### Music of the Spheres

June 30, 2010

In the classical Greek view of the world,everything was organized according to fundamental principles. The Pythagoreans' fascination with mathematics is one aspect of this search for order in Nature. That same idea has been carried over to this day in physics, where everything is a mathematical object. The most modern mathematical interpretation of Nature is String Theory, which tries to derive our universe from the principal properties of conjectured objects called strings.

The idea that the universe can be explained by mathematical principles is not new. In the days when the universe was thought to be just a little larger than our Solar System, Johannes Kepler proposed a model of planetary orbits that used nested polyhedra. [2] There are five regular polyhedra, which are solids built from the same types of regular polygons, and nesting these gave a good approximation to the ratios of the planetary orbits. Another law of planetary orbits, the Titius-Bode Law also had unaccounted predictive properties. According to this law, the average radii of planetary orbits, in astronomical units, are predicted by

r = 0.4 + (0.3)(2m), m = -∞, 0, 1, 2, 3, 4, 5...

This formula gives r = 0.4, 0.7. 1.0, 1.6, 2.8, 5.2. 10, 19.6, which correspond quite nicely with the average orbital radii of Mercury, Venus, Earth, Mars, Ceres, Jupiter, Saturn and Uranus. Ceres is not a planet. It's a large asteroid in the asteroid belt between Mars and Jupiter. Ceres fits the law, and since the asteroid belt is a planet that never formed, it's considered alright to include it. The law fails at Neptune and Pluto, with a 29% error for Neptune and nearly a hundred percent error for Pluto. Of course, Pluto isn't a planet anymore, a fact I mentioned in a previous article (Eight is Enough, August 25, 2006), so what's the problem?

Johannes Kepler.

There's also an intimate connection between music and mathematics, so physical laws can be associated with music, rather than mathematics. The Pythagoreans discovered that a plucked string produces a tone that depends on its length. More importantly, they found that rational cuts of the string produce harmonic tones; for example, a string divided in half by placing a finger on a fret will sound at double the frequency of the whole string. In musical parlance, it sounds an octave above the whole string, in a 2:1 frequency ratio. Likewise, a 3:2 ratio of frequencies will produce a perfect fifth, and a 4:3 ratio will produce a perfect fourth. This connection between music and mathematics was very important to its discoverers, who had the notion that the planets were playing harmonies as they orbited. This idea of universal music, or music of the spheres, influenced Kepler. Kepler wrote a book, Harmonices Mundi (1619), that merged astrological ideas with harmonic analysis. [3] Yes, even this astronomer who discovered three fundamental laws of planetary motion believed in astrology.

The music of the spheres is alive today in vibrations and radio emissions detected from the sun and planets. Astronomers at the University of Sheffield have found that coronal loops, the magnetic loops that emanate from the Sun's corona, vibrate like musical strings. These coronal loops are huge, some being more than 100,000 km long, so their vibration rates are slow. Using equipment that converts light modulation to sound, and then streaming the data at higher rates, the Sheffield scientists are able to present audible versions of solar activity. [4-5]

NASA spacecraft passing near Jupiter and its satellites have recorded intensity data of plasma waves, and Don Gurnett, a physicist at the University of Iowa, has done similar electronic signal processing to convert these data into sound. [6-9] Snippets of these sounds were musical enough to inspire composer Terry Riley to write a ten movement piece, "Sun Rings." Riley is a minimalist composer who composed "In C" (1964), which I have in my CD collection.