How Music Works

by David Byrne

  THE MUSIC OF THE SPHERES

  The followers of Pythagoras (around 590 BC) were called Acousmatics because they listened to his talks while he remained hidden behind a curtain. Maybe this was intended to help them focus on his words rather than on what might have been distracting gestures. Pythagoras surmised that there might be a divine reason behind our tendency to find specific harmonies and note intervals more pleasant to the ear than others. He pointed out that there were mathematical congruencies behind these notes—a phenomenon he first observed when he passed by a blacksmith’s shop and noticed that the pings of the various hammers fell along common musical intervals. Why? It was the proportions of the varying weights of the hammers—a twelve-pound hammer and a six-pound hammer produced pings an octave apart. Similarly, a string stopped at 3/4 of its length produces a note that is 1/4 above the octave—the sound of the full-length string. This fourth harmony is extremely common, and we find it pleasant. If the stop is 2/3 the length of the string, then the note is a perfect fifth. A stop at half the length produces a note that is an exact octave higher than the full length of the string. Needless to say, this is somewhat uncanny. Spooky, even. Why should this be?

  Pythagoras surmised that the gods generally prefer small numbers such as occur in these fractions, because simplicity is always more profoundly elegant. Pythagoras was a bit of a numbers nut, so the fact that there were mathematic underpinnings to the most common musical harmonies was very exciting for him. It was like unlocking a key to the universe. He further identified three kinds of music: instrumental, human, and celestial. Music played on instruments by mortals was viewed as a pale echo of the “original” celestial music, an idea that seems to presage Plato’s shadows-in-the-cave metaphor. The celestial music, the music we attempt to imitate—where the divine harmonies emanate from—actually does exist, Pythagoras said, and this music has its source in the spheres that “hold” the planets. He believed that the planets were attached to revolving crystal spheres (how else could they stay up?), and that each planet, along with its crystal sphere, produced its own unique tone as it whistled through the cosmic ether. Hence the Music of the Spheres. The distances between the spheres (and their planets) were, of course, based on a series of relationships that followed these same “harmonic” and mathematical ratios, or relatively simple combinations of them. So the whole universe, or what was known of it at the time (the stars were thought to lie on these crystal spheres as well), was like a giant mechanical instrument producing a shifting and ever-morphing chord as the spheres creaked through the ether. The implication was that all earthly harmonies—the harmonies of all things, dead and alive, both inside and out—were all based on those same ratios.

  This idea lingers still. NASA recorded inaudible electromagnetic signals— not even what we would call sound waves—as the probes Voyager and Cassini passed by a number of planets. Then these signals were processed and converted into sonic vibrations that fell within the range of human hearing. A collection of these sounds was released as an album with the title Symphony of the Planets. It’s basically a collection of ambient drones—quite nice ones, too, though Mercury is a little scary sounding. One online reviewer of these recordings credits the solar system with being a composer of ambient trance music. “As if creation were performing for you,” he wrote.

  Not surprisingly, these notes, as Pythagoras conceived them, produced the most divine harmony imaginable—a great cosmic chord that created us and everything else. The sound was so perfect, he said, that ordinary people like you and me couldn’t hear it. Pythagoras could hear it, though. It was claimed by his followers that Adam and Eve heard it, too, as God imparted to them the means to hear this perfect chord. Like links in a mystic chain, the Zoroastrians then passed the way of listening down to their disciples. It was said that Moses also heard it when he received the tablets of the ten commandments. According to St. Augustine (around 400 CE), all men would hear this sound just before they died, at which point the secret of the cosmos would be revealed— which is very exciting, although just a little late to be of much use. This secret was passed down through the ages, from prophet to prophet, although at some point, according to Renaissance philosophers, it was lost. Oops.

  Pythagoras was convinced that each musical scale, the varieties of that cosmic mode, have profound, specific, and unique effects on people. The Hypophrygian mode is one of the many variations of the diachronic scale where the intervals between notes have been altered. For example, a C scale (all white keys) and a C-minor scale are two different modes. According to Pythagoras, a tune in the Hypophrygian mode could totally sober up a drunk young man. In his day, the power of music was commonly accepted, and there were musicbased healing centers throughout Greece. The notes of the basic scale were associated with the Muses, and each tone had its own attributes and temperament. The seven planets that the Greeks could see had associations with the seven vowel sounds of Classical Greek, which were also considered sacred. The various names of God were formed out of recombinations of these vowels and harmonies—like Ho Theos, or God, Ho Kurios, or Lord, and Despotes, which means master, and is the root of our word despot. The cosmic harmonies informed every aspect of life—our speech, our bodies, and our state of mind. The weather, the cycles of crops, disease and health.

