Music Of The Spheres

Pythagoras taught that the entire cosmos is structured according to harmonic principles, just like a perfectly tuned musical instrument.He believed that the planets, stars, and heavenly bodies moved according to mathematical ratios - the same ratios that create harmonious musical intervals - and that their movements produced a kind of grand, cosmic music: the "Music of the Spheres" (Musica Universalis)

This whole number ratios found in music are:

• Octave = 2:1

• Perfect Fifth = 3:2

• Perfect Fourth = 4:3

• Major Third = 5:4

• Minor Third = 6:5

Harmonics, overtones

So the law of harmony which we find in music works on simple integer numbers. In other words if we take frequency, only whose will sound harmonically together which form this integer number-based relationships. Say, if we take note "A" = 110 Hz and double it we will have another "A", but 220 Hz but octave higher.

Because the wavelength of the fundamental frequency fits ideally with that of octave higher - two wavelengths fit into one fundamental wavelength.

If we triple 330 Hz we will get a perfect fifth and so on.

Also as you can see one note contains all others, this is what is called harmonics.

Harmonics of A2 ( 110 Hz )

The first few harmonics create music itself: A (root), E (5th), C# (major 3rd).

That’s literally an A major chord hidden inside one note.

So what is have to do with the planetary motions ?

It turns out that the harmonic series is not arbitrary. One note already contains a whole architecture of order. What appears in vibrating strings, phenomenon called standing waves is also found in the planetary motion.

Johannes Kepler and the Third Law of Planetary Motion

Johannes Kepler

Johannes Kepler  transformed our understanding of the universe. He lived at the turning point between ancient symbolic cosmology and modern science - and uniquely, he carried both.

Johannes Kepler was a German astronomer, who was also a musician. The most famous work of his works - Harmonices mundi libri V ("Five Books About World Harmony"), as if it were a piece of music which he had written

about , and not the planets.

Johannes Kepler  transformed our understanding of the universe. He lived at the turning point between ancient symbolic cosmology and modern science - and uniquely, he carried both.

Kepler's Three Laws of Planetary Motion (foundation of astronomy)

Kepler was the first one to notice, that celestial bodies move in elliptic orbit, and not circular. According to Kepler, God caused the planets to leave initially inherent circular orbits and to adopt complicated elliptic orbits to produce even more beautiful sounds. What is remarkable is that the planets in our solar system from the unlimited possibilities of orbits - chosen that orbits which oscillate and sound in proportions prevalent in our "earthly music"

Harmonices Mundi

The Three Laws:

1. Elliptical Orbits

Planets move in ellipses with the Sun at one focus.

2. Equal Areas in Equal Times

   A planet moves faster when closer to the Sun, slower when farther away.

3. Harmonic Law

   The square of a planet’s orbital period is proportional to the cube of its distance:

T2∝r3

This third law is literally a cosmic harmonic relationship - like a deep-scale version of musical ratios.

In his book Harmonices Mundi (1619), Kepler proposed something radical: Planets “sing” as they move. Not in sound you can hear, but in mathematical ratios equivalent to musical intervals. Each planet has a range of motion (fast ↔ slow). That range corresponds to a musical interval.

Example:

• Earth - small interval (like a semitone)

• Mercury - wide interval (almost a full scale)

Kepler indeed proved in his Third Law of Planetary Motion the concept of Music of the Spheres described by Pythagoras thousands years before him.

Willie Ruff and John Rodgers of Yale University programmed the angular velocities of the planets into a synthesiser. They followed precisely to Kepler’s orbital data (not modern recordings of electromagnetic “sounds” from space, but the mathematical relationships of orbital speeds) and transformed orbital mechanics into audible frequencies.

The piece of music they produced is called The Harmony of the World: The Song of the Planets (1979) as a direct homage to Kepler’s Harmonices Mundi. To nobody surprise , the sounds of the planet correspond to traditionally attributes qualities of this planets.Mercury - fast and relentless "The Messenger of Gods" .Mars, restless in its sharper intervals, pulses with urgency and heat. Venus, by contrast, hardly shifts her pitch, holding a nearly perfect constancy that mirrors her ancient reputation for balance, beauty, and enduring love. The Earth, with her plaintive Mi–Fa–Mi, seems to sigh in the very syllables Kepler once heard - a song of struggle, but also of faith, carried faithfully through the seasons. Jupiter has a majestic sound similar to church organ, and Saturn produce deep-mysterious drone.The sound spectrum of the six visible planets including Earth covers eight octaves, almost identical with the human hearing range. You can listen to this song in the internet.

