The “Music of the Spheres” in Greece and Beyond
By John South
Author’s Note: I wrote this essay in 2017 while taking the History of Music class at UA-Huntsville. It is not conventional “blog” material in that it is academic in tone and purpose, but I thought it was a good place to start my blog since it displays my interests in both music and astronomy, two fields I am very passionate about.
At first glance, music and astronomy hardly appear to be related fields. It is difficult to imagine, for example, music playing a role in Galileo’s discovery of Jupiter’s moons, William Herschel’s discovery of the planet Uranus, or Clyde Tombaugh’s discovery of Pluto. The reverse concept, astronomy inspiring music, is not so hard to imagine, especially given great works like Gustav Holst’s orchestral suite The Planets. Beyond considerations of how one field influenced the other, however, is the question of how they might overlap. Of course, both represent fundamental human needs, namely the desire to explore and gain knowledge, and the need to express oneself in a form more powerful than words alone. But can they, and do they, work together, and if so, how do they complement one another? As it turns out, astronomy and music were used right alongside each other as early as ancient Greece. Even up until the Renaissance, they were considered essentially two sides of the same coin. Although the views of ancient Greece eventually gave way to those of modern empirical science, that latter has shown, surprisingly, that the Greeks were not as far off as we might think. Indeed, if history has taught us anything about the relationship between astronomy and music, it has taught us that the two are inextricably linked, both from a historical and scientific perspective.
One day in the early years of the ancient Greek civilization, the great philosopher and mathematician Pythagoras stopped to listen to an intriguing set of sounds coming from a blacksmiths’ shop. The hammers the blacksmiths used produced several different tones when striking an anvil, and each tone had a unique relationship to every other tone. Investigating, Pythagoras took two hammers which sounded an octave apart when struck, and found that the hammer which sounded the lower octave was twice as heavy as the one that sounded the higher octave (Josic). He continued, taking two hammers which sounded a fifth, and found the ratios between their weights to be 3:2; for those sounding a fourth, 4:3.
Although this blacksmith shop anecdote is generally considered apocryphal, Pythagoras had allegedly hit upon something very important, something that would widely influence Greek philosophy and scientific thought. Namely, this was the belief that numbers governed the universe, and thus everything operated according to a certain set of mathematical proportions (Dicks 65). If harmonious musical intervals could be boiled down to a few simple ratios, then surely the rest of nature could as well, astronomy being no exception. Pythagorean thought maintained that stars and planets, with their large sizes and fast orbital speeds, surely made plenty of noise as they orbited. The tone each planet or star sounded depended on its distance from Earth, which the Greeks considered to be the center of the universe (Dicks 71).
Harmonic ratios on a string
The Greek geocentric solar system (cred. University of Connecticut)
Pythagoras went so far as to ascribe each celestial body a note in a musical scale, with the intervals between the notes representing the distances between them. Roman scholar Censorinus describes this scale in detail in his work De die natali. From the Earth to the Moon, there existed one whole tone; from Moon to Mercury, a half tone; from Mercury to Venus, another half tone; Venus to the Sun a tone and a half, Sun to Mars a whole tone, Mars to Jupiter a half tone, Jupiter to Saturn a half tone, and from Saturn to the stars of the zodiac, another half tone (Stephenson 23-24). Censorinus points out that in this arrangement, Earth and the Sun sound a fifth, the Sun and the zodiac sound a fourth, and the Earth and zodiac sound an octave, hearkening back to those elegant, “perfect” intervals Pythagoras supposedly discovered in a blacksmith shop.
