Music of the Spheres -- The Story

Music of the Spheres consists of twelve pieces inspired by the ancient Pythagorean conception of the Universe. It includes a wealth of musical symbolism based on almost a year of William's research into ancient through modern cosmology—mostly reading the ancient writers directly.

William writes:

The "Music of the Spheres" was an understanding of the Cosmos that held sway for about 2000 years. According to this view, each of the planets rode on giant crystal spheres, and each of these planetary crystal spheres emitted a musical sound as they moved. The combined sound of all the planets was "the Music of the Spheres".

The Music of the Spheres in Plato

William Zeitler Playing the Glass Armonica at Stonehenge

The original concept of the "Music of the Spheres" is credited to Pythagoras (c.569–475 BC), a musical-mathematical-mystic, but its first surviving written account appears in Plato (c.427–347 BC). At the end of his Republic, the spirits are giving Socrates a tour of the afterlife and a view of the planetary spheres. But for Plato they aren't true spheres, they are hemispheres, nested inside of each other with just the rims exposed, all rotating on a giant spindle of light, with a Siren assigned to each rim singing a note. (See the album cover above.) Here is the passage:

Now when the spirits which were in the meadow had tarried seven days, on the eighth they were obliged to proceed on their journey, and, on the fourth day after, he said that they came to a place where they could see from above a line of light, straight as a column, extending right through the whole heaven and through the earth, in colour resembling the rainbow, only brighter and purer; another day's journey brought them to the place, and there, in the midst of the light, they saw the ends of the chains of heaven let down from above: for this light is the belt of heaven, and holds together the circle of the universe, like the under-girders of a trireme. From these ends is extended the spindle of Necessity, on which all the revolutions turn. The shaft and hook of this spindle are made of steel, and the whorl is made partly of steel and also partly of other materials. Now the whorl is in form like the whorl used on earth; and the description of it implied that there is one large hollow whorl which is quite scooped out, and into this is fitted another lesser one, and another, and another, and four others, making eight in all, like vessels which fit into one another; the whorls show their edges on the upper side, and on their lower side all together form one continuous whorl. This is pierced by the spindle, which is driven home through the centre of the eighth. The first and outermost whorl has the rim broadest, and the seven inner whorls are narrower, in the following proportions --the sixth is next to the first in size, the fourth next to the sixth; then comes the eighth; the seventh is fifth, the fifth is sixth, the third is seventh, last and eighth comes the second. The largest (of fixed stars) is spangled, and the seventh (or sun) is brightest; the eighth (or moon) coloured by the reflected light of the seventh; the second and fifth (Saturn and Mercury) are in colour like one another, and yellower than the preceding; the third (Venus) has the whitest light; the fourth (Mars) is reddish; the sixth (Jupiter) is in whiteness second. Now the whole spindle has the same motion; but, as the whole revolves in one direction, the seven inner circles move slowly in the other, and of these the swiftest is the eighth; next in swiftness are the seventh, sixth, and fifth, which move together; third in swiftness appeared to move according to the law of this reversed motion the fourth; the third appeared fourth and the second fifth. The spindle turns on the knees of Necessity; and on the upper surface of each circle is a siren, who goes round with them, hymning a single tone or note. (Republic, 10)

The word here translated 'whorl' (SPHONDOLOS) is quite complex: it can mean 'vertebra', 'the circular whorl which balances and twirls a spindle', and the head of an artichoke. (See A Greek-English Lexicon (unabridged), Liddell-Scott).

In short, in Plato's view, the Cosmos is an enormous GLASS ARMONICA in the sky! If Plato's Sirens merely touched their rims with moistened fingers instead of singing, we'd be crediting Plato with the invention of the glass armonica instead of Benjamin Franklin (1706–1790).

The Music of the Spheres in Kepler

The concept of the Music of the Spheres probably found its greatest literal expression in the works of Johannes Kepler (1571–1630), who is now considered one of the founders of modern astrophysics. Kepler constructed a musical/mathematical theory of the solar system from which he derived his famous Kepler's Laws —one of the major foundations of Newton's physics and still taught in physics courses today.

The Celestial Spheres were making Music all the way from Pythagoras until Isaac Newton (1642–1727)—over 2000 years. Then, Newton founded modern science, and the Music stopped. Before Newton the Cosmos was full of Music; with Newton and modern science the Cosmos fell silent.

The Music of the Spheres and the Afterlife

In the Greek Gnostic imagination, when You were born you descended from the heavens, passing through the Spheres on your way to life on Earth, pausing at each sphere to acquire the quality associated with that Sphere. When you died, you ascended through the Spheres on your way to the afterlife, pausing at each Sphere once again to address the aspect of your life associated with that sphere—your "warrior" at Mars, your "lover" at Venus, etc. And since each of these is a musical sphere, it was of course the Muses who escorted you on your final journey.

