The discovery by the Greek philosopher Pythagoras that musical harmony is governed by simple mathematical ratios is amongst the most fortuitous of human discoveries. It is not only that the Western system of music is based on the Pythagorean ratios, but the idea also had a great influence on Western philosophy and mathematics.
By experimenting with a single stringed instrument, he demonstrated that the pitch of a vibrating string is directly related to its length. Halving a string’s length produced a note one octave higher. Plucking two thirds of the string’s length results in a perfect 5th, and plucking three quarters of a string’s length results in a perfect 4th.
Classical music and most popular music revolve around tonic the 5th and the 4th. For instance, with a chord structure based on the octave, the fifth and the fourth, you can play most of the old rock and roll songs and adding a 7th to the fourth you can play a typical blues sequence.
And it is not just Western music that is based on these ratios, nearly all the world’s musical systems center around the octave and the 5th. (One notable exception is the Gamelan music of Bali and Java. If you want to know why, though, you’ll have to consult the Internet.)
The Music of the Spheres
Based on the discovery that the simplest ratios – ½, ⅓, ¼ – give rise to the most harmonious tones, Pythagoras developed the idea that the cosmos contained similar ratios and proportions. This idea, in modern times, is sometimes called “the music of the spheres.” According to Wikipedia:
Pythagoras proposed that the Sun, Moon and planets all emit their own unique hum based on their orbital revolution, and that the quality of life on Earth reflects the tenor of celestial sounds which are physically imperceptible to the human ear.
The astronomer Johannes Kepler wrote a book titled the Mysterium Cosmographicum (Mystery of the Cosmos), that modified and expanded Pythagoras’ idea. Extending the idea he concluded that:
the Solar System was composed of two basses (Saturn and Jupiter), a tenor (Mars), two altos (Venus and Earth), and a soprano (Mercury), which sung in “perfect concord.”
Musical Creation Myths
Gregory Gronbacher published an article here on Oct. 26, 2023, titled ORAN MOR (Gaelic for Great Song), that discusses the Welsh creation myth. About this myth he writes:
the world came to be and was kept in being by a song – a symphony performed by the interconnected natural world. Those with ears spiritually attuned could hear the melody. Every part of nature contributed to the music, and each orchestra member played a necessary role in its continuation.
J. R. R. Tolkien uses a similar idea for the myth of the creation of the world in which the action of his The Lord of the Rings takes place. The myth is found in the first chapter of his book The Silmarillion. That myth is too complex to summarize here, but if you’ve never read it, I recommend it, particularly if you are a Tolkien fan.
That there is a music-like harmony underlying the cosmos is an idea common to the Music of the Spheres and Oran Mor. Although the discoveries of modern astronomy make these ideas seem rather ridiculous, still I find something rather beautiful about them.
The Fine-Tuning of the Parameters
Although “the music of the spheres” is now only a quaint metaphor, a different musical metaphor still has resonance, this is the idea of the “fine-tuning” of the fundamental parameters. The idea of this “fine-tuning” starts with the observation that the basic constants and laws of the universe seem to sit in a very narrow range that allows complex structures – and ultimately life – to exist. It goes on to the claim that if you changed some of these values even slightly, the universe would become radically different and life would not exist.
As examples: if the force of gravity were somewhat stronger, stars would burn out quickly, and if somewhat weaker, galaxies and stars wouldn’t form at all. If the electromagnetic force were somewhat stronger atoms would bind too tightly to allow for much chemistry, if weaker, atoms wouldn’t hold together. In either case, we wouldn’t be here to notice.
The idea of the fine-tuning has been challenged, particularly as it pertains to the Anthropic Principle. That there is something rather mysterious, however, about the existence of the various ratios among the fundamental parameters, is well evident. It is from these ratios that the so-called laws of nature arise, and because of these laws we live in a relatively organized and creational universe and have the ability to think about these things.
The ratios of this fine tuning are not at all like the simple ratios of the Pythagorean musical harmony. One of the most observable ratios is that between the strength of gravity and the strength of electromagnetic energy. Electromagnetic energy is roughly a billion trillion trillion times stronger than gravity. That is a long way from the idea that the simplest ratios produce the most consonant tones.
We can observe this ratio in action when we watch a ballet dancer performing grand jetes or a basketball player making a slam dunk from the free-throw line. A relatively small amount of electromagnetic energy in our muscles can overcome the entire earth’s pull of gravity. It is this ratio, so well balanced on earth for life, that is a kind of intelligible music, a music for the mind. Sometimes when I watch a bird flying or an old oak tree with its long limbs extending horizontally, I experience it as a kind of visual music, as I remember this ratio.
A Composed Life
Yet another musical metaphor is in play when we talk about somebody “being composed.” To be composed is to be in a kind of harmony with one’s self and the world.
To be composed amidst the turmoil and noise of daily life requires a disciplined mind – the ability to organize our mind based on some intention. That the mind is capable of such self-discipline is in itself a kind of wonder of Nature. Most of us do not have the innate talent required to compose great art, but we probably do have the innate talent to do a better job of composing our own life. One of the benefits of practicing some form of mindfulness is gaining a better sense of how to compose one’s mind and thereby one’s actions.
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Johannes Kepler accepted the idea of the music of the spheres. He wrote that though the music was inaudible to the ear, it could be heard in the soul.
In contemplation, sometimes I hear that inaudible music. Then my soul dances with the cosmos in a motionless dance.
Oh well, sometimes I just prefer a metaphorical world to the literal one.
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