  These musical and mathematical correspondences among all things were out there, and the idea was that we needed only to discover them. God, or the gods, put them there, and in the emerging Western tradition, the goal of science and the arts was to decode what the gods had written. The belief that the goal of science is to unearth pre-existing patterns forms the basis of much of scientific practice today. Even in the periodic table of the elements, where all the materials that make up our world are ordered according to atomic weight, there are “harmonies.” John Newlands, who worked on the table, discovered in 1865 that “at every eighth element a distinct repetition of properties occurs”—a pattern which he called the Law of Octaves.2 Newlands was ridiculed, and his paper on the subject wasn’t accepted. But when his prediction that “missing” elements should therefore exist was later proven to be true, he was recognized as the discoverer of the Periodic Law. “Musical” relationships, it seems, are still viewed as governing the physical world. The Music of the Spheres idea is, in slightly altered form, still with us.

  The astronomer and astrologer Johannes Kepler published his book Harmonices Mundi in 1619. In it he proposed that it was the Creator who “decorated” the whole world, using mathematical and musical harmonic proportions. The spiritual and the physical are united. In a search for these proportions, Kepler first suggested that the varieties of polyhedral shapes—three-dimensional figures made of pentagons, octagons, etc., and each nested inside a sphere and inside each other—might have guided the Creator’s plan.D

  Kepler wasn’t satisfied with its accuracy, so he looked at the musical and mathematical harmonic proportions. He wrote: “The Earth sings Mi, Fa, Mi: so that even from the syllable you may guess that in this home of ours misery and famine hold sway.”3 His calculations seemed to imply that the orbits of the planets had some wobble in them, and the resulting vibrato was sometimes unsettling and even discordant. This was not good. However, it did seem that they sometimes fell into perfect harmony—and one of these moments, he believed, was the moment of creation.

  On the following page is a simple chart from Stanley’s History of Philosophy, published in the 1600s, that shows the musical intervals that would naturally occur on an imaginary string stretched from the highest heaven, through Earth, and via the orbits of the various planets (which included the sun in the midst of the others rather than at the center, as that was where we, on Terra, were thought to reside).E

  The great seventeenth-century alchemist and scientist Robert Fludd made further elaborate renderings. He called the imaginary string the Mundane Monochord. “Mundane” refers to the whole world in this case, not to something banal and ordinary. At the top in his drawing, God’s hand is
reaching in to “tune” the universe.F

  In both Fludd and Stanley’s view, seven musical modes—which are sort of the equivalent of scales—correspond to the seven planets. Each planetary orbit and its mode had a character, such as saturnine (gloomy) or mercurial (fickle). Each musical key, as it were, was therefore associated with personality traits we might find in our fellow humans. Astrology—the influence of the heavens on our personalities—was in this way being given some “scientific” basis.

  This idea of a universe ordered according to musical harmony fell into disrepute and was more or less forgotten for hundreds of years, but recently it has been picked up by, of all people, the movie editor and sound designer Walter Murch. I saw Murch give a talk, and though he did discuss sound in films and his thoughts on editing, what he was really excited about was reviving the idea of cosmic ratios. Murch wondered why Copernicus, who gets credit for proposing the suncentric solar system, would make such an unintuitive and dangerous statement. A heliocentric system was unintuitive because, from our point of view, it really does seem like the stars and sun revolve around us. It was dangerous, because it was assumed that God made the universe the way the church said He made it—Earth-centric—and to question God’s plan and wisdom was heresy. Murch theorized that the explanation might lie in the fact that Copernicus knew about a Greek astronomer named Aristarchos of Samos (c.310–c.230 BCE), who had proposed his own suncentric system. Aristarchos even suggested that the moon revolved around the Earth, but by Copernicus’s time, his theories had been forgotten.

  Here is Murch’s theory of how Copernicus revived Aristarchos’s idea. Copernicus visited Rome after completing his studies, where he surely went to see the dome of the Pantheon, which was one of the wonders of the age.G Murch suggests that upon viewing that ceiling, Copernicus put two and two together and sensed that here, in this architecture, was encoded the secret order of the solar system. This sounds very Da Vinci Code, but read on.

  To the right, Copernicus’s suncentric system.H Below it is a superimposition that Murch did, placing Copernicus’s solar system over the concentric circles of the Pantheon’s dome.I

  In the suncentric system, the ratios (the distances between the planetary orbits) are still not absolutely “correct,” so we’re not in perfect celestial harmony just yet.

  In the 1760s, the director of the Berlin observatory, Johann Daniel Titius, published a paper that contained what came to be known as Bode’s Law. It proposed some mathematical formulas and constants that, Titus claimed, not only described where the orbits of the planets were relative to the sun, but also predicted where new planets would be found—and therefore where the next “harmony” should be. Shades of the periodic table! One can predict musical overtones in much the same way.

  As you can see in the diagram below, it all worked fine until the discovery of Neptune, which didn’t fit the pattern.J In 1846, Bode’s Law was therefore abruptly abandoned and thrown into the pile of discarded and lost science. Murch said:

  So it seemed more logical (to me) to abandon the Astronomical Unit and just concentrate on the ratios. Once you do that, the formula gets much simpler: it doesn’t have to do two things at once. This new formula is not only simpler, but it’s also lost its “Earth-centricity.” Now you can apply it equally to other orbital systems—the miniature “solar systems” of the moons around Jupiter, Saturn, Uranus, and Neptune, for instance—and you find the same set of ratios cropping up! Underlying all the orbits of these moons and planets, there is a pattern of ratios, like the musical ratios underlying a keyboard. Just as you are restricted to playing certain musical ratios on many instruments, so it seems to be with the arrangements of these moons. Some systems “play”—or occupy—certain orbits, while others are left blank. By playing different orbits these systems generate a variety of chords. Chords we recognize. If I wrote the simplified Bode formula down on a piece of paper and showed it to music theorists, they would ask: “Why are you showing us the formula of the overtone series…?” In other words, Bode’s Law gives a series of orbital ratios, which are mathematically identical to the common intervals in musical theory. They’re primarily variations on what we call the 7th chord: C, E, G, B flat.4

  You might say that the universe plays the blues.

  We’ve come back around to Pythagoras and the other Music of the Spheres and universal harmony proponents. Pythagoras’s computations were slightly off and didn’t quite match true musical ratios. It was Galileo’s dad, Vincenzo Galilei, who figured out the formula that generates a musical scale as we know it. The Renaissance architect Leone Battista Alberti said:

  [I am] every day more and more convinced of the truth of Pythagoras’s saying, that Nature is sure to act consistently… I conclude that the same numbers by means of which the agreement of sounds affect our ears with delight, are the very same which please our eyes and our minds. We shall therefore borrow all our rules for the finishing of our proportions from the musicians… and from those things wherein nature shows herself most excellent and complete.

  Alberti went on to develop the formula for perspective in painting—a way of mathematically organizing our vision.5

  Andrea Palladio, another, and rather more famous Renaissance architect, used these same ratios in the buildings that he built in the sixteenth century, which have been emulated all over the world as designed of harmonic visual and spacial relationships that are pleasing to the eye. Jefferson’s Monticello, hundreds of museums and monuments all over the world—they all owe their proportions to Palladio, and to the cosmic musical ratios that he and others believed gave structure to all things.

  Vitruvius was a Roman engineer and writer (born 70 BCE) whose ideas were revived during the Renaissance, particularly by Daniele Barbaro, who was also Palladio’s patron. Vitruvius espoused the ideas of symetria (symmetric objective beauty) and eurythmia (which is more about arrangement, and is subjective and experiential). It was to illustrate a reappraisal of Vitruvius’s book On Architecture that Michelangelo drew his famous Vitruvian man (as you can see on the following page, he was somewhat emasculated by NASA) that elucidated the divine proportions of the human body.K

  Barbaro wrote that what harmony is for the ear, beauty is for the eye, and this was made explicit in Palladio’s work. In the Villa Malcontenta (who would give such a name to their house?), there is a room that he describes as the “most beautiful and proportionate,” which is musically a major sixth. This room can be subdivided into smaller rooms, which work out to be a fourth and a major third.

  THE EAST

  In the ancient Far East it was also thought that sound played an essential role in the formation of the universe. In Tantric Buddhism there is a “sonoriferous” ether called the akasha, and from that ether flows the primordial vibrations. The akasha is self-generative—it didn’t come from something else, it made itself. But according to Tantric philosophy, this cosmic sound, which is sometimes referred to as Nãda-Brahman, actually comes from the vibrations that emanate when Shiva and Shakti have sex.L

  It is referred to as the Cosmic Orgasm, and from it the entire material universe was formed. A little more than a hundred years ago, Madame Blavatsky, who developed a mystical system called Theosophy that was for a while very popular, referred to this Nãda as the “soundless sound” or the “voice of silence.” Discrete, silent, true, esoteric, and momentous.

  The idea that vibrations permeate everything is indisputable—you don’t have to be a Tantric Buddhist or an Acousmatic to accept it. The Venn diagrams that contain spiritualist ideas, religious myths, and what we consider scientific fact do indeed overlap. Molecules vibrate at one hundred times per second, atoms faster than that. These vibrations produce what could be considered sound, albeit sound that we cannot hear. The composer John Cage said:

  Look at this ashtray. It’s in a state of vibration. We’re sure of that, and the physicist can prove it to us. But we can’t hear those vibrations… It would be extremely interesting to place it in a
little anechoic chamber and listen to it through a suitable sound system. Object would become process; we would discover… the meaning of nature through the music of objects.6

  None of these divine or ancient scientific theories really explains the why part—why we gravitate to the specific harmonies we do—unless you accept “God made it that way, end of discussion” as an explanation. However, in our world of little faith, we ask for proof.

  BIOLOGY AND THE NEUROLOGICAL BASIS FOR MUSIC

  The question, then, is not only why do we like the harmonies we do, but also does our enjoyment of music—our ability to find a sequence of sounds emotionally affecting—have some neurological basis? From an evolutionary standpoint, does enjoying music provide any advantage? Is music of any truly practical use, or is it simply baggage that got carried along as we evolved other more obviously useful adaptations? Paleontologists Stephen Jay Gould and Richard Lewontin wrote a paper in 1979 claiming that some of our skills and abilities might be like spandrels—the architectural negative spaces above the curve of the arches of buildings—details that weren’t originally designed as autonomous entities, but that came into being as a result of other, more practical elements around them.