In my pursuit of the philosophy of music, I am often asked, "How do you explain music to students?" My typical answer starts with, "How old are these students?" Are they third graders or graduates? Do they understand mathematics and numbers? Are they art majors or science aficionados? Because the theories of “music” extend far beyond time and well beyond the cosmos.

Come. Take a step into the minds and imaginations of great philosophers ahead of their time. Join me on a journey through the speculative science behind music as we traverse the annals of history and discover how the philosophy of music has shaped our understanding of the world in intriguingly harmonious ways.

Pythagoras, Plato, Aristotle, and Boethius (570 BC–524 AD)

Boethius, in his influential work De Musica (which deals not with practical music making but with music as a speculative science), described three categories of music:

  1. Musica mundana (referred to as musica universalis, or music of the spheres).
  2. Musica humana (the internal music of the human body).
  3. Musica quae in quibusdam constituta est instrumentis (sounds made by singers and instrumentalists).

The doctrine of musica univeralis states that all celestial bodies (stars, moons, and planets) move according to mathematical equations and thus resonate to produce inaudible symphonies. The theory, originating in ancient Greece, was a tenet of Pythagoreanism that incorporates the metaphysical principle that mathematical relationships express qualities or "tones" of energy that manifest in numbers, visual angles, shapes, and sounds – all connected within a pattern of proportion. Boethius believed that musica universalis could only be discovered through the intellect, but that the order found within it was the same as that found in audible music, and that both reflect the beauty of God.

Pythagoras, most securely identified with metempsychosis (“transmigration of souls”) and mathematics, first identified that the “pitch” of a musical note is in inverse proportion to the length of the string that produces it. And that intervals between harmonious sound frequencies form simple numerical ratios. He proposed that all celestial bodies emit their own unique hum based on their orbital revolution and that the quality of life on Earth reflects the tenor of these celestial sounds, which are physically imperceptible to the human ear. Plato (born Aristocles) later described music and astronomy as "twinned" studies of sensory recognition: music for the ears, astronomy for the eyes; both requiring knowledge of numerical proportions.

Aristotle characterised the theory by saying that the motion of bodies of that size and proportion must produce a noise since the motion of bodies on earth that are far inferior in size and speed also have that effect. He noted:

Their speeds (measured by their distance proportions) are in the same ratios as musical concordances. They assert that the sound given forth by the circular movement of the stars is harmony. Since, however, it appears unaccountable that we should not hear this music, the sound in our ears from the very moment of birth is thus indistinguishable from its contrary silence. Since sound and silence are discriminated by mutual contrast: What happens to men, then, is just what happens to coppersmiths, who are so accustomed to the noise of the smithy that it makes no difference to them.

Johannes Kepler (1571–1630)

The idea behind musica universalis continued to appeal to scholars until the end of the Renaissance, influencing many schools of thought, including humanism. This idea later stimulated the imaginations of Johannes Kepler, as he devoted much of his time after publishing the Mysterium Cosmographicum (Mystery of the Cosmos) [1596, and an expanded second edition in 1621] to looking over tables and trying to fit the data to what he believed to be the true nature of the cosmos as it relates to musical sound.

Kepler did not believe this "music" to be audible but felt that it could nevertheless be heard by the soul. And that it gave him a "very agreeable feeling of bliss, afforded him by this music in the imitation of God." In 1619, Kepler published Harmonices Mundi (Harmonies of the World), expanding on the concepts he introduced in Mysterium and positing that musical intervals and harmonies describe the motions of the six known planets of the time.

Kepler laid out an argument for a Creator who had made an explicit connection between geometry, astronomy, and music, and that the planets were arranged intelligently. He was certain of the link between musical harmonies and the harmonies of the heavens. He believed that "man, the imitator of the Creator," had emulated the polyphony of the heavens to enjoy "the continuous duration of the time of the world in a fraction of an hour."

For there is music wherever there is harmony, order, or proportion. And thus far, we may maintain the music of the spheres. For those well-ordered motions, and regular paces, though they give no sound to the ears, yet to the understanding, they strike a note most full of harmony. Whatever is harmonically composed, delights in harmony.

While Kepler did believe that the harmony of the worlds was inaudible, he related the motions of the planets to musical concepts. He made an analogy between comparing the extreme speeds of one planet and the extreme speeds of multiple planets with the difference between monophonic and polyphonic music. Because planets with larger eccentricities have a greater variation in speed, they produce more "notes."

Earth's maximum and minimum speeds, for instance, are in a ratio of roughly 16 to 15, or that of a semitone. Whereas Venus' orbit is nearly circular, and therefore only produces a singular note, Mercury, which has the largest eccentricity, has the largest interval, a minor tenth, or a ratio of 12 to 5.

This range, as well as the relative speeds between the planets, led Kepler to conclude that the Solar System was composed of:

  1. 1 soprano (Mercury).
  2. 2 altos (Venus and Earth).
  3. 1 tenor (Mars).
  4. 2 basses (Jupiter and Saturn).

And these “notes” had sung in "perfect concord" at the beginning of time and could potentially arrange themselves to do so again.

Kepler's laws of planetary motion (1602–1618)

Kepler stated that the five platonic solids (octahedron, icosahedron, dodecahedron, tetrahedron, and cube) define the orbits of the planets, in chronological order from the sun, and their distances from the sun. Kepler presented a metaphysical basis for this system, along with arguments as to why the harmony of the worlds appeals to the intellectual soul in the same manner that the harmony of music appeals to the human soul. Kepler describes in detail the orbital motion of the planets and how this motion nearly perfectly matches musical harmonies.

For any planet, the squares of the periodic times are to each other as the cubes of the mean distances.

(Kepler’s third law, 1618)

In Astronomia Nova (New Astronomy), Kepler explained how the ratio of the maximum and minimum angular speeds of each planet (i.e., its speeds at the perihelion and aphelion) is quite nearly equivalent to a consonant musical interval. Based on measurements of the aphelion and perihelion of Mars, he created a formula in which a planet's rate of motion is inversely proportional to its distance from the Sun. Later, he reformulated the proportion in terms of geometrical rate law to conclude:

Planets sweep out equal areas at equal times.

(Kepler’s second law, 1602)

He then set about calculating the entire orbit of Mars using the geometrical rate law and assuming an egg-shaped ovoid orbit. Two years and approximately 40 failed attempts later, he hit upon the idea of an ellipse, which he had previously assumed to be too simple a solution for earlier astronomers to have overlooked. Finding that an elliptical orbit fit the Mars data (Vicarious Hypothesis), Kepler concluded:

All planets move in ellipses, with the Sun at one focus.

(Kepler’s first law, 1604)

Conclusion

Returning to the question, “How do I explain music to students?” I invite them to consider: Are we dancers moving in proportion to the harmony emitted by celestial beings? Or are we akin to the mathematikoi ("learners" under Pythagoreanism) who possess the rationale to listen, observe, understand, conceptualise, transcribe, and recreate those harmonies into "tones"? And if we do, does that make us musicians? Or are we still simply akousmatikoi (“listeners”), weaving tunes ritualistically in reverence to our gods?

Ultimately, the exploration of music, whether through the audible sounds of instruments or the silent symphonies of the cosmos, is a journey into the heart of existence itself. By delving deeper into the principles of musica, we not only gain insight into the mathematical and philosophical foundations of harmony but also connect with a timeless tradition that sees the universe as a grand, orchestrated work of art reflecting the beauty of our creator.

In this way, music becomes more than just an art form or a science; it becomes a universal language that speaks to the very essence of our being through the harmonies emitted by the spheres and our souls. Whatever is harmonically composed, delights in harmony.