Disharmony of the Spheres 


This scream of pain delivered with the intensity of a banshee wail came from the poor, suffering HISTSCI_HULK upon reading an essay on The Conversation (Europe), A hymn to the stars: what happens when science puts the universe into music by the astronomer, Yaël Nazé.  

The Conversations banner states, Academic rigour, journalistic flair. Apparently, that bit about academic rigour doesn’t apply when an astronomer tries her hand at the history of science. 

The article is actually about sonification, which Ms Nazé turns her attention to rather briefly at the end of her essay. Sonification is a new technique in astronomy of turning satellite astronomical data into sound making the data available to blind people (as this article explains) but possibly revealing other aspects of the data not revealed by visualisation of the data.

There are other explanatory articles, both better than Nazé’s effort, here, and here

However, Ms Nazé thought she could give her essay on the topic a different spin by prefacing her comments on sonification with a look at the historical harmony of the spheres, a topic that should be well known to regular readers of this blog, and it is here that she caused old HULKY such anguish and drove him to distraction. Let us examine her excursion into the chilly waters of the history of science:

Music and astronomy: an ancient love story

Music and space might not seem like natural partners – after all, no air means no sound. But to our forebears, the links were obvious. In Ancient Greece, thinkers such as Aristotle believed the Earth lay at the centre of the universe. This didn’t make it an unchanging ideal, however: to the ancients, terrestrial phenomena were ever-changing, a reflection of our planet’s imperfection. The sky, by contrast, was seen as immutable and eternal, and so worthy of emulation.

Well, it might be true that “no air means no sound”, but our forebears had no idea that there was no air in the heavens. Not just Aristotle, but it was obvious to almost anybody with half a brain that the Earth lies immobile at the centre of the visible heavens. It’s actually very, very difficult to prove otherwise, without a couple of thousand years of evolution of astronomy.  

There is more:

A few of the stars moved with respect to others – so-called “planets” in the etymological sense (for planet means “wandering star”). The ancients knew of seven of them: Mercury, Venus, Mars, Jupiter and Saturn, plus the Sun and the Moon. That number would go on to inform the composition of the days of the week as well as of the music scale.

Planet does not mean “wandering star”, it simply means wanderer. The Greek expression for wandering stars is asteres planetai,” from planasthai “to wander, asteres is of course stars. If you are trying to prove your linguistic sophistication, it pays to get things right. 

The next sentence is simply bullshit. There was an intense discussion on HASTRO_L recently as to where the seven-day week comes from. The answer is we don’t actually know but it certainly predates the astrological week, which gave the weekdays their names based on the planetary hour that begins each day, which seems to be what Ms Nazé is referencing. Ms Nazé obviously doesn’t know very much about music as the seven-tone scale, most commonly used in western music, is only one of numerous music scales with varying numbers of tones. The Pythagorean scale, which is actually from ancient Mesopotamia and falsely attributed to Pythagoras is a twelve-tone scale. Very widespread throughout the world are pentatonic scales with five-tones. The oldest form of Greek music was based on the tetrachord, a scale of just four-tones. I could go one…

On a sidenote although Ms Nazé links to a rather bizarre website about Pythagorean music theory, as error strewn as her own efforts, nowhere in her excurse on harmony of the spheres does she mention the Pythagoreans, who actually invented the concept

Ms Nazé can be very inventive:

Indeed, to the Ancient Greeks, each planet hung on a sphere, which, in turn, revolved around the Earth. Given that movement emitted sound here – such as when two objects rubbed against one another or when feet hit the ground – it made sense that the moving spheres in the cosmos should also produce sounds. 

I have no idea where she got this idea, and although I’ve read quite a lot about the harmony of the spheres, I’ve never come across an explanation remotely like this, so I must assume she simply made it up. Especially, as according to most accounts the music of the spheres could not be heard by normal mortals.

Contrary to those heard on Earth, these were thought to be perfect, prompting the Ancients to use the stars as a template for terrestrial music. [my emphasis]

They didn’t! What the Pythagoreans did was to apply the concept of terrestrial music to the planets.

