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Harmonics, the basis of sound design

Truth is in nature, there's no sound that vibrate at only 1 frequency at a time.

A sound that vibrate at only one frequency is a sine wave, that's what only one frequency sounds like.

Any other sound is in fact always a cocktail of a lot of frequencies.


Among them, the lower frequencies is called the fundamental - that's often the note we hear and that we can sing, and all the other frequencies are called overtones.


We split these overtones into two families : the harmonic overtones and the inharmonic overtones


The harmonic overtones participate to the musical note we hear in the sound, the one that we can sing. 

They are part of the harmonic series of the fundamental. Wich means that their frequency is a multiple of the fundamental's frequency. The Fundamental being the first harmonic.

The 2nd harmonic being twice this frequency, which is the octave.

 the 3rd harmonic is 3 time this frequency, which is the fifth.

then the 4th harmonic is another octave, the 5th harmonic is the third, etc...

They all participate to the musical note we hear in the sound.

In fact, when a string of a guitar vibrate, all these harmonics are present in the sound you hear. 

When you play "natural harmonics" you isolate these frequencies that were already there.

With an open string, we hear the fundamental.

With your finger touching the string above the 12th fret, which is the middle of the string, you hear the second harmonic. With your finger touching the string above the 7th fret, which is at 1/3 of the string 's length, you hear the third harmonic, etc...


All the other overtones that are not part of this harmonic series are called inharmonic overtone and participate to the tone of the sound.

If a sound have too much inharmonic overtones then we can't really hear a note in it.

In this case we talk about inharmonic sounds.

It's the case of percussive sounds like a snare or a cymbal for example.

Drummers know that you still have to tune your drum kit. This is because the sounds found in nature are rarely 100% harmonic or inharmonic, but more often a mixture between the two. 

And these inharmonic overtones affect the tone of a sound.


As practical examples:

A pure sine wave is the only sound that have no overtone. Because that's how one frenquency sounds.

Then if we add odd overtones for our harmonic series. The fundamental being the 1, so we add the 3, the 5 and so on. Then our sine wave begins to be a square wave.

Then if be begin to add the other overtones of our series, our wave turns into a sawtooth wave.


This means that a sawtooth wave is richer in overtones than a square wave, which is richer in overtone than a sine wave.

But these 3 waves are 100% harmonic sounds and are at the basis of sound design in any synthesiser.

As an exemple of a 100% inharmonic, you have white noise, which is all the frequencies between 20Hz and 20kHz, all at the same level. Which is at the basis of synthetic snares of cymbals.


Mix harmonic sounds with inharmonic frequencies, and you can theorically recreate any sound you've heard.

In fact, overtones are the reason why a piano and a trumpet sound different. It's because they don't have the same overtones in it - harmonic and inharmonic, and each overtone resonate at different levels.

There is a functionality very useful to visualize that in Serum, let me show you.


In the last video, we said that in a major scale, the most consonant sounds with the tonic were the fifth and the forth,

Then it was the third and the sixth, 

And then came the 2nd and the 7th.


In fact the more consonant two sounds are, the more overtones they have in common.


So if we take a sound with its first harmonic overtones, and compare it to the notes in the scale than are the more consonant with it, we can get see these overtones lining up. For the fifth, the forth, the third and the fifth, and for the 2nd and 7th.


If you're in a choral singing a note and a bunch of people sing the fifth of that note, you can actually hear the harmonic overtones bounce in the room around you, and that's pretty awesome.


A trained ear can hear some overtoned within one note, and we can use that to tune some instrument. 

That's what we'll talk about in the next video.

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In the meantime, thanks for watching and I'll see you next time!

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