After Kepler's death, three further planets (Uranus, Neptune, Pluto) were discovered, and of course their orbits also fit perfectly into Kepler's laws, corroborating them. Since these planets have very low orbital velocities (Pluto's orbit around the sun, for example, takes 248 years), their transposition into sound would be below the human hearing capacity. The orbital ellipses of these outer planets, however, can be made audible to the human ear as rhythms, because rhythm have lower vibrations than tones. Ruff, who is not only a scientist but also a jazz musician, commented: "I knew there just had to be rhythm out there."

All this summarised: The six visible planets with their elliptical orbits form a "six-part harmony motet" (expression coined by Kepler) and the three outer planets add the "rhythm section" (in Ruff's words) in which Pluto, the most distant, beats the cosmic "bass drum".

The Kepler's Laws are not just historical ideas. They are actively used today in modern technology, space missions, and even Earth systems. The 3rd Law is huge for Planetary Science & Astronomy. It is used to calculate distance of planets from stars and to discover exoplanets. Scientists observe how long a planet takes to orbit, use Kepler's law and find its distance and mass relationships. Even at extreme scales: stars orbiting black holes, matter spinning in accretion disks. Kepler’s laws (with Newton/Einstein corrections) still apply as a base model.

We discussed the planets, but how about the moons ?

For example Jupiter’s moons Io, Europa, and Ganymede follow 1 : 2 : 4 resonance

Image of Saturn. NASA

Saturn’s system also shows beautiful whole-number resonances. The moons Enceladus and Dione orbit in a 2:1 ratio. Enceladus completes 2 orbits. while Dione completes 1 orbit.This gravitational resonance is extremely important because it: flexes Enceladus internally, produces tidal heating, powers its famous water geysers. So a simple musical ratio literally drives geological activity on that moon. Another pair is Mimas and Tethys. They also follow a 2 : 1 orbital resonance. Again octave.Because of this their gravitational pulls repeat in a regular rhythm and their orbital shapes remain stable for millions of years. A more unusual ratio appears between Titan and Hyperion. Their orbital relationship is approximately 4 : 3. Meaning that Titan completes 4 orbits while Hyperion completes 3. The 4:3 ratio corresponds to the perfect fourth in music. If you converted orbital periods into sound frequencies, the moons of Saturn and Jupiter would literally form harmonic chords evolving over time. That’s why astronomers sometimes describe planetary systems as a real physical version of the ancient idea of the “music of the cosmos.”

Saturn's rings. NASA

Saturn’s moons also shape the rings. For example, gaps in the rings appear where ring particles fall into resonance with moons. One famous gap is the Cassini Division, created partly by resonance with Mimas, discovered by by Giovanni Domenico Cassini in 1675.This particles also follow the 2:1 ratio, but with the moon - Mimas. On top of that, rings themselves act as the giant resonating disk. The rings of Saturn are made of countless ice particles orbiting the planet. When moons gravitationally pull on the ring particles, they create density waves - spiral ripple patterns moving through the rings. Think of a drumhead being struck. But in Saturn’s case, the waves are created by orbital resonance.When a ring particle orbits in a simple ratio with a moon, the gravitational pull repeats at the same location each orbit. Ring particles in a 2:1 resonance with Mimas get pulled every second orbit. This repeated “kick” creates a standing wave pattern in the ring.Something even more fascinating happens, Saturn himself plays the rings. The internal oscillations of Saturn (like seismic vibrations) create gravitational ripples that propagate into the rings. This phenomenon is studied in ring seismology. Scientists discovered that: Saturn vibrates with internal modes, these modes create wave patterns in the rings - the rings act like a giant detector. So astronomers can literally study Saturn’s internal structure by observing waves in the rings.Why is this like a drum ? A drumhead vibrates in standing wave modes. Each mode forms a specific geometric pattern. Saturn’s rings show analogous modes, caused by orbital resonances and planetary oscillations, so the rings behave like a cosmic drum membrane.

Nikita Ierisov

Philosopher, Jyotish Astrologer