The MUSICAL SYMBOLISM of the Individual Tracks

In the history of Western civilization until relatively recent times the line between "science" and "magic" has been rather fuzzy. This would certainly be true of Pythagoras, to whom is ascribed both the idea of "mathematical proof" and the invention of mystic "numerology". This blurring between "science" and "magic" was still true through Newton: recent research suggests that Newton himself may have gotten some of his important ideas for modern physics from his extensive alchemical experiments. Newton was also heavily involved in esoteric Bible research.

Consequently I felt that the Music of the Spheres ought to have both "mathematical" and "mystical" elements drawn from the history and lore of the Music of the Spheres.


In the ancient Music of the Spheres model, the Earth is at the center of the Cosmos. Ancient thinkers developed a mathematical model based on this assumption that allowed them to predict the positions of the planets in the night sky. These efforts reached their culmination in Ptolemy (c. 87–150 AD). His most famous work, the Almagest, was a mathematical treatise on practical astronomy that worked within the accuracy of the astronomical instruments then available, and was the standard work on mathematical astronomy until the 16th century. As technology improved, so did astronomical measurements, and discrepancies between Ptolemy's system and the new improved measurements ultimately resulted in Ptolemy's system being replaced by the model developed by Copernicus, Galileo, Kepler and Newton. (As the accuracy of measurements continued to improve, Newton's model was itself replaced by Einstein's for exactly the same reason.)

Ptolemy's Epicycles
If you follow the positions of the planets in the night sky, it quickly becomes apparent that they move in complicated ways. The Ptolemaic theory accounted for these complications by assuming that the planets move in circles within circles, called "Epicycles".

Tracks of the Music of the Spheres album use the actual Ptolemaic ratios of the planets in musical ways (discussed below in the section about the tracks themselves).

Ptolemy's model—that the planets moved in "circles within circles"—was later replaced by Kepler's model—that planets move in ellipses with the sun at one of the foci. (But it can be shown mathematically that Kepler's model is a special case of Ptolemy's more general model).

The Ptolemaic ratios would be a "mathematical" dimension of the Music of the Spheres.


Pythagoras taught that everything is arranged and defined by Number — which is still an axiom of modern science. The Pythagoreans went further, however, and asserted that "Number represents a celestial power working in the divine sphere, a veritable blueprint of creation. Consequently Number is itself divine and associated with the divinities." [JCSG p.25]

Numerology is the study of the mystical significance of numbers. In numerology, a number is assigned to each letter of the alphabet, so if you add up all the numbers that correspond to the letters in, for example, your name, you will arrive at a unique number that has mystical significance for you. An ancient form of numerology called "gematria" (geh-MAY-tree-uh) goes back to Babylonian times, around 700 BCE. [JCSG p.27]. By the time of Pythagoras, two centuries later, gematria was probably well known to the Pythagorean School. [JCSG p. 75]

In modern times we have a separate set of characters for our numbers ('0' through '9') as opposed to our alphabet ('A' through 'Z'). But the ancient Greeks used their alphabet for both numbers and letters:

The Greek Alphabet & Numbers (for Gematria)

Thus, in ancient Greece, you would write "123" as "Rho-Kappa-Gamma." For numbers greater than 1000 they'd add an accent mark ('), so "123,123" would be rho', kappa', gamma', rho, kappa, gamma. Thus they could express numbers up to one million—more than adequate for most accounting purposes. The ancient Greek reader would have to distinguish between words and numbers by context.

Because, for the ancient Greeks, the letters of their alphabet were already assigned to numbers, their cognitive leap to gematria would be much smaller than ours today.

Gematria was used heavily in early Christianity, and even occurs in the New Testament itself:

"Here is wisdom. The one having understanding, let him count the number of the wild-beast, for it is the number of a man. And his number is six hundred sixty six." (Rev.13:18)

Interestingly, the gematria value of 'Jesus' is '888'.

For "musical gematria" in the same spirit, here is an example of a simple mapping of rhythms to the ancient Greek alphabet that was used on one of the tracks:

An Example of Musical Gematria Using the Greek Alphabet

Naturally, when doing Greek gematria like this, you would want to use the ancient Greek names of the planets.

Gematria would be a "mystical" dimension of the Music of the Spheres.

The Circle of Fifths

Circles play a central role in the Music of the Spheres, and the most famous circle in music is the "Circle of Fifths". Here's how it works:

If you sing to yourself the "Do-Re-Mi-Fa-So…" song, the two notes Do and So are a fifth apart.

An Example of Musical Gematria Using the Greek Alphabet

Pythagoras discovered that the fifth, or the "perfect fifth" as it is also known, is governed by a simple mathematical property: if you have two strings at the same tension and identical in every way except that the lengths are in a ratio of 2 to 3 (for example, the first string is 2 feet long and the second is 3 feet long), the two strings will always sound a perfect fifth from each other.

If you start at Middle C, and move to the note a fifth above that (G), and then the note a fifth above that (D), after 12 of these steps you'll be back to C again—hence it's a "circle".

Consequently a sojourn through the circular Spheres would naturally have to use the Circle of Fifths. And, in fact, starting with Earth, the ascent through the planets on the Music of the Spheres album ascends through the circle of fifths.

The Musical Symbolism of the Individual Tracks:

The fundamental concept of Music of the Spheres is to portray the soul's final journey from life on Earth ascending through the planetary spheres to the Afterlife.

On the soul's journey to the afterlife, I imagined that "understanding" would be the priority of the first half, but "acceptance" would be the priority of the second.

Consequently, both the Ptolemaic ratios and Musical Gematria are only used in the "first half" planets (since they fall in the "understanding" portion of the soul's journey), but not in the second half (since they are concerned with the "acceptance" portion of the soul's journey).

NOTE: there are only seven planets on Music of the Spheres because only seven "planets" (including the sun and moon) are visible with the naked eye. Seven was the total number of known planets until 1781, when Neptune was discovered by William Herschel.)

1. Earth

This is, musically speaking, the simplest piece on the album. I'm reminded of that saying: "Now we see in a mirror dimly, but then face to face." The imagination for this track is that we know nothing now, but after death all will be made clear. Given how little we are able to understand in this life, there is a certain logic to "Eat, drink, and be merry!" I used no Musical Gematria or Ptolemaic ratios on this track. I imagined this as my "Mr. Roger's Neighborhood" track—appropriate for children, which metaphysically speaking is what we are in Life on Earth.

2. Moon - the Sphere of Intuition

The music for all of the other planetary spheres is very structured; that for the Moon is not at all—it's "constructed"entirely intuitively. It's also the first sphere you'd visit after leaving your life on earth, so there would be shock and confusion, and wonder.

Both Musical Gematria and Ptolemaic ratios were used on this track.

3. Mercury - the Sphere of the Mind

The Sphere of the Mind is boundlessly optimistic: everything is ultimately understandable by the mind. At least that's the assumption of the mind in general—and modern science.

Both Musical Gematria and Ptolemaic ratios were used on this track.

4. Venus - the Sphere of Love

At the Sphere of Venus the soul pauses to reflect on all of the ways that Love manifested itself during life. Love is a two edged sword: sometimes it is bliss, and sometimes it is sorrow.

Both Musical Gematria and Ptolemaic ratios were used on this track.

5. The Sun- the Sphere of the Will

This is the halfway point of the soul's journey to the afterlife. Up to this point the soul has largely been concerned with "understanding". The focus now shifts to "acceptance".

Musical Gematria and Ptolemaic ratios were not used on this track, nor on any subsequent tracks, as the soul finishes the second half of its journey.

6. Mars, the Sphere of the Warrior

At the Sphere of Mars the soul pauses to reflect on all of the ways that it had to be a Warrior during earthly Life.

7. Jupiter, the Sphere of Aspirations

At the Sphere of Jupiter the soul pauses to reflect on all of its aspirations during life; how they gave life so much meaning; how they must all be left behind now for the greatest aspiration of all—God—which is now its destination.

8. Saturn, the Sphere of Wisdom

At the Sphere of Saturn the soul pauses at the last sphere in the ordinary Cosmos to experience true wisdom for the first time (because all other earthly concerns have been left behind). It is now time to cross over into the next realm.

9. The Fixed Stars, the Frontier to the Beyond

You'll notice that there's a fixed note that plays on the wine glass chorus all the way through this piece, and the armonica does its musical thing against that fixed note. The fixed note gently fades in and out, "twinkling" in slow motion, but it's present all the way through the piece. And, the wine glass chorus, which plays this fixed note, has its own kind of shimmer—like the stars do.

10. Primum Mobile ("PREE-mum MOH-bee-lay"), the Prime Mover of the Spheres

Below is a diagram of the circle of fifths with the 12 notes indicated around the circle. The three chords are indicated which are used in a huge amount of harmonically simple music (which may, of course, be quite sophisticated in other ways) - the blues, "Happy Birthday To You", and "Twinkle Twinkle", for example. Having a piece in different keys would just rotate the triangle around the circle, but it would still have the same shape:

Chord Diagram of a Simple Song (Like 'Twinkle Twinkle')

This diagram shows the chords used in "Venus", just to choose one more or less at random:

Chord Diagram of 'Venus' from Music of the Spheres

But Primum Mobile and Empyrean are the two spheres that are outside of normal reality. Here are the chords that are used on Primum Mobile:

Chord Diagram of 'Primum Mobile' from Music of the Spheres

It's a perfect square.

11. Empyrean ("em-PEER-ee-en"), the Sphere of God

See the discussion for Primum Mobile just above, and observe the chord diagram for Empyrean:

Chord Diagram of 'Empyrean' from Music of the Spheres

Naturally it's an equilateral triangle (three equal sides).

12. Centrum, the Still Point at the Center of the Spheres

If you could stand at the center of all the spheres, you would see what would almost look like a giant cosmic clock, each of the spheres moving in its own rhythm. This piece is built on several independent melodies, each moving at their own speed, each taking a different amount of time to complete — just like the planets.

Now that we're at the center of all the spheres, if we were to start moving outward again, the first sphere we would encounter would be Earth. Thus the Music of the Spheres album itself has closed its own circle.