Platonic Concepts (pt. 4)
The Monochord
Dear readers,
This post will be admitedly the hardest in the series —quite possibly even harder than the concept of the One to understand—UNLESS you are literate in music theory. There are many metaphors aside from musical ones that I could use to illustrate my point and clarify the next stage out from the One. However, I have personally found those metaphors to trap the mind in mechanics and optics that may breed further confusion.
So my dilemma was rather agonizing: go for a metaphor that requires less technical expertise but may create further confusion, or a more technical metaphor that might require some effort to grasp but give a clearer picture of the subject under discussion once understood?
I dithered back and forth for a while—as I always do—but I have decided to go with the latter for now and clarify with cruder metaphors later on if parts of this metaphor fail to register. Hopefully, however, we will go at a good pace, allowing ourselves time to ponder, reflect and to meditate on the points raised.
A Short Recap
We have established that the One is not a being but the source of being, not a unity among other unities as it is THE ONE but it is the source of all Unity. We have also said that it cannot have parts and a structure as it would rely on what it allegedly produces in order to stay together, so it must be absolutely simple. Not because it lacks anything, but because it is so utterly self-sufficient, so ‘full’ of itself that nothing can be added to it or be removed from it. Its fullness is not inert and unproductive; it overflows. Not in time because it preceeds time, nor in motion for nothing can cause it to move, but as a kind of metaphysical necessity. The World exists and Unity is observed everywhere. Therefore, the source of unity and consequently of the World MUST be productive NECESSARILY; otherwise nothing would exist.
Let’s set all this aside now.
(What?! We just got here!!)
Yes, yes!! I know!! But there is method to my madness and I want you to see some stuff that will clarify a lot not just with respect to what we’re talking about now, but it will also link to future posts all the way down to worship, ritual, meditation and many more mundane matters.
Who’s the guy with the beard and auntie Soula’s head wrap?
Enter: Pythagoras!
I am sure that everyone has heard of him but if you haven’t, the lowdown on him is that he was a polymath, a philosopher, a vegan (sacrilege!) and that he had a obsessive relationship with numbers and math (unforgivable).
You may have heard of his explanation and codification of the Pythagorean theorem in geometry, named after him —no, it was not himself who named it so.
If you’re interested in more details about him we WILL be speaking about him in greater detail much later down the line but —for now— a good introduction to him you can find in the relevant Wikipedia (*spits on the ground with a grimace of disgust*) article here .
Pythagoras’s obsession with numbers and math lead him to explore the world almost exclusively through them and as he did, he saw a deeper mathematical harmony in things and how they work and interact with each other. Math was so ubiquitous that Pythagoras and his students ended up thinking that numbers were not just abstract concepts. They believed them to have a more fundamental, ‘divine’ quality and connection to the cosmos. They ended up investing specific numbers with specific metaphysical properties as well.
For instance, the number 1 (wink, wink!) symbolized Unity (ahem!) and the origin of ALL things (cough, cough!).
The number 3 (cough cough!) was seen as a building block for all subsequent numbers and for them marked the actual beginning of counting!
We can expand on their numerical beliefs when we talk about them in more detail in a later article, but for now let’s stop at the numbers 1 & 3 and just say that, in short, they thought that the interplay of numbers and the relationships and ratios between them reflected a deeper order and harmony in nature.
Lastly —and this will come to haunt us more as we meditate on the concepts we will be introducing in this article—it is important to note yet another, rather extreme (or is it?) belief of Pythagoras: that the Numbers were the causes of all Gods and Daemons and therefore held tremendous power and influence over the spiritual realm.
(By the power of three times Three, make them see, make them see…)
The Monochord
Like we’ve said, Pythagoras had an unhealthy obsession with numbers and ratios and their relationship with one another and that obsession was turned on pretty much ANYTHING, including sound.
The strange-looking implement in the picture above, is attributed to Pythagoras himself. It consists of a single string, stretched over a wooden body that depending on its hollowness can also act as a boom box or an amplifier of resonance. In the middle it has a moveable pointy thing called a ‘bridge’ which when moved around presses against the string at different points like your finger would on a guitar string. This particular one in the picture also has a ruler in order for the user to know precisely at which point along the string the bridge is pressing.
Fiddler on the Roof (Get the bucket ready…)
So Pythagoras was twanging annoyingly on this single piece of string.
The string vibrated in this low, humming deep tone —dong!
Today, we call this the ‘tonic’.
