The Overtone Series: What It Is, and Why You Should Know It?
In lessons, there's a subject that comes up at some point with every student, and I get both excited and slightly anxious when it happens...excited because I find it fascinating, anxious because I'm not positive I'm explaining it 100% correctly (almost certainly not to anyone who really understands acoustics and physics) and because...there's no way to explain it super quickly and move on to the main agenda of the lesson.
It's something that exists in the world of acoustic music called many names, but most commonly the Overtone Series or the Harmonic Series.
If the next section causes you to zone out from boredom, please know that by the end, we'll go over how this can be accessed in instruments, and how understanding it can make you a much better improviser, composer, or arranger.
What it is (as basic as I can explain it)
Before continuing, I need to confirm that this is something that happens on acoustic instruments (that is instruments produced with strings, your breath, or some other physical element) as opposed to purely electric instruments (like a digital keyboard). An electric guitar is an example of something with the same physical mechanisms as its acoustic counterpart. The only difference is that it requires amplification but, because the physical method of making the sound is the same, it works on instruments like electric guitars and similar.
It's easiest for me to explain this using a piano keyboard, but I'll explain how this works on other instruments as well by the end.
On a piano (again, not a keyboard, but an acoustic piano), play an A2 (for reference this is a 10th or an octave + a 3rd BELOW middle C). This works off of any key on the piano, but I can do the math better with this key. Yes, sorry, but there is math involved.
You play the A2. How many different sound waves are vibrating? If your answer is ONE, then you answered a different question. The question you answered would be...how many sounds do you actually hear? And one is most likely correct, unless you have an exceptionally resonant instrument in an acoustically rich room. The question I asked was: How many different sound waves are vibrating? And the answer to that is...a lot!
What you're actually hearing is called the fundamental part of the pitch. If you were to play a sine wave, something synthetic and stripped of resonance, you would hear this note played like this:
(Press the small play button on the bottom left, not the big one in the center)
It's a razor-thin sound. The reason it sounds thin is because, in this case, the fundamental note is the only sound wave. Resonance (or the richness to a sound) comes from the presence of overtones along with the fundamental.
WHAT ARE OVERTONES?
When an acoustic instrument sounds a note, you hear the fundamental note, but there are many other sound waves for other notes that are vibrating. We don't hear them unless we isolate their frequency (something I'll get to in a moment), but they add the richness to the sound.
Warning: Here comes the math!
Overtones exist in a relationship of Frequency times partial. A partial is what we call each note in the overtone set, including the fundamental. The fundamental of A2 is 110hz. It is F(1), so the first sound wave is 110 (1) which is A2 or A-110. The first overtone (or 2nd partial) of the series is an octave higher at F(2) or 110(2), which is A3 or A-220. Frequencies get exponentially higher in number as you go up because each octave is double the previous number. If you know anything about orchestra, you know that the next A (A4) is 440 hz or A-440. Well, that's partial 4. Partial 3 or F(3) is E4 or E-330. Then A-440. Then C#-550, E-660, G-770, and A-880. It looks like this.
It then keeps going in a series of 2nds like this.
And it can keep going and going, but we'll stop there.
Okay, if you're still here, I think the tedious part is done. Now let's get to the cool part!
Let's listen to how we can hear various instruments can MUTE the fundamental to access the overtones.
In this first video, I'm on my slightly out-of-tune piano. I first silently hold down partial 2 (A3) while I quickly and loudly play the fundamental A2. Listen to the various chiming sounds that occur when I do that, and then switch to higher partials (E3, A3, C#4). Those chiming sounds are not full resonate pitches, but are audible only when the lower partials are muted. This happens when certain combinations within the overtone series happen together.
In this 2nd video, I've asked my wife to play viola on an open A, then lightly touch the spot where she would play an octave above the string, then a 5th above, then a 4th above. Listen to the ghostly sounds, and how the sound gets higher as she lightly presses closer to the bridge. If she were fully pressing the strings, she'd be getting rich fundamental notes that were getting lower. Because she's lightly pressing the string, she's muting the fundamental but getting higher notes as she's moved closer to the bridge.
The chiming sounds can be done the same way on a guitar by lightly touching the 12th fret, or the the 7th, or the 5th (for example). It can also be done on harp by moving away from the resonant part of the string, and plucking toward the the top of the instrument.