Solar system “scale” developed by Pythagoras
This concept of the “music of the spheres” was explored further by other Greek philosophers, especially Plato. In his dialogue Timaeus, Plato takes the precise mathematical nature of the universe speculated by Pythagoras one step further, attempting to describe in detail how the universe was created. The Creator, according to Plato, formed the ingredients of the universe into a strip, and divided it up by specific intervals, coming away with 1 part, then 2 parts, then 3, 4, 8, 9, and 27 parts (“The Platonic Solids”). This harmonically-divided strip was then itself sliced into two strips, and then one strip was laid across the other like an X. The ends of the X were joined together, effectively forming two circles similar to the mathematical symbol for infinity (∞). One of these circles, the outer circle, was a pure, undivided circle, which rotated to the right. This obviously referred to the celestial equator, which, to an observer in the northern hemisphere (i.e. Plato), appears to move to the right. The other, inner circle, rotated to the left, and was further divided into seven circles according to ratios of two or three. These circles became the seven planets known to the Greeks, including the Sun and Moon (Stephenson 17-18). One planet’s distance from the preceding planet in the lineup was directly related to the division of the universe (1, 2, 3, 4, 8, 9, 27). In this arrangement, the Sun and Moon were an “octave” apart (1:2), the Sun and Venus were a “fifth” apart (2:3), Venus and Mercury were a “fourth” apart (3:4), and so on (Stephenson 20). There is, of course, disagreement among Pythagoras and Plato concerning the exact distances between planets, but nevertheless, the importance of Pythagoras’s discovery is clear.
It is obvious, then, that the Greeks considered music and astronomy to be directly related to each other, the same principles governing one also governing the other. If one understood how music worked, he understood how astronomy worked, and vice versa. This way of thinking carried over into ancient Rome, which adopted much of ancient Greece’s science, philosophy, and art. The Greco-Roman astronomer Ptolemy drew considerable influence from the Pythagorean and Platonic theories of celestial harmony in his works, especially in his treatise Harmonics. In this work, Ptolemy discusses harmony not only as it relates to music theory, but also to science and the human soul. His views on music and astronomy were not much different than those of the Pythagoreans- that simple mathematical ratios governed the universe, and those found in music could also be found in the heavens (Stephenson 33). Ptolemy, however, went further than his Hellenistic counterpart in uniting music and astronomy. He theorized that the motions of the planets themselves were musically significant. Specifically, the rising and falling of planets in the sky corresponded to rising and falling in pitch, with any given planet “sounding” its lowest note when rising, continually rising in pitch until it reaches its highest point in the sky, and then falling in pitch until it sets. Furthermore, exactly which range of pitches the celestial bodies had was dependent upon their positions relative to the sun; this was considered analogous to the notes within the tetrachords of the Greater Perfect System, the fundamental units of Greek music theory (Stephenson 36). Thus, when summarizing Ptolemy’s views, one can imagine the planets themselves as being “notes,” while the celestial equator and the ecliptic plane make up a “staff” which give meaning to the exact pitches of the notes.
As the Catholic Church grew in power and Western civilization moved in to the Medieval period, philosophers and scientists as well as musicians looked back to ancient Greece for knowledge and guidance. Boethius, a prominent Roman politician, wrote extensively on ancient Greek music, and his writings would come to define Medieval musical theory. He drew heavily on the viewpoints of Plato and Aristotle, both of whom believed that music was important in education and had the power to move the human soul, but had a difference of opinion concerning how it should be used. Plato viewed music suspiciously, opining that its power to seduce the human soul should relegate it solely to academic study. Aristotle, Plato’s student, had no such suspicions, and believed that music could be listened to for pleasure (Whitfield 13). Boethius, apparently, sought to reconcile these viewpoints. In his treatise Consolatio, Boethius describes the music of the human soul in the same rational, precise manner as Plato in Timaeus, but also ascribes to it much the same spiritual and moral qualities that Aristotle espoused (Chamberlain 83). Boethius’s most important contribution, arguably, comes from his landmark work De institutione musica, where he names three types of music which govern the universe. Musica instrumentalis is that which comes from man-made music, specifically instruments and the human voice. Musica humana governed the human body and soul, uniting it according to those elegant ratios to form a complete, harmonious being. Finally, musica mundana governed the heavens, determining the motions of celestial bodies, the course of seasonal change, and the basic elements of matter (Whitfield 14). This concept would prove to be profoundly important to Medieval thinkers, and formed the basis of much of their musical and philosophical thought.