This is why in the Middle Ages astronomy and music were grouped together in the quadrivium, which also included arithmetic and geometry, and lay the foundations of the liberal arts education.

Astronomy and music, the theory of proportions, were both part of the quadrivium–arithmetic, geometry, music, astronomy­–but arithmetic and music were paired, and geometry and astronomy were paired. Music was arithmetic in motion, and astronomy was geometry in motion. 

But how to weave together notes and planets? This is admittedly the trickiest part. Some scientists have linked a sound’s pitch to a planet’s distance, others with its speed. To add more intricacy to the compositions, at the time perceptions differed in the relative positions of the planets in the solar system.

Of course, the use of the term scientist is totally anachronistic, the people in question are astronomers or philosophers. Once again, I fear that Ms Nazé is simply making things up. I know of no great technical discussion, as to just how the music of the spheres was created. 

The German astronomer Johannes Kepler (1571-1630) was one of the scientists to most notably draw on this Ancient Greek concept of “music of the spheres” (also known as musica universalis) to map out the planetary system. 

She got something right! But it doesn’t last

Kepler’s findings would catapult us into the modern cosmos: he determined that not only was the Sun not at the centre of the solar system – as Nicolaus Copernicus had proposed in the previous century – but also that the planets revolved around it in an elliptical rather than circular motion. 

[“…he determined that not only was the Sun not at the centre of the solar system…” Wow! Some really bad copy editing here. That should, of course, read the Earth. Even corrected it’s not true. Kepler, like everybody else, couldn’t actually deliver proof of the cosmos was heliocentric.]

Addendum 5 February: As can be seen in the comments a debate has developed in the comments about Ms Nazé’s  statement and my interpretation of it, which I now believe to be wrong and have placed in square brackets. I think she is correctly saying that Kepler removed the Sun from the centre of a circle, where Copernicus had placed it and positioned at at one focus of an ellipse. It is actually correct to point out that in Copernicus’ system the Sun is not actually at the centre of the circle but, for mathematical reasons, slightly offset and in reality his system is strictly taken not heliocentric but heliostatic. However, as most people are not actually aware of this, I’m going to be generous and not criticise her for saying that Copernicus had placed the Sun at the centre of the solar system.

As a result, distance and speed changed in the course of the orbit. It became impossible to associate a single note with a single planet, driving him to the conclusion that planets sung melodies.

Here we have something that gets repeated ad nauseum on the Internet. By showing that the planetary orbits were ellipses, Kepler did not show that “distance and speed changed in the course of the orbit.” This had been known for centuries, as could be demonstrated by any good set of ephemerides. What he did, with his elliptical orbits, was to show why this was the case.

The bit about single notes and melodies is once again made up. In his Harmonice Mundi, Kepler investigated every possible arithmetical ratio of all aspects of a planets orbit, looking for harmonic ratios–octave, thirds, fifths etc. Out of these he then constructed melodies for each planet.

Of course, all this had to remain harmonious: for a planet to produce a melody, the highest sound had to chime well with the lowest. Eventually, Kepler abandoned his tunes to concentrate on spelling out his third law on planetary motion in 1619. [my emphasis]

It was at this point, that the HISTSCI_HULK, who had become increasingly agitated as he perused Ms Nazé’s essay. Let out the scream of anguish with which I opened this post.

Let us repeat her sentence:

Eventually, Kepler abandoned his tunes to concentrate on spelling out his third law on planetary motion in 1619.

It would appear that Ms Nazé is not aware of the name of Kepler’s third law or where it originated. The third law is the Harmony Law and is the high point of the Harmonice Mundi! Far from abandoning his tunes, Kepler saw the discovery of his Harmony Law, as validation of his investigations of the harmony of the spheres. 


Filed under History of Astronomy

16 responses to “Disharmony of the Spheres 

  1. Valeriu

    ‘ “…he determined that not only was the Sun not at the centre of the solar system…” Wow! Some really had copy editing here.’

