Yours truly studied jazz composition at Berklee back in the day. Walking back and forth from the Beacon Street pad to Berklee, I leaned how sharps and flats connected to each key signature by endlessly repeating the Cycle of 5th pattern set as seen below.
To yours truly, it's not much of a stretch to see how a talented composer could see the "resonance chain" where the “years” of each orbiting body relate to one another as simple ratios. For every eight times the innermost world races through its day-and-a-half-long orbit, the next planet goes around roughly five times, the next one after that orbits three times, and the next one two times. And so on.
With this in mind, the orbital harmonics of the TRAPPIST-1 system puzzled researchers to no end until jazz guitarist Matt Russo looked at the problem and built a major 9th chord, based on the ratios of the differing planetary orbits, as start point, to creating a very cool music composition & video that intuitively shows how the TRAPPIST-1 planetary system operates in actuality.
The seventh planet, h, orbits about once every three weeks. Sped up some 200 million times and expressed in sound waves, that frequency is a C note. From there, the known ratios between planets determine every other planet’s signature note. Together the notes form a major ninth chord. “It’s really remarkable that it worked out like that,” Russo said. “Even with a different pattern of resonances, you wouldn’t get a chord that sounds as good.”
A Major 9th = CEGBD as the key of C has no sharps or flats.
How cool is that? :)
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