It was not until the Renaissance that music or astronomy saw much deviation from the authority of Boethius and Ptolemy, or ancient Hellenistic philosophers and scientists. Medieval education was built upon the Platonic quadrivium, which includes the study of four subjects: arithmetic, geometry, astronomy, and music (Grout 24). The Medieval student was thus exposed almost solely to the works of accepted authors, especially those from classical Greece, rather than new advances based on practical observation. Where music is concerned, the Catholic Church held very strict views, holding that the purpose of music was to remind us of God’s perfect nature, similar to the views of Plato. While the prevailing view of the Church was that music should be viewed with caution lest it seduce the human soul, some clerics came to deeply love its beauty and power, among them St. Augustine (Grout 25-26). The Renaissance, however, saw profound changes to both music and science. Music, even in sacred settings, began to wean itself from the strictness of the Medieval Church. For centuries, the Church had insisted that the only real, harmonious intervals were those “perfect” Pythagorean ones that could be expressed in simple numbers. Renaissance musicians, clearly no longer wanting to limit themselves to the Pythagorean intervals, broke the rules to allow for the free use of intervals like thirds and sixths (Paxman 52). This broadening of the tonal system, against the long-accepted grain of the Church, reflected Renaissance humanism, which uplifted the basic dignity of the human mind and spirit and allowed greater artistic independence. Science and astronomy also benefited greatly from this concept, which allowed scientists to put the claims of accepted authority to the test. The long-accepted concept of the music of the spheres was among the many old beliefs to be scrutinized, and great scientists would pioneer revolutionary changes in the thinking of astronomers and musicians alike. Among these scientists was German astronomer Johannes Kepler, who spent considerable time examining that ancient doctrine. Kepler, however, did not overturn the doctrine; rather, he was one of the last great scientists to develop it, attempting to reconcile it with empirical science in his work Harmonice mundi, published in 1619 (Stephenson 125).
Reflecting the period’s advances in astronomy and scientific thought, Kepler starts his analysis of harmonic astronomy by rejecting the authority of Ptolemy entirely. He embraces Copernicus instead, telling his readers that in order to understand what they are about to read, they must understand that the Earth and planets revolve around the Sun, even acknowledging the eccentricity of their orbits (Stephenson 135-136). To acknowledge the latter was in direct conflict with Medieval thinkers, who believed that heavenly motions and bodies were all perfect circles and spheres, a reflection of the creator God’s perfect nature. And if planetary orbits are elliptical rather than circular, that would obviously imply that the music of the spheres is imperfect, varying in pitch from time to time. At first glance, this seems contradictory, especially for a deeply religious man like Kepler. How did he reconcile the idea of a perfectly created universe from a perfect Creator with the empirical data known to him in his day?
Kepler acknowledged that planets orbit not in a circle, but in an ellipse with the Sun at one focus. (Wikimedia Commons)
Kepler suggested that the Creator did not in fact construct harmony from the planets’ orbits themselves. Since Hellenistic times, it was believed that the music of the spheres was inaudible to the human ear, not because the heavens make no noise, but because it is so constant that we are used to hearing it and thus cannot perceive it. Kepler rejected this notion, arguing that the very fact that we cannot hear harmony as a result of planetary orbits makes it a useless concept (Stephenson 148). He instead proposed another sort of harmony, a more visual instead of auditory one. The only harmony to be found in the heavens was in the positions of the planets at aphelion (furthest distance from the Sun) and perihelion (closest distance). The ratios between these distances determined any given planet’s harmonic proportions, thus removing the need for the planets to have perfect orbits in specific ratios relative to each other. In Kepler’s system, it was still possible for two adjacent planets to create musical intervals together, but only during the rare occurrence when one planet was at aphelion and the other at perihelion at the same time.
