The Orbital Music Box plays a song based on the orbital resonance of Jupiter’s three inner-most moons: Io, Europa, and Ganymede. They orbit in a 4:2:1 ratio, respectively, meaning that Io completes four orbits for every two of Europa’s, and so on. These resonances occur due to the gravitational interaction the moons have as they pass each other in orbit. The song is based on an A minor triad chord (notes A, C, and E), and each moon is assigned one note at their starting position. Each time the moons pass each other in orbit, their assigned notes are played and then shifted up by a third on the scale to represent their exchange of energy and influence on each other. Read on to learn more.

This art project is focused around the orbital resonances of the three inner-most Galilean satellites, which are Io, Europa, and Ganymede. These moons orbit Jupiter in a rythmic, periodic pattern due to their complex gravitational influence on each other. They have a 4:2:1 resonance, which means that for each time Ganymede completes 1 orbit around Jupiter, Europa completes 2, and Io completes 4. I have always felt that orbital resonances are one of the universes most elegant demonstrations of physics. So, it is my wish to create a music box that uses this 4:2:1 resonance to play a planetary song. A note (or a set of notes) will be assigned to each moon, and the note(s) of each moon will be played when it passes another in orbit. So each time two moons pass each other, their notes will sound. The Wikipedia article on orbital resonances has a great animation that helps to visualize this.

First, I needed to calculate how far apart the notes would be based on their orbital motion. This plot shows a line for each moon, with dots at each time its note is played. The x-axis is really the only important one here – notice how the dots always come in pairs through time, as notes only play when two moons pass each other. The actual numbers on the Time axis don’t matter because it can be scaled to any length as long as the ratios between notes stay the same.

While I was doing the calculation for the timing, I plotted the position of each moon as a function of degrees around Jupiter. The result was this delightful-looking pattern (below), which I love and plan to eventually turn into a fabric pattern. It reminds me of flannel. (Speaking of which, did you know the Scottish register of Tartans has official patterns for Mars and Enceladus? I love this!)

To actually develop and play the music, I bought a DIY music box from Amazon. They use punched cardstock to play songs, so you can buy blank strips and write music to your heart’s desire. I didn’t make the wooden box it came in- you can get music boxes with or without enclosures, and with varying numbers of notes. Smaller pieces come with only a chromatic scale, the larger ones (as below) have a full set of notes including all sharps and flats. The one I bought came with one pre-printed song that I punched to try it out (Spirited Away’s “Always With Me”, a song I love and am learning on the harp!). The cardstock strips work quite well, and the box has quite a big sound! The music box is not perfectly in tune, but to me that is part of their charm and aesthetic. I also learned quickly that it’s really interesting to flip the strip over or put it in backwards to play different and sometimes eerie tunes.

I used the easy, online melody editor over at Music Box Maniac to help me write the tune. They even have presets for different brands of music boxes so that you can output the song you created in the right format for easy transfer to the punch strips. On a practical note, here are a few lessons I learned about making and playing the punch strips:

• There is a limit (the size of the hole punch) to how close together you can put notes together in the song. There is also a limit to the resolution of note timing you can achieve- you can punch notes on and between the printed lines, but if you write a song with a bunch of 32nd notes there is no way to punch them all perfectly timed in the space between two lines. Keep this in mind as you write for these boxes.
• The cardstock is kind of waxy. Make sure the pen you use to mark the notes before you punch them isn’t going to stay wet and get all over your hands.
• If you punch a hole in the wrong place, just put tape over it.
• Parts of the roll that are bent or curly don’t make good starting places for a song, as sometimes you have to help guide the edge through the exit slot in the box. It helps to cut the end of the strip on a diagonal so only one corner feeds through at a time.
• I tried taping the ends of the strip together to make the song loop, but I was using painter’s tape (so I could remove it later) which meant it started to come apart when the joint went through the machine. I read a tip online to cut the ends of the strip on a long diagonal to help with this, but didn’t leave enough room to do it here.

At first, I tried assigning each moon the number of notes equal to its resonance factor. There is no time that all three moons pass each other at once, so I just had to be sure that each combination of two moons played a chord during their interaction. (This would have probably taken me less time to figure out if I had more music theory, but I’ve only been playing the harp for ~9 months and we don’t really spend much time on academics.) So, I assigned Io a four note chord (C-E-G-B), two notes (A-D) for Europa, and one note (F#) for Ganymede. I normalized the length of the song to be 18 seconds so that the moon interactions would all fall on quarter and eighth notes. Then, all I had to do was mark punch the cardstock strip!

This result was interesting, but ultimately since the timing of when the notes play is fixed I didn’t really feel like it came out very song-like. It would have sounded repetitive and boring to just loop the chord pattern over and over. So, taking a different approach, I decided instead to assign only a single note to each moon. I used an A minor triad (A-C-E). In this case, each time two moons pass each other the note assigned to each is stepped up by a third on the scale. In other words, Io is first assigned A, and then when it passes Europa it is stepped up to a C. In order to prevent times where two moons were playing the same note at the same time, the notes for all moons are stepped up during every interaction (including the one that doesn’t play). The song continues this pattern up the scale until I ran out of notes on the music box, and then wrapped around to the beginning. After going through the cycle three times the song eventually returned to the beginning configuration. Take a listen. The delightful arpeggio at the beginning of the video is just a result of inserting the strip.

I really like how this came out. The stepping of the notes kind of represents the gravitational interaction and exchange of energy between the moons. It emphasizes that they are really influencing each other, rather than just simply passing each other in orbit. The song also has a much more dynamic feel than the previous one. It feels like it’s going somewhere, and the long cyclic pattern, to me, really captures the sense of endless planetary motion. I’m sure there are other interesting ways to do this, so perhaps there are more songs to come in the future.

Note that the key of the song did not come out as originally intended because there is a known problem with the manufacturer of these DIY music boxes. I punched out my melody based on the scale printed on the music strips that it came with, but it turned out my music boxes was tuned to a different key. The resulting sound is kind of eerie and strange, so I kept it!