You Don't Understand Saturation

saturation is one of the most important concepts in music production but most of the explanations about what it is and why we use it are pretty vague saturation along with eq and compression are the most important tools we have at our disposal now before we learn how to properly use saturation it's good to know how it works now this video is going to get pretty deep but i promise if you make it through you'll learn something new about some fundamental ideas in audio i gotta warn you though if you're looking for quick saturation tips this isn't your video now before we go any further i have to clarify some people call it distortion some people call it overdrive drive fuzz warmth grit some plebs even call it gain but in this video i'm going to call it what i think is the most umbrella term that music producers use which is saturation what is saturation saturation changes the shape of a wave and it does this in such a way that it adds new frequencies to that wave and eq changes what's already there but a saturator adds stuff that wasn't there before saturation is important for two reasons it compresses sounds so it lowers dynamic range and can help glue a sound or group of sounds together it also adds new frequencies which can make a mix sound more full or more tonally interesting saturation is what's called a non-linear process which is just a fancy way of saying changing the input by a certain amount changes the output by a disproportional amount put simply saturation takes the amplitude at each point in the wave and scales it to another value changing the shape of the wave in fact another word for saturation is wave shaping let's take it slow let's just look at half a sine wave for now the way wave shaping is usually visualized is like this the x-axis of this graph represents the input level of the wave so low amplitudes are down here and high amplitudes are up here the y-axis of this graph represents the output amplitudes of the wave again low amplitudes are down here high amplitudes up here the thing that connects the input to the output is our saturation curve right now the saturation curve is a line so this point on the wave will be scaled to the same output so the wave remains unchanged it's linear however if i add a slight curve to this it becomes a non-linearity the input amplitudes don't equal the same output amplitudes for example this point on the wave will be scaled to this amplitude now now by doing this i've changed the shape of the wave and this means that i've changed the frequencies that make it up saturation is taking every point on the wave and scaling it by some amount we take a point on the wave stick it on the x-axis and find how the curve changes that point okay so far we've only been dealing with the positive parts of the wave what the is that you try to make a professional youtube video anyway where were we so far we've been dealing with the positive parts of the wave you might have noticed though that waves tend to be wavy waves aren't just made up of pills there's also valleys just like life now this entire time the x-axis has only represented positive amplitudes from zero up to the maximum but we're missing all the negative amplitudes a wave can have so we have to extend our graph to include negative amplitudes now it's getting tricky we can affect the wave differently when it's above the x-axis and then when it's below the x-axis remember when we're looking at the wave itself we're looking at amplitude over time when we're looking at a saturator we're looking at the input amplitude versus the output amplitude so everything i talked about earlier can be applied to the bottom part of the wave and changing the top of the wave differently from the bottom has some interesting effects which i'll talk about later that light pop quiz time i hope you've been taking notes if i have a sine wave and i pass it into this curve what would it look like after [Music] this last one is just the original wave with its face flipped if you got those correct congrats so this is fun but how does any of this pertain to what we hear when we change the shape of the wave new frequencies are added to the sound more precisely harmonics are created harmonics are whole number multiples of the fundamental frequency so for a wave with a fundamental at 100 hertz the second harmonic would be 200 hertz the third harmonic 300 hertz and so on but this begs a question why does changing the shape of the wave add frequencies think of what changing the shape of the wave actually means let's use our old friend the sine wave sine waves are pure tones meaning they're made up of one frequency let's assume there's no phase shift so the shape of the wave only changes due to saturation if i clip the peak i'm changing the shape of the wave but one way to look at it is that instead of me clipping the wave i'm adding on a new wave that looks like this this is because this new wave is doing the same thing as the sign just flipped upside down so when we take our sine wave and add this new wave the peaks of the sine are cancelled giving us the clipped wave these two ideas are equivalent so changing the shape of the wave in any way must change the frequency content the added frequencies from clipping are just the frequencies of this new wave okay so saturation changes the shape of a wave which adds new frequencies but what's the relationship between the saturation curve and the harmonics added to our wave there are two kinds of saturation curves symmetric and asymmetric a symmetric curve means what's on the left side is symmetric with what's on the right side whereas an