The overtone series has an importance in brass instruments since it's what makes playing it even possible. If a brass player doesn't play any valves at all (or a trombonist keeps their slide in 1st position), with a fully developed lip skill they can play the entirety of the overtone series starting with a low Bb for trombone, tuba, and trumpet, and an F for French Horn. The French horn is notable for being the most difficult of brass instruments because of the overtone series. While the other brass instruments begin the most common octave on the 2nd partial (where the next notes are spaced a 5th and 4th apart), the French horn begins on the 4th partial (where it already is only 3rds and then quickly 2nds apart, and almost no margin for error). Multi-brass player Harlan Feinstein demonstrates.
Now, as I mentioned, this doesn't work on true electric instruments like a keyboard. A keyboard, even one with a good piano sound, is really just recordings sampled into the instrument. The sound is not being created from physical means. So...check this out. This is the 2nd half of the Gavotte 2 (Musette) from Bach's English Suite No. 3
Notice the tie of the G3 (in the bass) that never ends. I'm going to play it as written on the keyboard.
At the end, I'm holding on the G3, but all sound is gone. The fundamental sound of the G3 dies halfway through that passage. Holding it down does no good on an electric instrument and for that reason, some editions have separated the tie so that you re-strike the note.
But, don't you suspect that Bach knew what he was doing? Play this on an acoustic instrument, without re-striking the G3, and listen to what happens!
The fundamental, once again, disappears long before the passage is done. But by sustaining the key and letting that key's strings vibrate, they are reacting to the notes above that happen to be partials (notably the G4 and D5), and by the end of the piece, those are the notes you hear, not the G3 you started with.
HOW KNOWING THE OVERTONE SERIES IMPROVES YOUR COMPOSING AND IMPROVISATION
When it comes to either playing from a lead sheet and choosing how to interpret the chord symbols, or making up your own music through composing and improvisation, it helps to look at the model shown by the overtone series. Let's look at it again.
Look at just the first 5 partials, something you could play with 2 hands. The distance between partials 1 and 2 is an octave. Then you go up a 5th to partial 3, and then a 4th, and then a 3rd. The partials continue in 3rds before they progress by 2nds. If you have a piano or keyboard handy, play partials 1-2 with the left hand at the same time as partials 3-4-5 with the right hand. Isn't that a rich chord?
Part of why it's so rich is because it's including partials of the overtone series without a break, so all the notes fully compliment one another. But what does this tell us about creating chord voicings?
Although every pitch has its own overtone series, the fundamentals that start in treble clef are increasingly too faint in volume to do much with, so we generally start from a low register. If you go to a piano and play around with intervals on the bottom octave or 2, nothing sounds good between 2 notes - not even a 5th, and definitely not 3rds. The one exception is...the octave! The octave sounds great in any register. Once you're past C2, you can try a 5th, then a 4th. Past C3, we can now go to 3rds. Rich harmonic texture will, generally, include a structure of an octave and/or 5ths at the bottom of the chord, and 4ths and/or 3rds as you get higher. Densely harmonic structures like 9th chords and upward will usually be added as 2nds ALWAYS in the upper register.
You don't have to start every chord with an octave, or even a 5th or 4th. You can start on any partial you want, or even go out of order with some of the notes. You don't have to start on partial number 1 or 2. There's nothing wrong with the traditional closed C-E-G from bottom to top in 3rds. However, because of the overtone series and resonance, it will sound much better if you do that on C3 (an octave below middle C) and above. It's notable that it sounds good, but it's not nearly as resonant as an open voicing from the bottom.
A NOTABLE EXCEPTION to all of this is Ludwig Van Beethoven. Look at the left hand staff of this excerpt and just how low these closed-voicing chords are!
It's worth pointing out that Beethoven does this so often in his music that it's actually a distinct characteristic to his music, so that means: (1) Rebelling against the overtone series model when creating chords like this doesn't necessarily make you revolutionary, but it might make you sound like you're imitating Beethoven, and (2) Beethoven's music is great, and he doesn't always do this. In fact, his grand chords in his Symphonies are almost always overtone friendly. (3) When he does do this closed voicing low, it sounds fine, and he uses it well...but it's not resonant.
Checkpoints when creating chords
- Spread out notes at the bottom.
- You can be bold with 2nds in the upper half of your chords
- Jazz musicians: only put the Root-3rd-5th-7th in the bottom half of the chord. 9th-11th-13th and other color notes should be reserved for the top. When you do arpeggio runs off chords in the upper register, focus on those color notes. Leave the fundamental notes at the bottom if you don't want to sound too "vanilla". But, this is probably a topic for another time.
This is a confusing topic for many. Send me a message or comment below if something specific needs more clarity. If you'd like to check out this full presentation as a video, you can here:
You can also listen to this episode as a podcast.
Did you miss the previous episode talking about Jazz Piano 101 with Federico Pivetta, you can catch that here: