Music about Data

Gafurius's Practica musice, 1496 showing Apollo,
the Muses, the planetary spheres and musical ratios.

Science and music, like other arts, have a longstanding, close connection. Music can be described in terms of physics; notes translate to waveforms at a certain frequency, or equivalently certain pitch. Acoustics, tempo, rhythm, tones and overtones, harmonies and more can be explained in terms of physics. We can likewise discuss our physical world in terms of music.


In ancient Greece, Pythagoras and his followers placed a mystical meaning on his discovery of the mathematical underpinnings of music; he found that the length of a plucked string determined its pitch and that   simple (rational) ratios of a given length produced harmonies. They turned this idea on its head and apparently concluded that other fundamental patterns in nature were due not so much to mathematics, but that there was a musical underpinning to the known universe. Hence, the idea of the 'music of the spheres' and the hypothesis that planetary motions obeyed mathematical equations corresponding to musical notes and that the whole solar system together played its own symphony.

Kepler's musical notation for planetary motion and the range of sound
he ascribed to Saturn, Jupiter, Mars, Earth, Venus and Mercury

The idea was so persistent that when Johannes Kepler (1571- 1630) was developing the best model of our solar system to fit the beautiful dataset gathered by his mentor Tycho Brahe (1546-1601), one of the first notations he used was not mathematical, but musical. In fact, the idea was pervalent, and Kepler ended up embroiled in a priority dispute with Robert Fludd (1574-1637), whose own harmonic theory had been recently published in De Musica Mundana. While we tend to think of Kepler with his rational, more precise elliptical version of a Copernican heliocentric solar system as one of the first, modern scientists, he progressed from his musical notation, to a model based on a rather mystical appreciation for the Platonic Solids. That is, rather than explaning planetary motion in terms of his laws, as we know then today, he tried to make a model spacing of the planets from the sun based on the relative size of a nested spheres just large enough to coat a  series of special shapes called the Platonic Solids: the tetrahedron, the cube, the octahedron, the dodecahedron and icosahedron. He progressed from there, in his Harmonices Mundi (literally, harmonies of the worlds) to describe planetary motions in musical terms. He found that the difference between the maximum and minimum angular speeds of a planet in its orbit was very close to a harmonic proportion. For instance Earth's maximal angular speed relative to the sun varies by about a semitone (a ratio of 16:15), from mi to fa, between aphelion (the furthest point from the sun on its elliptical orbit) and perihelion (its closest point to the sun). In his words, "The Earth sings Mi, Fa, Mi", and he built up a choir of similarly singing planets. He found that all but one of the ratios of the maximum and minimum speeds of planets on neighboring orbits approximate musical harmonies within a margin of error of less than a diesis (a 25:24 interval) - to use a musical term.

Today we would attribute these patterns to the underlying mathematics of planetary motion, or the physics of music, rather than a music of the spheres underlying everything. Nonetheless this trick of Kepler's, of mapping observed patterns onto music, or of writing data as music still has its place. I recall a professor extolling the virtues of plotting data as it was collected, because we are wired to see patterns and would for instance, recognize a friend's face in a crowd with much greater ease than their phone number from a list of 7-digit numbers. The same can be said of sound; we are wired to recognize musical patterns. We can both appreciate the beauty of regular data mapped onto sounds we can hear, or use what we hear to recognize patterns.

Galileo Galilei (1564-1642) was the son of a famous lutenist, composer, and music theorist, which may have primed him to be observant of the measure of time, rhythm and periodic patterns. In Galileo's Daughter, author Dava Sobel argues that in the absence of accurate time pieces, music likely played an important role in his experiments. Many experiments involved timing repeated observations as precisely as possible and it is likely that he may have used song as his yardstick of time.

A couple of contemporary examples of expressing experimental data musically have been in the news of late.




The European CERN particle physics lab in Switzerland celebrated its 60th birthday with this delightful composition by physicist and musician Domenico Vicinanza, which turns data from four detectors at the Large Hadron Collider into LHChamber Music. Performed by CERN scientists and engineers, the result is surprisingly musical, like Baroque chamber music. Vicinanza has 'sonified' data before (including the satelitte Voyager I's magnetometer data), employing an algorithm to assign a musical note to each measurement created by experiments, so that the same data is presented as a musical score, much like Kepler did.



Sonifying data also allows scientists to hear patterns, to cope with massive datasets and find complexity which may otherwise have escaped them. Above, cicada calls are replaced with notes. The University of Uppsala team explains their sonification and visualization of the data:

The circles represent recording stations in the Australian bush that pick up the calls of cicadas. The intensity of the circle’s colour and its size is proportional to volume of sound in that area of the forest at that time (the videos is 15 x real time).

They could also add the sound of the cicadas themselves (speed up 15 times), but in the words of researcher James Herbert-Read, "that would be horrific". Instead they decided to translate cicada calls into music.

Each one of the four different coloured block of recorders also plays a different chord (we chose the standard I–V–vi–IV progression in the key of C major). By doing this, you can now not only see, but hear when cicadas in different areas of the forest start to sing, when other cease singing, and listen to the additive effect of all individuals singing together across large swathes of the forest.

The video is the cicada 'morning chorus' beginning at 5:30 am when light strikes the right hand side of the area shown, where the  first cicadas call. You see and hear other cicadas join, the early oscillations in volume and then the crescendo to full volume for the remainder of the chorus.

Locals had noted waves of cicada song moving through the forest and the researchers wondered whether they could prove the cicadas were in fact synchronized. They found quantifiable waves did in fact move through the forest. Though, they theorize that this is an emergent pattern, where each cicada follows his own rules and does not consciously try to synchronize with his neighbours.

Mathemagical Solar System Song

Daniel Starr-Tambor’s Mandala (above) is a musical palindrome of 62 vigintillion (10⁶³) notes, which represents musically all the rotational frequencies of the planets (and Pluto) in our solar system! (via Brain Pickings) I've always been a fan of the palindrome (which is something which remains the same if write forward or backward) since my name (Ele) is one of the shortest palindromes. Mandala boasts that it is the longest palindrome ever written, and I do not doubt it.

It's perhaps surprising how lovely the music is to hear, for such a mathematical approach to music composition - though the two languages, math and music, are quite naturally intimately entwined. He's not the first to think of the planetary motions in terms of music. He alludes to Bach (and Bach’s The Art of the Fugue) explicitly, with its contrapunctal mathematical and arguably Pythagorean structure.* The concept of the Music of the Spheres was quite a common way for scholars to think about the motions of heavenly bodies, up to the Renaissance and the Scientific Revolution. It can be traced back to the ancient Greek mathematical-mystic Pythagoras, who first linked musical pitch to the length of a vibrating string which produced it. Further harmonious sounds were produced by strings with simple (rational) length ratios. This fit well with his adoration of rational numbers.** Pythagoras, in his theory of the Harmony of the Spheres, proposed that celestial bodies (Sun, Moon, and the known planets, Mercury, Venus, Mars, Jupiter and Saturn) each emitted a hum based on their period of revolution. Recall, that it was assumed that the Sun, moon and planets orbited around the Earth. Further, that the ratios were harmonious, like those produced by strings of simple length ratios. Thus, for Pythagoras, music and astronomy were two sides of a single mathematical coin. Ptolemy's model of the geocentric solar system, wherein each of Sun, Moon, known planets, and stars (quintessence) were more-or-less pinned to a series of transparent, nested, rotating spheres encapsulating the Earth, dominated the Western world view for 1500 years. Thus "Music of the Spheres" referred to the 'harmonies' of the motions of these imaginary spheres.



The first real shift in thinking is of course attributed to Copernicus, who proposed a heliocentric model, where the Earth, like the planets, circled the Sun, and the Moon circled the Earth. This model was famously improved by Kepler, who, thanks to Tycho Brahe's immaculately recorded data, was able to show that planetary orbits are in fact elliptical (slightly more oval than a perfect circle), with the Sun at one of the two foci of the ellipse. He further showed that a line joining a planet and the Sun sweeps out equal areas during equal intervals of time. And, that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. These three facts are known as Kepler's Laws of Planetary Motion. You'll see that they refer to geometry and ratios, just like Pythagoras did before him. In fact, while we tend to honour Kepler as some sort of harbinger of modern science, his worldview was in many ways still Medieval. He did not think in terms of the simple, beautiful, elliptical solar system (as we still know it today). He was obsessed with proportions and attempted to explain astronomical (and worse, to the modern mind) astrological ratios in terms of music, in his own favorite publication Harmonices Mundi. His very first attempt to articulate his discoveries, now known as his three laws, was written in terms of musical notation (above). He wrote, "the movements of the heavens are nothing except a certain everlasting polyphony." (He ended up embroiled in a priority dispute with Robert Fludd, whose own harmonic theory is illustrated as the "THE MUNDANE MONOCHORD WITH ITS PROPORTIONS AND INTERVALS", the stringed instrument with planetary orbits, From Fludd's De Musica Mundana above). He also conceived of it in terms of polyhedra; he imagined the five Platonic solids (octahedron, icosahedron, dodecahedron, tetrahedron, cube) circumscribed by spheres, nested one within the other. This, he claimed, could explain the ratio of orbits of the six known planets (Mercury, Venus, Earth, Mars, Jupiter, and Saturn). Kepler's insights, along with the concept of centrifugal force from Huygens, allowed Newton, Edmund Halley, and possibly Christopher Wren and Robert Hooke to deduce that gravitational attraction between the Sun and its planets decreased with the square of the distance between them. This in turn lead to Newton's Universal Law of Gravitation. So, we owe this groundbreaking idea as much to musical theory, and imaginary geometrical patterns, as rational, mathematically-based reasoning.

*For how Bach encoded his name into The Art of the Fugue, see one of my favorite books, Gödel, Escher, Bach by Douglas Hofstadter.

**We all recall Pythagoras for Pythagoras' theorem (the square of the hypotenus is equal to the sum of the squares of the other two sides for right angle triangles). Imagine his, and his cult's horror when they realized that for one of the simplest triangles, where "the other two sides" each have length of 1 unit, the hypotenus must have an irrational √2 length! The irrationality of √2 did not fit into the tidy rational, mathematical world of the Pythagoreans. It was perhaps the first of a long series of instances where the beauty of mathematics was mistaken for something tidy and controllable.