These occurrences and their proportions show many hallmarks of Renaissance musical thought. As mentioned earlier, Renaissance musicians expanded the tonal system, allowing the use of intervals such as thirds and sixths to become accepted practice. Sure enough, according to Kepler, the ratio between Mars’s distance at aphelion and Earth’s at perihelion forms a major sixth. Perhaps even more remarkable about Kepler’s harmonic ratios is that none of them are absolutely perfect. Earth at aphelion and Venus at perihelion, for example, form the ratio 20:27 (Stephenson 147). While this ratio appears inelegant, it is very close to a perfect fourth (3:4); all that is needed is to add one to each number and then reduce the fraction. For planets that do have perfect ratios between their aphelia and perihelia (Saturn and Jupiter’s octave, for example), Kepler was forced to round up the observed figures for the planetary distances to obtain them.
After Kepler, the concept of the music of the spheres was no longer taken as seriously as it once was. As science progressed, and became more dependent on empirical observation than ancient Greek philosophy and the wary opinions of pious clergymen, astronomy and music were mostly relegated to their own respective doctrines with little to no overlap. The heavens were no longer seen as a vast realm of divine music; indeed, such mysticism came to be frowned upon, and was abandoned in favor of the cold, hard facts, laying the foundation for modern science. One might be led to wonder, however, if the Greeks were really dead wrong in assuming the existence of celestial music. Of course, there cannot be literal music in space, since sound does not travel in a vacuum. But what about those “perfect” ratios that Pythagoras found in a blacksmith shop? Could those, or the ratios of other intervals, be found in space?
Dione (front) and Enceladus (upper right) with Saturn and rings in background. Taken by NASA’s Cassini probe
As it turns out, musical ratios can in fact be found in the orbital motinos of many planets, moons, and asteroids. Astronomers have documented several instances of what are called mean-motion resonances in the Solar System. These resonances occur, according to Malhotra, “when the orbital periods of two planets are close to a ratio of small integers” (Malhotra 1). One such resonance can be found between two of Saturn’s moons, Titan and Hyperion. Titan’s orbital period is about 15 days, while Hyperion’s is about 21 days (“Table of Moons in Solar System”). Rounding Hyperion’s orbital period to 20 days would yield the ratio 15:20, which reduces to 3:4, a perfect fourth in musical terms. Two other Saturnian moons also show a musical resonance: the orbital period of Enceladus, 1 day, and that of Dione, 2 days, creates a ratio of 1:2- an octave. The orbital periods of the planets Uranus and Neptune are within 2% of the same ratio (Malhotra 6). Perhaps the most remarkable example of mean-motion resonance in the Solar System is found in three of Jupiter’s Galilean moons: Io Europa, and Ganymede. Io has an orbital period of 1.8 days; Europa twice that of Io (3.6 days), and Ganymede twice that of Europa (7.2 days)- a 1:2:4 ratio. One could say that two octaves exist within the first three Galilean moons of Jupiter. It is clear, then, that the ancient Greeks’ assumptions about the nature of the universe should not be discarded out of hand. Although there is not literal music in the cosmos, it is remarkable that simple ratios, including some of those “perfect” ones Pythagoras discovered, do in fact exist in outer space.
It is very obvious, then, that music and astronomy are not as disparate fields as we might think. From the time of ancient Greece, the civilization that jumpstarted the Western world, both disciplines were seen as inseparable, united under the doctrine of the music of the spheres. The Greeks, convinced that the heavens made divine music, passed on their beliefs through history, resulting in any university student from antiquity until the Renaissance learning music and astronomy side by side. Although modern science has made the concept of the music of the spheres seem like little more than a charming fantasy, the actual motion of the planets and moons in the Solar System reveals that the Greeks were not entirely wrong. There is indeed “music” in space, and although it does not manifest itself in the same manner that the Greeks thought it did, we have them to thank for laying the groundwork for our modern-day discoveries, and for being the first to unite these two endlessly fulfilling disciplines.
Sources:
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