Space Music I: Kepler and the Harmony of the Worlds

PLUTO Credit: NASA

by Henry Myers

If you’ve been online recently, then no doubt you’ve heard about the NASA New Horizons spacecraft’s flyby of Pluto, which culminated an almost 10-year long journey across the solar system (space is really, really big) to collect data and take a number of photos, including the one above. Until just a few days ago, the small, icy world had remained tantalizingly out of reach, close enough to know about but much too far away (in fact, almost 40 times our distance to the sun) to be knowable by any other means. For the first time in history, 85 years after its discovery, we now know what Pluto looks like (outside of a few unhelpfully blurry photos from 2003). I can hardly contain myself about it: dwarf planets aside, I’ve been daydreaming about space, checking NASA.gov daily, and otherwise finding cool space things to look at and read about.

As you might have guessed, I’m something of a space nerd. Growing up, Carl Sagan’s Cosmos was always playing on the tv, and among other reasons (such as the fabulous Saint Louis Science Center), I’ve had a lifelong passion for science and astronomy. My enthusiasm is manifest in several ways: most visibly, my Billions and Billions of science/space t-shirts, of which three portray Carl Sagan (and two of those also featuring Neil deGrasse Tyson); the sheer amount of Star Trek I watched growing up (TNG especially); and finally, my love of science fiction (recently I spent a year reading through Isaac Asimov’s entire 16-book Foundation compendium—highly recommended!). Warp drives and wormholes aside, space exploration has always struck me as one of the most thrilling, crucial tasks we can undertake as a species.

Clearly, I’m all revved up to write about space. But this is a music blog, after all, and not a space blog. So we’re going to talk about both: in lieu of the New Horizons mission, this series will discuss music that is about, inspired by, or otherwise engages with notions of outer space and cosmology.

To be sure, there’s quite a diversity of ‘space music’ out there. Some of it is familiar to us, such as Gustav Holst’s iconic suite The Planets, Op. 32, a feat of color and orchestration, as well as one of the most fun, engaging pieces of music ever written (and a staple of my childhood, I listened to the Dutoit/Montreal/1987 recording we had on CD constantly). Some of it may not be so familiar: maybe you’ve heard of the jazz visionary Sun Ra, for example, but I bet you don’t know who in the heck Lucia Pamela is. We’ll get there in subsequent posts, but first, someone you’ve heard of (but probably not in the context of music).

JOHANNES KEPLER

Johannes Kepler. Credit: Wikipedia

Johannes Kepler was a German astronomer, mathematician, philosopher, astrologer, polymath, and overall coolguy. One of the key figures in the history of astronomy, he’s credited with discovering the Three Laws of Planetary Motion, which state that:

1. The orbit of a planet is an ellipse (not a circle!) with its sun at one of the two foci (not the center!). Yes, the Earth technically has an elliptical orbit. But its eccentricity is so small (0.0167) that it’s practically circular. Pluto has a higher eccentricity (0.25), so its orbit is comparatively elliptical. And Halley’s Comet, which probably came way, way, way far out from the Oort cloud, has a super-eccentric (0.967) and thereby super-elliptical orbit.

2. In any given amount of time, a line drawn from a planet to its sun will sweep out the same amount of area. For example, any given 10 days of a planetary orbit will sweep out 10 days worth of area, regardless of where the planet is in its orbit.

3. The square of the orbital period of a planet (P²) is proportional to the cube of the semi-major axis (a³) of its orbit. In other words, the length of time it takes a planet to complete an orbit is directly related to the distance from its star. Therefore, the value of (P²)/(a³) is identical for all planets orbiting a particular star. This is a pretty important one, as it led Isaac Newton to discover his Universal Law of Gravitation, which stated that gravity, just like light, becomes weaker the farther away you get from the source (by way of what is called an “inverse square law”).

Great, that’s super cool. But what in Space does Kepler have to do with music? Well, turns out quite a bit. At the monastic school where he was educated, Kepler had weekly lessons in music theory, and partook in the daily singing of four-part psalms and hymns. He was also evidently interested in musical tuning systems, performing various experiments and eventually creating his own. Additionally, he’s part of the gang of mathematicians who wrote or talked about music, which also includes the likes of Newton and Albert Einstein. But for Kepler, music was more than a simple interest: he believed that musical harmony was fundamental to the nature of the cosmos.

In fact, Kepler’s most famous work is called Harmonice Mundi, or “The Harmony of the Worlds”. The basic premise for this work, which contains his Three Laws, is that God (Kepler was a devout Lutheran) created the universe such that certain mathematical or “harmonic” interrelationships stand expressed in natural phenomena. Coming directly from ancient Greek philosophy, this idea (also known as the “concept of congruence”) was shared by a number of giants of the scientific revolution, including Newton, who in his Opticks posited that there were correlations between the color spectrum and the musical scale (a belief subsequently adopted by both Voltaire and Brook Taylor).

