmonic considerations that underlay music and astronomy. Elsewhere, particularly in his professional capacity as court mathematician, Kepler wrote astrological prognostics in profusion. He collated ephemerides (daily tables of the calculated positions of heavenly bodies) with his own meteorological records and strove mightily to associate the vagaries of central European weather with the contemporaneous aspects of the heavenly bodies. He wrote several booklets, both in German and in Latin, to explain how planetary aspects affected the weather, the character of people born while the planets were in aspect, and the course of human affairs generally. Within this astrological oeuvre, book 4 of the Harmonice mundi occupies the position of a treatise on theoretical foundations. Kepler believed that astrological influence occurred when harmonic aspects among the heavenly bodies were perceived by souls, human or otherwise, on Earth. Meteorology was an important special case: the soul of the Earth itself was excited by aspects that it somehow was able to perceive, and in its excitement it exhaled vapors from its interior, which gave rise to winds, rain, and all kinds of storms.
The last of the five books making up the Harmonice mundi dealt with the astronomical harmonies of the world. It described in great detail the harmonic considerations involved in the large-scale structure of the world. These began, as a first approximation, with the nesting of "Platonic" regular polyhedra among the planetary spheres, to determine both the number and the sizes of those spheres. This theory had no musical content, but to Kepler it was nonetheless a harmonic theory. The regular polyhedra embodied the geometrical principles of abstract harmony, and he had discussed them already in book 2 as applications of those principles. Their appearance in the heavens illustrated the pervasiveness of harmonic proportions in the created world.
In the Mysterium cosmographicum Kepler had not really been able to resolve the discrepancies between the proportions implied by the polyhedral theory, on the one hand, and the relative distances of the planets according to astronomy, on the other. He had hoped that a proper reconstruction of heliocentric astronomy would clear up these problems. Since then, he had carried out the reconstruction himself; it had turned out to be much more thorough than he could have imagined beforehand. Yet it did not yield the distances he wanted, the distances implied by nesting the polyhedra among the planetary spheres. Accordingly, he summarized near the beginning of book 5 the state of the art in planetary astronomy—namely, his own theories—and then set out to show that the apparent motions of the planets, as perceived from the Sun, embodied all the proportions, all the variety, all the harmonic devices used to convey emotional nuance in contemporary polyphonic music. The mortal musicians who had invented all these things on Earth had been mere "apes of their Creator"; for the harmonic proportions involved existed eternally and had been embedded in the fabric of Creation.
Showing this much accomplished the goal Kepler had set for himself in his youth. The period-distance relation that he discovered while completing his Harmonice mundi enabled him to go much farther. In 1618 Kepler discovered this third or "harmonic" law, too late to weave it deeply into his tapestry. He stated it proudly enough in chapter 3 of book 5 but with only a few early and clumsy corollaries. He had not then decided (perhaps he never did decide) whether it was only an approximation, applying to orbits that were very nearly circular, or a fundamental result applying to all orbits whatever. In a few months of what must have been very intense labor, during the summer and fall of 1618, he managed to combine the new discovery with some of his other results, using it effectively at the end of book 5 to calculate the relative distances of the planets from the sun and showing thence that even the eccentricities of the individual planetary orbits were harmonically constrained to be what they were. The harmonic law bound together the different orbits and brought the book to a satisfying close. The whole planetary system was shown to be as beautifully constructed as it could possibly be. Kepler justified the few remaining dissonances not on aesthetic grounds—he was not so modern as that—but by showing that they were logically entailed by the other and more fundamental harmonies in the world.
Historians evaluating Kepler's harmonies have often overemphasized relatively trivial portions, such as the individual songs of the planets in chapter 6 of book 5, which make a nice illustration (see figure 9.9 in chapter 9). Important parts of the theory—the latitudo tensionis, or range of tuning in the universal harmonies, which permitted the harmonic configurations to occur far more frequently, and the highly desirable presence of extreme motions in those chords, which extended the duration of those harmonies—have been neglected. Above all, the roles played by Venus and the Earth, the "planets that change the type of harmony," have not been appreciated. The overall design made no sense if these roles were overlooked, for some of the actual proportions observed were excruciatingly unpleasant. Kepler explained such intervals by showing how they arose from the need to express harmonies of all possible types in the heavens.
Ironically, Kepler's revival of the ancient theory of celestial harmony came at just the time when a more exact knowledge of planetary distances and motions—which he himself had brought about—was making it nearly impossible to sustain the old theory. The Harmonice mundi was the final flowering of that theory, a fantastically detailed attempt to stretch the original idea to accommodate the New Astronomy that Kepler himself had created.
Kepler and Mysticism
In the three and a half centuries since Kepler published his Harmonice mundi, it has acquired a certain notoriety as the expression of an unscientific or mystical side of his personality. To be sure, Kepler's harmonic theories were fanciful, even for their time. In part this was simply due to his boldness as a thinker; he was not afraid to draw far-reaching conclusions where others, even if they agreed in principle, might lack the intellectual courage to follow him. A more important reason, I think, is that his theories were inspired by a theistic view of the world. This viewpoint could still be taken for granted in seventeenth-century Europe; it can no longer be taken for granted today. For most scientifically literate people in the twentieth century a blind mechanism—or something even stranger, such as probabilistic quantum mechanics—has replaced Kepler's Creator as the organizing principle of the world. Kepler's theories about the intimate details of Creation seem unscientific and irrational because they presuppose a created world in which humanity occupies a uniquely important place. This is, I think, the most important reason why his harmonic theories are condemned or praised (according to the taste of the critic) as "mystical."
Such descriptions are anachronistic and an abuse of language. Beliefs that are "mystical" are either held in opposition to reason or at least not subject to rational criticism. It may be possible to claim that any belief in a Creator, in the twentieth century, is inherently mystical; it is not possible for the seventeenth century. If Kepler was mystical because he believed that God had created the world and had created mankind in his image, then all of Europe espoused mysticism in the seventeenth century—and there is no point in using the word.
If the word mystical is to have any use in historical writing, it must be applied to ideas that are less rational, more transcendent, than the commonplace ideas of their time. The Harmonice mundi presented no ideas opposed to reason, nor any that claimed to transcend reason. The harmonies that Kepler discerned in the heavens were entirely rational. They had been created by divine reason; they were intended, Kepler assumed, for the enjoyment of a rational soul; and they were accessible to a sufficiently diligent exercise of human reason. Their foundations, after all, were in geometry, not in some vision vouchsafed to Kepler in a dream. The strangeness of the Harmonice mundi today arises not from any lack of rationality in the discussion but from the diligence with which Kepler applied his reason to ideas that are not today deemed worthy of rational discussion. Its strangeness in Kepler's time arose from the dogged persistence with which he tried to reason about matters that his contemporaries thought to be beyond the reach of reason.
Excerpted from The Music of the Heavens by Bruce Stephenson. Copyright © 1994 Princeton University Press. Excerpted by permission of PRINCETON UNIVERSITY PRESS.
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Table of ContentsPreface and Acknowledgments
Ch. I Introduction
Ch. II Earlier Theories of Astronomical Harmony
Ch. III Jofrancus Offusius: Scientific Astrology Based on Harmony
Ch. IV Distances to the Planets
Ch. V The Polyhedral Theory of the Mysterium cosmographicum
Ch. VI Kepler's First Harmonic Planetary Theory
Ch. VII The Reconstruction of Ptolemy's Harmonics
Ch. VIII The Harmonice mundi
Ch. IX Book 5 of the Harmonice mundi
Ch. X Conclusions