    Charitable reading: she meant the Sun was excentric, i.e. not really at the center of the system.

    • Actually, you’re right, will edit later

    • typo: “bad”, not “had”.

      I don’t think the charitable reading works, since in the same sentence she says that Copernicus had proposed this in the previous century. Copernicus also had eccentric orbits for the planets (with epicycles as well), so Kepler didn’t correct him on that point.

      But we can be charitable with the first quote. She doesn’t actually claim that the ancient Greeks knew that space is air-free. Interpret the first sentence as referring only to modern sensibilities. Her statement about Aristotle is correct, even if it understates the case. And then there’s Aristarchos, so you can’t say that geocentricity was obvious to everybody in ancient times. Proof is another matter, but she doesn’t bring it up here.

      Since her post goes way off the rails pretty quickly, you have plenty of material to criticize without this. (But your blog, your choice, of course.)

      • Michael Wright

        I think that parenthesis about Copernicus is ambiguous: it could be read either as saying that Copernicus had proposed that the Sun was at the centre of the system, or that he had proposed that it was not. Not to mention how hard it is to tell whether or not “Sun” is a typo for “Earth.”

      • As I interpret what she says about “no air means no sound” leading on to a silent despite this, I remain by my criticism.

        So, one man in Antiquity, according to hearsay proposed a non-geocentric system, about which we know no details whatsoever, especially not his motivation for doing so of his justification for having done so. I apologise, but I did say almost anybody!

  2. “What he did, with his elliptical orbits, was to show why this was the case.”

    Not sure what you mean by this. Kepler had non-uniform speed long before he came up with the elliptical orbit. First with an equant, then later with his 2nd law, which as you know quite well he discovered before his first.

    He also had eccentric circular orbits before he came up with the ellipse.

    Whether the 1st and 2nd laws really explain why the distance and speed changes, well that’s a philosophical question.

    • That the orbits are ellipses with the Sun at one focus and the planets are driven around there orbits by a constant force emanating from the Sun, as Kepler hypothesised, perfectly explains why the planets speed in non-uniform.

      • Okay, so you’re combining the elliptical orbits with Kepler’s physics. Makes sense. But I will note, as you already know from Voelkel’s book, that Kepler had eccentric circular orbits with the same physics well before he came up with the elliptical orbit, which led him to his 2nd law well before his 1st.

        Also, the elliptical orbit is a second-order effect—the eccentric circle plus the 2nd law accounts for almost all of the non-uniformity. (The famous 8 seconds being the residuum that ultimately led him to the ellipse.)

      • We only know about Kepler’s earlier but rejected models for the orbit of Mars, because he discussed them in his correspondence and in the text of his Astronomia Nova. He never presented them as finished or conclusive, but discusses why he rejected them. What he presented the world as the conclusion of his efforts was his first two laws of planetary motion, as they are still taught today.

    • Eight minutes of arc, Michael, not eight seconds.

  3. You would think at some point that authors and editors of books dealing with the history of astronomy would learn to submit their work to HISTSCI_HULK for review prior to publication, in order to avert being pilloried.

  4. Two small typos:
    but possibly revealing other aspects of the data not reveal by visualisation of the data. revealed

    There are other explanatory articles, both better that Nazé’s effort, here, and here missing hyperlink on second here

    I have had cause on several occasions before to point out errors of fact in “The Conversation” articles. Unfortunately, with them blocking all comments on many of their articles it is becoming increasingly difficult. This one though is by a long way the worst I have come across.

  5. YT

    Excellent article. Although, for what it’s worth, the idea of the eight spheres, from the stars to the moon, these two extremes being “in agreement” (so, I guess, an octave apart?), together producing the eight sounds of a scale can be found in Cicero’s Dream of Scipio. Is this where Ms Nazé took it from? no idea.

    • YT

      (There too is the idea that it is the movement of the spheres that produces their sounds (the faster, the higher note), which cannot be heard by mortals only because they have grown deaf to it by constant exposure.)

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