Delving in any way deeper into the heart of music theory, one is never very far from the hulking form of mathematics, bearing it’s breath down on all unsuspecting visitors. Numbers are inherently valuable throughout music, enabling us to communicate our intentions and aims with collaborators and band members with ease and on the fly.
Numbers are so all pervasive in music and music theory that it begs the question: did we make / discover music? or did music creative / discover itself? Has it always existed? or is it our own invention? Or perhaps it is both, a combination of natural sound and humans impressing themselves and their logic upon it?
Much as with mathematics, it’s very difficult, if not impossible, to tell. But this ought not deter us from trying, especially since these numbers are everywhere. It can sometimes feel as though we are in some orchestral version of the Matrix, with lines of code streaming down our vision like snotty green rain.
But what if I were to tell you that even such a thing as a simple note, seemingly devoid of mathematics as it is not a multiple of anything, is throbbing with these very same numbers, so apocalyptically everywhere?
That’s right! Take the most simple sound, a sound that has been around for millennia, the tweet of a bird for example, and it will almost certainly be comprised of multiple different notes, all bolstering each other from within. Take out your scalpel, make the incision, and before your eyes it multiplies!
Down, down goes the rabbit hole, and down we go, sucked into it by our boundless curiosity…
What Exactly is a Harmonic Series in Music?
We can think of the Harmonic Series in music much like in physics we might think about light. Pure white light can seem of its own, unfiltered and unadulterated. However, it is itself comprised of several other shades, those being the ones found in the color spectrum of the rainbow.
This seemingly singular and pure beam of light can be revealed for what it is when fed through a prism of glass. Yes, just like the infamous album cover for Dark Side of the Moon by Pink Floyd, the light fed through the prism indeed fans out, expanding into the rainbow that it is. Just because we can’t see it with our own eyes, doesn’t mean it isn’t there.
And the same very much goes for sound, too. Much as this single beam of light appeared to stand on its own, so too does a single note, played or sung or struck, on or with any instrument.
When we say we are hearing a note, we are actually saying that we hear its average pitch, almost always the fundamental or lowest pitch. Just as our eyes are drawn to certain colours, our ears, even in those untrained or unversed in the theory, seek out those fundamental pitches, and thus will scarcely have any conception of there being more than one note inside a note.
Even thinking about it in these terms makes it sound utterly ludicrous, but this is theory that touches on the very nature of sound which, as was alluded to in the introduction, has been around a lot longer than we might even dare to guess. This is the theory that makes even your voice or your particular guitar sound the way it does. Without any overtones or any harmonic series in music, all sound would be as flat as a theoretically perfect sine wave.
The Basic Building Blocks
This is pretty lofty stuff, so we will take it slowly and attempt to digest at a reasonable pace each new piece of terminology and its place within this concept and the wider musical and theoretical landscape. Since we are delving and dissecting deeper than a single note – what would have previously appeared as the smallest building block of the musical universe, so to speak – we will thus be using some new terms to place this piece of musical matter under the microscope and investigate what makes it tick.
Fundamentals: A Foundational Ground Zero
No matter our depth (or lack) of musical training, our ears are magnetically drawn to the lowest note of the harmonic series in music. We refer to this note as the fundamental, for without it there would be no harmonic series, in music or anywhere, to build upon it, nor any music as a result. This is the base sound that the human ear is somehow permitted to perceive, the pure white light that we actually hear and that is comprised of the various other colors, or pitches.
In calculating the musical harmonic series of what we normally perceive as an individual note, we work from this fundamental upwards, following a specific formula that remains unchanged no matter what pitch you begin on. Thus, the fundamental is the lowest possible note we will be working with, so important that it is often included by some in the harmonic series itself, though this is a real point of contention and debate among aesthetes.
Since this is something inherent to sound as found in nature, it’s surely enough to feel like there is a god or divine presence, one that isn’t Robert Fripp I mean!
Overtones: The Harmonic Series’ Musical Digits
So, if the fundamental is the base from which we calculate, the white light of the physics analogy, then the overtones are the various other colors and pitches of which the individual note is comprised, which color the fundamental and provide it with the detail that our ears so hungrily feast on.
Since the fundamental is the base, laying the groundwork for the harmonic series in music so to speak, there are only overtones, at least in this concept. They are operating over the top of this foundational pitch and are entirely informed by it, the fundamental being the root from which we calculate the musical harmonic series entirely.
When we say overtones we are referring to every single pitch above the fundamental, hence the title. However, some are inclined to call them partials, seeing as they are part of a whole, working towards the transit and delivery of the central fundamental pitch.
Harmonics: A Common Currency
Of the overtones, the most common we come to know as harmonics. Those less learned or less inclined towards the theoretical will no doubt have still heard them in action.
On the guitar, they can be easily sounded by lightly placing your finger, without pressing firmly, on any of the strings on the 4th, 5th, 7th, and 12th fret. There are plenty more all along the fretboard, though these are likely to provide the most obvious results to the untrained ear:
- 4th fret – Major 3rd
- 5th fret – Perfect 4th
- 7th fret – Perfect 5th
- 12th fret – Octave
Building a Harmonic Series in Music
Interesting to note is the way that, when sounding the harmonic in the 5th fret, it plays the note two octaves up from the open string. This is a bold echo of the fact that the musical harmonic series itself repeats the same intervals as it ascends, exactly the same each time but for the addition of another interval.
Just as the colours of the rainbow appear in the same spectrum of order each time, the notes of the harmonic series in music always repeat themselves thus, perpetuating the same series of intervals from the fundamental tone.