And like the rebelious devil that he was, he thought to himself: “What if I moved the bridge right in the middle of this string?”
Now the string vibrated in two equal halves, each at twice the rate of the whole string.
This gave a tone that was higher, clearer but unmistakably related to the original ‘dong’. In fact, it was the same note, just at a higher pitch.
He had found the ‘octave’ —a duplication of the original tone but at a frequency rate of 2:1.
Same identity, just a different register.
Hmm, I can already see ratios…
“Now what if I halved one of the halves and then twanged the string again?”
Now the string was vibrating in quarters and the pitch had jumped higher still.
So he then noticed something: every time he halved the string, the pitch doubled.
But this wasn’t just about doubling or halving—he was starting to hear relationships.
This new tone felt eerily familiar.
Different, yes—but clearly echoing the first. A kind of perfect resonance.
He was onto something.
He began to experiment further, carefully placing the bridge at different points along the string.
He found that certain fractions: thirds, fifths, fourths, created tones that sounded pleasing, even beautiful. Others didn’t quite click.
What he was mapping weren’t just sounds, but proportions. Some struck the ear as harmonious, others not.
Then came the breakthrough:
If he divided the string using certain ratios, he could get a series of notes—a sequence that felt complete, almost gravitationally drawn back to the original dong at the end.
He marked the positions on the string, noting their exact ratios.
First, the original tone —the tonic. Then, the octave—its higher echo.
But in between, he discovered other notes, each with its own unique relationship to the tonic and the octave. These weren’t random. They formed a coherent structure.
And, lo and behold, he realized something wild:
There were six more notes—six more distinct points on the string—that fit perfectly between the tonic and its octave.
Add the tonic and octave themselves, and you get a total of eight notes.
And that, my friends, is how the octave, and its eight notes were born, all thanks to a single, annoyingly twanged string.
This scale, this succession of eight notes, is also known as the diatonic scale in western music.
However, the story did not end there.
Eventually, someone thought:
“What if we split the gaps between those notes?”
And when they did—bam!—five extra pitches emerged, evenly spaced between the original seven bringing the total number to…12…( wink wink!) known in music as the chromatic scale—a more productive, nuanced, buffed up diatonic if you will.
Now, theoretically we can keep halving forever, but for some bizarre reason, our ears and our perception of sound, seem to prefer these twelve pitches. Further subdivisions either escape us, or even annoy us. It seems that we perceive melody and harmony almost exclusively within this domain of sound. It’s almost as if melody and harmony live within a twelve-tone fence.
Hmm, I wonder if this is connected to the Twelve G…umm maybe more of that later.
For now, it’s just food for thought…
WHAT IS A NOTE?
Let us go back to our undivided string.
Let’s give it a twang…
DONNNNNG!
That first, distinct sound we hear is called the fundamental frequency —the pitch that strikes us as most clear. We perceive it as a note, in this case, our tonic.
But if we listen more closely, we will find that this DONG! isn’t so simple. It reverberates, not as an echo, but as a ‘fullness’ of sound. Hidden within that sound are other tones, quieter but real. These are known in music as ‘harmonics’ —and they’re not random at all. They are pure, mathematical resonances that arise naturally from the string’s vibration.
They are exact multiples of the fundamental tone, not added or imposed. They are built into the note’s being.
Even if we shorten the string and produce a higher note (say, by halving its length and raising it by an octave) the same thing happens: the new note that emerges has its own set of harmonics. No tone ever sounds alone.
We could even say that it is these hidden, inner tones that make the note itself clear, manifest and perceivable as itself.
Each one emerges accompanied by a fullness that shapes it into what it truly is.
Hmm…
We’re going somewhere with this, arent we?
Yes, petal…we are.
BUT, I’m going to be an annoying git and I will leave you here for now, so that you can read through this article and digest everything that we have mentioned here. I want you to intuit where we’re going with this. I promise you, we will pull everything together in the next article and hopefully, if you have done your homework —no cheating allowed— it will all make sense together as we move on out from the One to the Many.
For those who would like to have someone more proficient explain all this music stuff to them, I would recommend the following YouTube video by Andrew Huang:
As a second best, I would also recommend the following video:
Both, are explained quickly and simply and hopefully it will all begin to click together.
Now before I leave you here, frustrated and alone —just like your ex—I would like to apologize to any music theorists for any mistakes or any oversimplifications that I may have made.
To my defense I treat my own subject matter with the same disrespect, rather deliberately. Take it not very personally.
Until next time.