Famously, Kepler tried to prove that there was a congruent relationship between the spacings of the planets and the “Platonic solids”, a set of five regular, convex polyhedrons described by Plato. Well-known to the Ancient Greeks (and, supposedly, to the neolithic people of Scotland at least 5,000 years prior), the Platonic solids, in their geometric perfection, have always had a kind of mystical appeal. Indeed, Plato assigned to each one an element (earth, wind, fire, water, and aether), asserting some kind of relationship between the solids and the composition of the universe. And in the spirit of the Greeks, Kepler created an elaborate model of the solar system consisting of the five solids circumscribed by a series of spheres.

Of course, at the end of the day all of this was simply an effort to contrive divine mathematical relationships into existence, and when his model was compared to the scrupulously-recorded data taken from the ridiculous, gold-nosed Tyco Brahe and his equally-ridiculous observatory, Kepler was forced to give up on his intriguing but ultimately goofy Platonic solid theory. The data did, however, lead him to find a successful model of planetary motion in his three laws. Nonetheless, Kepler continued his search for congruence expressed in mathematical relationships.

One such relationship that he sought was that of musical harmony and planetary motion. Kepler’s fascination with the harmony and the harmonic series (also called the overtone series) was indebted to another ancient Greek philosopher, Pythagoras, who discovered that justly-tuned musical intervals, of which the harmonic series consists, can be expressed as simple ratios (i.e. a perfect fifth is constituted by two pitches whose frequencies are in a 3:2 relationship). In a moment of inspiration, Kepler began looking for a way to reconcile harmonic relationships with the orbits of the planets. He first tried, unsuccessfully, to match the ratios of the spacings of the planets with justly tuned intervals: for example, Mars to Jupiter might have constituted a perfect fifth, and so on. But this didn’t really work out, so Kepler tried to assign musical intervals to planets based on the ratios between their maximum and minimum speeds. Turns out, this sort of worked: Earth, for example, with a max-min ratio of about 16:15 (in reality 30.29:29.29), was to be a justly tuned diatonic half step, and Venus, with a 25:24 ratio (actually 35.26:34.79) was a chromatic half step (back when diatonic and chromatic half steps were different things). The implication here is that the intervals Kepler delineated to each planet are reflective of their eccentricity.

The Harmonies of the Worlds. The last one represents Earth’s Moon.

This was a better attempt, and at the time the available data probably fit decently (better than NASA’s current measurements do, at least). But in lieu of Newton’s discovery of the Universal Law of Gravity (in combination with Kepler’s laws), the reality of the situation is that such ratios don’t  depend solely on the eccentricity of a planet’s orbit, but also the mass of the planet, as well as the mass of the planet’s sun. And that simply has to do with the way our solar system happened to form (although to tell the truth, I wasn’t around 5 billion years ago to know how that happened, protoplanetary disks notwithstanding).

The idea that natural phenomena have congruent or ‘harmonic’ relationships is an obvious anthropocentrism: that is, it has more to do with conceiving the universe to be in accordance with one’s personal beliefs (thereby placing humanity at the center) rather than with scientific fact. Of course, an enormous part of science is hypothesis, and for Kepler and Newton, who were at the cutting edge of their fields, it’s perfectly acceptable that not everything they believed was true (not everything I believe is true…), and it’s impossible to underrate their achievements. Still, I find it beautiful and powerful to imagine music and harmony as fundamental to the cosmos, because for me, at least, they are.

To be continued in Part 2: Holst, Mysticism, and ‘The Planets’

Sources:

Grayzeck, Edwin J. “Earth Fact Sheet.” NASA. NASA, 1 July 2013. Web. 20 July 2015.

Grayzeck, Edwin J. “Venus Fact Sheet.” NASA. NASA, 09 May 2014. Web. 20 July 2015.

“The Harmony of the World.” Kepler’s Discovery. N.p., 2007. Web. 12 July 2015.

“Isaac Newton.” Whipple Library. University of Cambridge, n.d. Web. 22 July 2015.

Jeans, Susi, and H. Floris Cohen. “Kepler, Johannes.” Oxford Music Online. Oxford University, 25 July 2013. Web. 10 July 2015.

“Kepler’s Laws.” Georgia State University, n.d. Web. 10 July 2015.

Weisstein, Eric W. “Platonic Solid.” Mathworld. Wolfram Alpha, 16 July 2015. Web. 22 July 2015.