asymmetric curve is one where the left side isn't symmetric with the right side now we're going to go into depth about both these cases and hopefully by the end of this you'll understand that everything that has to do with saturation and distortion and all this stuff comes down to this interplay between symmetry and asymmetry let's start with symmetric like i said symmetric curves have a symmetry between the left and right side for example this is a symmetric curve more precisely it's called an odd symmetric curve because the left side is the opposite of the right side it's odd because most saturation curves that look like this can be represented as equations with odd powers of x for example x to the power of 3 gives this curve the left side is the opposite of the right side this makes sense because say x equals one then the output is one to the power of three which is one but if the input is negative one negative one to the power of three is negative one i promise we're almost done with the math this odd symmetry where the left side is the opposite of the right side adds odd harmonics to our sine wave in this case it would add the third harmonic the same thing also applies to any combination of odd curves now the classic saturation curve most people are used to looks something like this so if we send a sine wave through it the added harmonics will all be odd and there will be infinitely many of them remember what harmonics are they're whole number multiples of the fundamental frequency so the odd harmonics would be one which is the fundamental three five seven nine and so on what it comes down to is this when the left side of the saturation curve is the opposite of the right side you affect the top and bottom parts of the wave in the same way and this creates odd harmonics and as you can see it pushes our sine wave to be more square like in fact a square wave is made up completely of all the odd harmonics but all this math aside why does affecting the bottom and top part of the sign create odd harmonics and why do odd harmonics create square waves sine waves exhibit a property called half wave symmetry this means if we draw a line down the center the two sides are opposites now we know odd saturation curves saturate the top and bottom parts of the wave in the same way this forces odd harmonics to be created the easiest way to understand why is to look at another symmetry sine waves have if we just look at half the wave there's another symmetry down the middle this is called quarter wave symmetry as we start to saturate the sine and get closer to a square wave we can see the symmetry is still there odd saturation curves preserve these symmetries and because of this only odd harmonics can be created let's look at the first three harmonics of a square wave so the first harmonic the third harmonic in the fifth harmonic this is what the wave looks like and you can see it kind of has that square shape now let's just look at half the wave right now this wave has quarter wave symmetry the three harmonics that make up this wave look like this if we look at the fundamental for every hump of the fundamental odd harmonics have an odd number of humps for example the third harmonic has three humps while the fifth harmonic has five this means that there's no way you can have an equal number of humps above and below the zero point like if you have an odd number of things and you try to divvy them up evenly there's going to be one left over that you have to put on one of the sides because of this there's a symmetry down the middle and so the composite wave must be the same on either side now if we look at the other half of the wave it's the exact same all the harmonics are just flipped upside down shaping the top and bottom in the same way forces the only possible harmonics to be odd harmonics because those are the harmonics that give humps in the right places to preserve this symmetry any wave that has half wave or quarter wave symmetry is made completely up of odd harmonics and this is why square waves are purely odd harmonics triangle waves also have this symmetry and are also completely made up of odd harmonics although it gets a little weirder just like before for there to be a symmetry over half a cycle of the wave for every hump of the fundamental each harmonic must have an odd number of humps however unlike square waves every other harmonic has its phase flipped 180 degrees so it alternates back and forth this causes all the humps to overlap in the center but the humps cancel out more and more the closer you get to the edge and the more harmonics you have the steadier the wave moves towards the zero point in the square waves case when you're near the edge the harmonics stack on top of each other so the more harmonics you have the less steady the wave will move towards the zero point if you have a perfect square wave with an infinite number of harmonics it doesn't approach the zero point at all not even here it just jumps instantaneously to the bottom there's another difference between square and triangle waves the harmonics of triangle waves fall off faster than square waves with square waves the amplitudes of the harmonics decrease with the harmonic number so if my fundamental has an amplitude of one the third harmonic is a third is high the fifth is a fifth and so on but with triangle waves the amplitude of the harmonics decreases with the square of the harmonic number so if my fundamental is at one the third harmonic is only one this high the fifth is 1 25th this causes triangle waves to sound less harsh to our ears because the higher dissonant harmonics sound quieter there's also an