Planets outside our own solar system are called exoplanets. Over the past couple decades, scientists have discovered thousands of exoplanets throughout the Milky Way galaxy. Check out the video below for a visualization of the discovery timeline:

## TRAPPIST-1

In 2017 a team of astronomers announced the discovery of a particularly interesting system of planets coined TRAPPIST-1 (named after the instrument used to make the discovery). Research showed that three of the seven planets are the right temperature to host liquid water and thus potentially habitable. These planets are orbiting very close to their red dwarf parent star compared to our solar system. For the outermost planet (TRAPPIST1-h) a single orbit around the star takes around 18.76 days, while for the innermost planet (TRAPPIST1-b) a single orbit takes only 1.51 days! This closely packed configuration of planets presents an interesting problem. When scientists ran computer simulations of the seven planets, they found that gravitational interactions between the bodies quickly threw the simulation into chaos with the planets either colliding, getting pulled into the star, or flung into outer space. So how can this planetary system even exist in real-life? Turns out that the seven exoplanets are in a chain of *orbital resonances* with one another. This means that respective orbital periods form simple small-integer ratios with their neighbors. For example, in the time it takes TRAPPIST1-b to complete 5 orbits, the next planet outwards (TRAPPIST1-c) completes 8 orbits (forming a 5:8 ratio between the two). TRAPPIST-1 is the longest known chain of orbital resonances; this is why the system has remained stable through time.

## What does TRAPPIST-1 sound like?

To the musically inclined, the small-integer ratios of the seven planetary orbits in TRAPPIST-1 may be familiar. These orbital resonances are analogous to common musical intervals, which are similarly formed by sound waves with small-integer frequency ratios. Essentially the same principles which allow the TRAPPIST-1 system to remain stable are also the building blocks of our musical scales! The astrophysicist and jazz guitarist Matt Russo illustrated this connection as part of a sci-art outreach project, in which he and colleagues scaled the relative orbital frequencies of TRAPPIST-1 into the audible range. You can listen to the result in his excellent TEDX talk. Also take a look at the video below, which provides a nice animation of the TRAPPIST-1 system and its inherent “musicality”:

## Other exoplanet systems?

Let’s extend this idea to other exoplanet systems. How would they sound if subjected to the same type of analysis as TRAPPIST-1? Perhaps we can find some more interesting orbital resonances and musical intervals out there! First we need to get the exoplanet data, which can be freely downloaded from the NASA Exoplanet Archive. A myriad of parameters are available for analysis including names, orbital periods, orbit semi-major axes, and transit times (when an exoplanet passes in front of its host star, from earth’s point of view). For our purposes, the orbital periods are most important. Once we have the data, lets simply go through every known exoplanet system, and for each system: (1) convert the orbital periods to frequency in units of orbit/day, i.e. the fraction of their orbit they complete in a single day (2) calculate the frequency ratios of every pair of exoplanets in the system (3) check how many of the resulting frequency ratios are close to small-integer musical intervals. By summing the number of orbital frequency ratios found (those which are close to our ideal small-integer ratios), we can calculate a “score” for each system, then select the top-scoring systems for further analysis. Without further ado, below is a list of the top 25 most “musical” planetary systems known to humankind in 2019 (according to our metric). As expected, TRAPPIST-1 is at the top of the list, followed by Kepler-223, Kepler-80, and Kepler-444:

- TRAPPIST-1
- Kepler-223
- Kepler-80
- Kepler-444
- HIP 41378
- K2-138
- KOI-351
- Kepler-102

- Kepler-11
- Kepler-1542
- Kepler-226
- Kepler-402
- GJ 876
- HD 215152
- K2-239
- K2-285

- Kepler-176
- Kepler-208
- Kepler-24
- Kepler-305
- Kepler-31
- Kepler-32
- Kepler-326
- Kepler-33
- Kepler-341

Now the fun part. What do these exoplanet systems sound like if we scale their orbital frequencies into the audible range? Lets try it. We shift up (in octave intervals) every system of interest, until the planet with the lowest frequency in each system reaches at least a C3 note (130.81 Hz). Then we synthesize pure sine waves at the resulting frequencies. Listen to the result:

While many intervals are not perfectly in-tune, they are close enough to build interesting (and some jazzy-sounding) chords. There are plenty of (approximate) fifth intervals and octaves, with a few other things mixed in too. The TRAPPIST-1 planets form a chord with a second interval rather than a third, making it neither major nor minor but rather a sus2, with with a major 7th stacked on top. The Kepler-223 system is made up of only fifths and octaves, and so forms a simple five chord. Kepler-80 is a similar story, but has another 2nd interval thrown in, making it a sus2 chord. Things really get interesting with Kepler-444. It almost forms a 6add9 chord, which is often used in jazz as a more harmonically ambiguous substitute for a major chord. Except here Kepler-444 has a flat five instead of a normal five, giving it a more dissonant and unresolved sound.

Name | Constellation | Chord |

TRAPPIST-1 | Aquarius | Asus2maj7 |

Kepler-223 | Cygnus | Db5 |

Kepler-80 | Cygnus | Dsus2 |

Kepler-444 | Lyra | Ab6b5add9 |

## Composing a song

Many other exoplanet systems have interesting orbital resonance chains which also make nice-sounding chords. Just for fun, lets select a few other systems and put them together to create a chord progression. In the video below, the Kepler-60, Kepler-223, and TOI-270 exoplanet systems create a Bb-Db5-Ebmin progression. In this case the frequencies have been tuned ever so slightly to align with our 12-tone equal temperament tuning system. I also added an organ, synthesizers, drums, and some crunchy guitar layers for your enjoyment:

Exoplanet resonance chains are a great example of the inherent musicality of our universe, and highlight a connection between the entropy of physical systems and the human perception of music. Thanks for reading and listening!