Taylor Made: Singing planets

After Nicolaus Copernicus found that the planets orbit the sun, Johannes Kepler went further and attempted to describe their orbits. He came up with what was arguably his most important scientific contribution: three laws of planetary motion.

His laws stated that the orbit of each planet is an ellipse with the sun at one of its two focal points; that a line between a planet and the sun sweeps out equal areas during equal intervals of time; and that the square of each period of orbit is proportional to the cube of that orbit’s semi-major axis (aka one half of the produced ellipse’s major axis). In recognition of Kepler’s contributions to our understanding of the planets, NASA has named multiple missions after him. 

What I find most interesting about Kepler’s planetary studies is his connection between the orbits of planets and musical harmonies. Kepler found that the ratio of each planet’s top speed to its lowest speed corresponds with a harmonic interval. He explained this in his book, Harmonices Mundi (Harmony of the Worlds). These intervals were later referred to as the celestial harmonies. Going deeper, he determined that harmonic relationships could also describe the planets’ relations to each other, except for the relationship between Mars and Jupiter—it would later be found that an asteroid belt occupies the region between the orbits of these two planets.

Hundreds of years earlier, Pythagoras unwittingly laid the groundwork for Kepler’s discovery when he found that harmonic intervals could be described by whole number ratios. For example, dividing a vibrating string in half (a ratio of 2 to 1) creates an octave. To give context, this is achieved on string instruments by playing two strings such that they vibrate in the ratio of 200 to 100 Hz. 

In similar fashion, the orbital frequencies of the planets can be used to determine the musical pitches each planet makes. Note that the actual notes the planets physically produce are found to be up to 37 octaves below middle C. Some composers have used the identities of the planetary notes as inspiration for compositions.

Music isn’t usually the first thing we think of when we look at outer space, and yet Kepler and others have found measurable connections. When you look beyond the surface, you can find similar “hidden” relationships that connect many seemingly separate concepts. Having an understanding of how your idea connects to relevant phenomena from different scientific and artistic fields can help you produce a more informed design, product, or service. As engineers, we all have to remember that our craft does not live in a bubble; it permeates other fields of work, just as those fields permeate ours.

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