Since an interval is merely the distance between two different notes, measured in steps (or frets if you prefer), the intervals of which the musical harmonic series is comprised begins with those that are harmonically strongest, to those that can be deemed harmonically weakest.
Interval of an Octave
The series thus begins with the strongest, the octave, the same note as the fundamental but twelve half-steps (or frets) up. This first perfect interval is therefore deemed most perfect, harmonically strongest. This would seem to be the reason that when plucking the harmonics of the fifth fret of the guitar, you hear the octaves of the open strings reflected back at you.
Interval of a Fifth
Sequentially, the next strongest would be that of a fifth, found 7 half-steps (or frets) up on the fretboard. We see this reflected in our harmonics on the guitar too, where the next strongest harmonic, after the octave found on the 5th fret, is the fifth as reflected on the 7th fret.
This, alongside the octave detailed previously, is all you need to construct a power chord, the foundational and harmonic basis of punk and punk-influenced music: simple music, to the point of being fundamental, rallying against an authority that comes to show itself in the established rules of harmony, harmony which they use for their own devices; using the master’s tools destroy the master’s house.
Interval of a Fourth
Then we have the interval of a fourth, coming in as third strongest of intervals from the fundamental. When looking into the theoretical detailing of scales, they are often presented to us in terms of their scale degrees, removed from a musical context.
If we were to look at these scale degrees closely, those of the tonic (I), perfect 4th (IV), perfect 5th (V), and an octave (I) are the only degrees marked with capitals. In terms of the chords within a scale, those highlighted are those that will correspond to the given key, major or minor as it be. With these first three strongest intervals being those very same highlighted on the chart of scale degrees, it’s no surprise that they are so fundamentally perfect and strong.
We Three Perfect Intervals of Harmonic Series Are!
These three intervals are thus referred to as perfect intervals, so recognisable as they are to even the untrained ear. It would be difficult to dissect these most fundamental building blocks down any further, as these are often likened to the basic primary colors, singular as they are formed of themselves.
These so called perfect intervals can, of course, be changed and distorted and moulded as one sees fit. If ascended or sharpened, it would be referred to as augmented. Likewise, if descended or flattened, we would call it a diminished interval. However, these modified intervals don’t appear anywhere in the harmonic series, imperfect as they are, formed as they are from combinations of other intervals.
Growing Weaker… And Weaker…
There are more than just these perfect intervals present in the musical harmonic series, however much weaker they may be, and they are always accompanied by these perfect intervals.
We might think of these, in comparison, as secondary colors, which further add depth to the color spectrum despite being inherently weaker for being composed of other colors or tones:
- Major 3rd (strongest) – four half-steps (frets) above
- Minor 3rd – three half-steps (frets) above
- Major 2nd – two half-steps (frets) above
- Minor 2nd (weakest) – one half-step (fret) above
It ought to be easy to see that as the strength of the interval diminishes, so too does the gap between the two notes of which it is comprised.
The Final Result: The Harmonic Series All Told in Music
It’s not an underestimation to say that every single note, aside from those specifically crafted to be devoid of overtones, is brimming with them. As alluded to earlier, it’s the character of these very overtones that subsequently lends character to individual sounds, whether they be a lover’s voice or your own axe (what’s the difference ho ho ho).
This kind of character, that which gives a sound its identity and allows us to discern one from the other, is called its timbre. If the same note on the same pitch were sung by two different people, there would be cross-pollination of overtones in the air which was vibrating and carrying the voices forth. Theoretically, however, one could modify these overtones digitally so that there would be no way to discern the voices, rendering them theoretically pure.
What makes this so difficult is that, at points, it does defy the logic of Western classical music so firmly rooted in our minds, that of equal temperament and perfect tuning and the like. In doing so, it reveals itself for what it is, namely the logic of sound itself, something that each harmonic system attempts to make sense of, the West’s included, but which none can truly master, for it is inherent in the logic, mathematics, and physics of sound itself.
This is obviously some pretty lofty stuff, but it doesn’t have to be unapproachable. The main priority is to figure out what this knowledge can do to you. If you are content to be without the theory, simply happy to play, then that is more than okay.
However, I would argue that even a subconscious knowledge of some of the topics, both large and small, covered today would be of immense use in so many more contexts than you might initially expect. As a composition tool it could be invaluable, in composing melodies or harmonies, in using the more unusual interval combinations to create songs or hooks, or even to use them to improvise and set yourself apart from other guitarists who might be more inclined to mimic their heroes.
My only wish of you today is simply that you open up your ears as much as you can. Not so much that you are overwhelmed and short-circuit, but just enough that you begin to hear the complex panoptic spectrum of sounds going on around you all the time.
A junction at rush hour can be a war zone, so maybe start off small, focusing your ears on the tiniest sounds in your home, those that you have heard a million times before, and see if you can hear anything new, see if you can suss what makes that sound tick, what makes that sound its own unique self. Each sound has its own identity, its own harmonic series, outwardly musical or not, much as you are built up of all the microscopic loops of logic that make you your own unique self, no matter which overtones you are prioritising at any given time.
FAQs Harmonic Series Music
It is the foundation upon which all harmonic and melodic information is laid. There are several thousand harmonic systems throughout the world, owing to both small and vast differences in the development of tonality in different cultures, as well as to the priorities different musical styles and identities place on these things.
The only real way to tell if a series of notes is following the formula of the musical harmonic series is to begin from the root and work your way up, following the formula from memory or from a resource. However, with minimal training you ought to be able to discern the series, perhaps listening out for the large leaps at the beginning which gradually become smaller until infinitesimally minute.