intuitive reason for what this is but it's a little convoluted i might make a video about it but i want to stay on topic there's a lot to cover odd harmonics tend to sound harsher to our ears and this is because they're at more dissonant musical intervals and i'm going to show you what i mean by that i'm going to play all the odd harmonics and take this low-pass filter and just slowly sweep it up the spectrum to bring each odd harmonic in so that you can hear the dissonance [Music] so the higher you go the more dissonant the tones become so we know what happens when a curve has odd symmetry what about when it has even symmetry when the left side is the mirror image of the right side if we pass a sine wave into this only even harmonics would be created similar to before curves that have even symmetry can be represented as even powers of x this means sending a sound into a saturator with an even curve like this spits out a wave where the bottom part becomes the same as the top part not equal and opposite like odd curves but the exact same now in practice this usually means the positive part is remaining the same and the bottom part is being flipped to be positive also this is called rectification and for a sine wave it adds even harmonics so what we're left with are the second harmonic the fourth harmonic sixth eighth and so on you'll notice though that the fundamental is gone because the fundamental is the first harmonic and one is an odd number wait what what happened to the fundamental all we did was flip the bottom part of the wave to the top all of the wave is still there so where did that frequency go well to answer that we need to know what is a fundamental frequency a fundamental frequency is determined by the time it takes a wave to repeat itself called an oscillation if i have a wave that did one full oscillation in one second it would be a one hertz wave but when i flipped the negative part of the wave to be positive all of the sudden what was originally one oscillation turns into two oscillations because the wave now repeats itself over a shorter time so the length of one oscillation is now half a second or two hertz by flipping the negative parts of the wave to be positive we've doubled the fundamental frequency so is that frequency lost forever is there a way for us to have even harmonics with the fundamentals still there is if we just take the left side of the curve and put it to zero this adds the fundamental back and keeps all of the even harmonics what was originally two oscillations now goes back to being one oscillation the basic shape that's made up of even harmonics doesn't change it just repeats itself half as frequently this is called half wave rectification even harmonics don't sound as harsh as odd harmonics and this is because they're at more stable musical intervals and you can hear it if i just play the even harmonics [Music] [Laughter] [Music] even harmonics just sound more buttery okay so odd curves give odd harmonics to our sign even curves give even harmonics crazy small caveat to this rectifying a square wave flips the bottom part of the wave and gives silence a nice warm dc offset but dc offset is a frequency of zero and so you can think about it as the zeroth harmonic so this rule i guess still holds what if i don't make our curve symmetric at all so the left side is different than the right side if i send a sine wave through it now both even and odd harmonics are created the closer the curve is to an odd curve the more odd harmonics are created and the closer it is to an even curve the more even harmonics are created now i gotta remind you that i've been using sine waves this entire time however you might have realized in your time listening to music that most people don't play sine waves real instruments and synthesized sounds have much more complex frequency distributions and you can't necessarily know what the new frequencies will be just by looking at the saturation curve harmonic distortion technically only means distorting a sine wave if there's any other frequencies present you'll get harmonic distortions big brother intermodulation distortion which is much much more complicated so this is a really important point probably the most important thing in this video what you're passing into your distortion plugin is just as important if not more important than how you're distorting it the best sounding distortion comes from properly processing the sound before you even send it into your distortion and i'm going to do a whole video on that so i think this video is a good introduction to the basics of saturation and harmonics but the next few videos i'm going to be talking about specific saturation techniques and a bunch of the different kinds of saturation and how we can use the principles in this video to get the sound we want as of right now that video is not made so i want to hear from you guys what are you guys curious about with saturation are you struggling with anything in particular and not just in music maybe just in life let me know below thanks for watching [Music] you

Channel: sseb

Views: 154,936

Keywords: saturation, mixing with saturation, tape saturation, harmonics, harmonic distortion, even odd harmonics, tube saturation, tube vs tape, what is saturation, mastering with saturation, analog saturation, waveshaping, ableton saturator, You Don't Understand Saturation, audio saturation explained, saturation techniques, saturation tutorial, saturation for beginners, saturation mixing, saturation for mastering, Dan Worrall, How to use saturation mixing

Id: YuojAtE8YCY

Length: 17min 0sec (1020 seconds)

Published: Sat Apr 10 2021