BEHIND THE SONG: The Music of (All) the Spheres and Kepler Jam

Our Kepler song was written by Luis and contains material and inspiration from a song called "El Cielo no es el Limite" ("The Sky is not the Limit") by Luz de Riada, written by our very own Ramsés. The main content of the song is meant to be a rock song with interesting and dynamic parts largely written independent of specific math. Working with Luis, I came up with the programmed sounds at the beginning and end of the song.  These are based on astronomer Johannes Kepler's 1619 work Harmonices Mundi ("Harmonies of the World"). I've heard the title "Music of the Spheres" used too for this content.

Famous composers like Philip Glass and Mike Oldfield have composed larger pieces entirely based on Kepler's life and work, but I believe I did some calculating others haven't.

Kepler is best known for his three laws of planetary motion, briefly:

1. Planets follow elliptical orbits with the sun at one focus of the ellipse.
2. A planet's orbit sweeps out equal areas in equal times.
3. The amount of time an orbit takes is proportional to the planet's distance from the sun* raised to the power 3/2.

* sticklers may notice that if an orbit is elliptical, the distance from the sun isn't constant. The real distance this law uses is called the semimajor axis—this is half the distance from the perihelion to aphelion shown here (source: Brittanica):

A takeaway from this is that planets move faster if they are closer to the sun. Earth and Venus have orbits that are nearly circular, so their orbit speeds are pretty consistent. But other planets in the solar system have much more oblong orbits, which means that from the sun's perspective, these planets pass through the sky at different rates.

Kepler saw significance in this—he noticed that the ratios in the rates the planets move through angles in the sky are similar to those found in musical scales. From a translation of his work here:

"Accordingly you won't wonder any more that a very excellent order of sounds or pitches in a musical system or scale has been set up by men, since you see that they are doing nothing else in this business except to play the apes of God the Creator and to act out, as it were, a certain drama of the ordination of the celestial movements."

The link above contains very detailed descriptions of Kepler's view that each planet in this cosmic symphony has a specific voice and that at certain times, they create beautiful intervals together.

Here is a reproduction of a figure from Kepler's work:

From Kepler's Harmonices Mundi (1619), with text translated to English

The thing to notice is that Mercury has a wide range of notes (because its orbit is elliptical and its speed varies a lot) and planets like Venus and the Earth don't have a wide range—their orbits are more circular.

I duplicated some of the calculations, including the other planets.

By doing computations with the maximum and minimum distances, I could calculate for each planet the ratio of maximum to minimum angular speed, and compare this to musical intervals.

I found the answers Kepler got for Venus, Earth, and Saturn made a lot of sense. Jupiter is close to what I expected, but Mars was a little off—the perfect fifth shown in the scale above implies something like a 3:2 ratio of angular speeds, but my calculation came up short of that. Also, in Kepler's time, Uranus and Neptune weren't discovered, so I found the small intervals applicable to those planets also.

Each synthesized track at the start and end of our song represents an additional planet. The track begins with Neptune and goes in. Each planet inward starts with a higher (arbitrary) starting pitch, and the interval each goes up and down depends on its orbital motion. I made the total time for a single planet's "loop" proportional to how long the year was - so Mercury's very large up and down swing happens quickly over one measure, and (for example) Saturn's trip through a major third happens over 122 measures because Mercury makes 122 trips around the sun in the time it takes Saturn to go around once.  

It's a bit mechanical, yes, and I didn't make any fancy corrections to Kepler's original ideas for the original six planets. But for a synthesized intro, it was fun to put this together. The bleeping and blooping is scientifically inspired and sets up nicely the soft acoustic introduction to our song.