In ancient Greece, Pythagoras and his followers thought that celestial bodies made music. This diagram attempts to represent such theories about the earth’s relationship to other planets—an idea, based in physical truths and metaphysical beliefs, that the divine and poetic order of the universe could be known.
Pythagoras had already discovered the workings of musical pitch by way of vibration. In his book Fermat’s Enigma, author Simon Singh quotes fourth-century scholar Iamblichus to describe this account:
“Once, he was engrossed in the thought of whether he could devise a mechanical aid for the sense of hearing which would prove both certain and ingenious. Such an aid would be similar to the compasses, rules and optical instruments designed for the sense of sight. Likewise the sense of touch had scales and the concepts of weights and measures. By some divine stroke of luck he happened to walk past the forge of a blacksmith and listened to the hammers pounding iron and producing a variegated harmony of reverberations between them, except for one combination of sounds.” (14)
Pythagoras reportedly examined the hammers, and concluded that the hammers that were harmonious with one another shared a relationship in their respective weights—they were simple fractions such as one half or one quarter. Thus, he rationalized that 1:2 ratios produced an “octave” — the same note with a higher pitch. Other ratios produced different harmonies. This can be evidenced in string instruments, where strings of different lengths (ratios) produce different tones.
String instruments also make visible the vibrations that become sound. The human ear hears sounds when objects are in motion. Pluck a guitar string and watch the resulting vibrations and accompanying sound. Moving the string creates corresponding ripples of movement reverberating through its length, and through the air. These vibrations—sound waves—travel to the middle and inner ear, where the same frequencies of vibration are transmitted then amplified.
Pythagoras, extrapolating these effects, reasoned that, because objects produced sound when in motion, planets moving in orbit should also produce a sound. In the geocentric diagram above, there are eight steps from the earth to the “highest skies” (summum caelum). Between the earth and the moon, there is one full tone (tonus); between the moon and Mercury, one half tone; and between Venus and the sun, one and a half tones. He measured distance based on relative speed: faster moving planets were closer to the earth, and slower-moving planets farther away. These ratios corresponded to tonal musical intervals in the Pythagorean scale. (Plato, criticizing such theories, noted that “The error which pervades astronomy also pervades harmonics. The musicians put their ears in the place of their minds…” downplaying aural culture in his view.)
So, objects in motion vibrate and produce sound, and planets are very large bodies in motion, therefore they must also produce a sound. Given that their relative distances were concordant with musical intervals, Pythagoras surmised that the resulting sound must be a harmony—a “music of the spheres.” However, in this theory, the resulting sound should be so remarkably loud that humans should hear it on earth, and yet they do not seem to. Why was this sound inaudible? Pythagoras and his followers surmised that, because it was continually sounding, humans had no point of comparison—no real sense of silence or difference—and therefore could not distinguish it from our known idea of silence.
While knowledge, for the ancient Greeks and throughout history, has been associated with the visible, physical world, Pythagoras introduces another level of understanding based on the audible and the inaudible. Theorist Douglas Kahn notes that this mythic notion of panaurality, or “all sound,” is itself a pervasive idea, suggesting the longevity of such allegory. (202)
In the 17th century, Johannes Kepler picked up the idea, setting about to prove it in his Harmonices Mundi. Now working from a heliocentric, Copernican model of the universe, Kepler used Platonic geometry to determine the distances between planets and to further refine the harmonics of the universe, resulting in his “Third Law” determining the elliptical – not circular – motion of planets. Arthur Koestler quotes Kepler’s writing, showing that his theories came closer, mathematically, to proving planetary concord, despite the music’s literal inaudibility. Nevertheless, Kepler maintained their metaphorical and metaphysical sounding:
The heavenly motions are nothing but a continuous song for several voices (perceived by the intellect, not by the ear); a music which… progresses towards certain pre-designed, quasi six-voiced clausuras, and thereby sets landmarks in the immeasurable flow of time. (245)
Douglas Kahn’s insistence on the pervasiveness of allegory finds resonance in a contemporary cosmological view. Within particle physics, since the 1970s, string theory has been an actively researched model for understanding the universe. Rather than visualizing the smallest particles of matter as miniscule points, string theory posits that quarks and electrons may be visualized as sub-microscopic “strings” that vibrate, much like on a musical instrument. The tone at which a string vibrates determines its physical form. At present, they remain invisible and are thought to exist in other manifold as-yet-invisible dimensions. Many theoretical physicists, including Stephen Hawking believe that string theory could be a “theory of everything,” a fundamental way of describing the makeup of the universe. Auditory culture is thereby extended to the smallest particles and the largest galaxies. Pythagoras was known for saying, “There is geometry in the humming of the strings, there is music in the spacing of the spheres,” thus also linking the visual and the aural.
Dana Samuel, Humanities PhD Student, Concordia University
Brown, Andrew. “The Music of the Spheres,” Andrew Brown’s Blog. The Guardian. Thursday November 5, 2009. Web.
Calter, Paul. “Pythagoras & the Music of the Spheres” Math 5: Geometry in Art and Architecture Online. Dartmouth College. 1998. Web.
Greene, Brian. Making Sense of String Theory. Ted Talks. February 2005. Video.
James, Jamie. The Music of the Spheres: Music, Science and the Natural Order of the Universe. New York: Springer Verlag, 1995. Print.
Kahn, Douglas. Noise Water Meat: A History of Sound in the Arts. Cambridge: MIT Press, 2001. Print.
Koestler, Arthur. The Sleepwalkers: A History of Man’s Changing Vision of the Universe. New York: MacMillan, 1959. Print.
Singh, Simon. Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem. New York: Walker and Company, 1997. Print.
Stanley, Thomas. The History of Philosophy, in Eight Parts. London: Humphrey Moseley, and Thomas Dring, 1656. Print.
image: from Thomas Stanley’s The History of Philosophy, c. 1656.