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Introduction to Subtractive Synthesis 08/14/2003
Subtractive synthesis, something that every newbie to Industrial tries to learn, and many don't do so well. Here's a guide that will help you understand all those pretty knobs.

GENERAL ASSUMPTIONS IN THIS ARTICLE: This lesson assumes that when you think of tuning, you think of A-440, which is the note "A" above middle C. Just understand that as we use "A" in this example, we are really talking about any note you please, but when explaining the mathematics, the A notes are easiest to do the math around because whole numbers are easy. Also, the patch we discuss was originally written with a Virus B in mind. Since most synthesizers only have two oscillators, ignore the bass triangle wave unless you have a synth with more than two oscillators, or if you have two oscillators and a sub oscillator that is a sine wave, you can use that too.

Subtractive synthesis is the most common method of synthesis today. While other methods such as frequency modulation and additive synthesis have some popularity, when most musicians think synthesizer the first thing that comes to their head is a subtractive synth (or one of those generic ROMplers that flood the market today, but that's another story for another time and another genre).


Oscillators:

The first section we are going to approach is the oscillator section. The oscillators are technically the only things that make sound unless you count self oscillating filters (more on that later). Everything else is some form of modification to this sound. The average synthesizer has 2 oscillators, while others have three or more and some have only one oscillator.

All sounds, no matter what, consist of "harmonics". When a sound is made, it consists of "sine" waves (explained below) that combine to create the sound. A natural harmonic is any sine wave in the sound that is a multiple of the lowest sine wave (for example, on the note "A", which has a base of 440Hz in the A above middle C, possible natural harmonics are at 880Hz, 1320Hz, 1760Hz, 2200Hz, and so on, adding 440Hz each time). There are also unnatural harmonics, which is basically any wave that does not occur within those bounds, but is still in the waveform.

The "saw" wave oscillator creates a waveform that is characterized by a vertical leap from the highest point of the wave or lowest point (the other way around is common, but it doesn't make a difference in sound). After this leap, the wave moves back to the point where the leap was made in a straight diagonal line. Honestly it is pointless to describe the shape of the wave, because the shape isn't important, the harmonic content is. What makes the saw wave special is that it contains every single natural harmonic that a wave can contain in gradually decreasing levels. As a result of this, the wave has a very "buzzy" sound to it.

The "square" or "pulse" oscillator, in it's normal form, contains only the odd numbered harmonics, resulting in a bright yet hollow sound similar to that of a clarinet (except much much brighter). However, on many synthesizers the width of the pulse can be adjusted, which affects the harmonic content of the wave. As the width of the wave becomes less and less balanced, the wave starts to gain a buzz similar to a saw wave, but not exactly the same.

The "triangle" oscillator contains very little harmonic content, but just enough for there to be a noticeable "edge" to it's sound.

The "sine" wave is the simplest of all sounds. It has no harmonic content, just the base pitch with nothing else on it.

Many synthesizers offer waveforms other than this (noise, formant sounds, etc.). Feel free to experiment with those waveforms to get a better understanding of their sound. The best way to get a grasp of an oscillator's sound is to either deactivate or totally open the filter and turn any and all modulations such as envelopes or LFOs off. This will make more sense later.

While these explanations don't offer much of an explanation for the reason a certain wave is used in a certain context, it is impossible to explain why certain waves are used when unless we understand the filter first.

The one thing that can be explained is why certain tunings are used. Normally, a synthesizer will offer a set of tuning options that should consist of "coarse" tuning and "fine" tuning. Coarse tuning sets the pitch of the oscillator in relation to the note played in one note increments. The most common usage of the coarse tune function is to change the octave in which the oscillator plays. This allows you to do something like create a patch that uses two saw waves, but has a triangle wave one octave (12 notes below normal) below the two saw waves. This will basically be a loud saw wave (when you use any combination of oscillators, they add on to each other. always) that has a "low note" below it. Hearing it is better than trying to explain the physics of it.

Fine tuning is like coarse tuning, but extremely mild. Instead of changing the pitch in semitones (basically a note up or down the entire keyboard), the pitch is changed in fractions of a semitone (depending on the synthesizer. Most true analogs will go an infinite number of fractions up or down a note, some digitals only go 64 fractions each way, some actually divide it into "cents", which is 1/100th of a note, and some "fine tuning" knobs, like on the Korg MS2000, change pitch slightly at first and gradually increase until the change becomes almost as drastic as a semitone per value). The best way to explain how this would work is to look at our two saw waves and a low triangle wave again. If we were to take the fine tune knob of one of the saw waves and turn it up some, a very slight type of "noise" (dissonance to be technical about it), will start to come in, which leads to a more natural and organic sound. It's kinda like hearing two people sing the same note. Neither one gets it perfect, and as a result you can tell it's two people singing it.

 


The best way to get a grasp of an oscillator's sound is to either deactivate or totally open the filter and turn any and all modulations such as envelopes or LFOs off.


Filters:

Now that you know what's making the sound, let's talk about changing a sound (which is really what everything but the oscillators do). How filters work is that they are assigned a certain frequency (which can be modulated by various sources, but more on that later) and, depending on the type of filter, remove all frequencies above (lowpass), below (highpass), not close to (bandpass), or close to (band reject). A lowpass filter makes a tone seem "darker", a highpass filter makes a tone seem "brighter", and bandpass and band reject simply remove a section or two of harmonics which can have some interesting results. Once again, not all synths have all of these filters. Band reject isn't very common, and some synthesizer only have a lowpass filter, which leads to what I call "lowpass hell" (writing a song that has so many sounds made by lowpass filters that it's all low frequencies and sounds like beating on a large dead animal). Filters almost always have two main settings, cutoff and resonance.

Cutoff rate is usually stated in "poles", or more understandably, decibels per octave (6 x the number of poles). For example, with a 2 pole lowpass filter (12db/oct), every harmonic located an octave above the filter is 12 decibels quieter. This means that if on the note A at 440Hz you set the cutoff at 2200Hz, the harmonics would decline at a rate such that the 4400Hz frequency is 12db quieter, the 8800Hz frequency is 24db quieter, and so on and so on. With a highpass filter, this means that 1100Hz is 12db quieter, 550Hz is 24db quieter, and so on. On bandpass, 1100Hz and 4400Hz are 12db quieter, 550Hz and 8800Hz are 24 db quieter, and so forth. On a band reject filter, this means that 1100Hz and 4400Hz are 12db louder, and so forth.

As the cutoff rate increases, how quickly the filter reduces the volume before, after, or around the cutoff point increases. On a lowpass this means that the sound will become "darker" as the cutoff rate is increased because the higher harmonics are less and less audible.

When you increase a filter's resonance, you basically increase how loud harmonics near the cutoff point are. Using only a little resonance, you can make a sound seem a tad brighter in it's harmonics around the cutoff. There are three possible scenarios when you crank the resonance extremely high, depending on your synth. Most modern synthesizers will compensate for the gain created by the filter's resonance and you will hear only the harmonics closest to the cutoff. On many synthesizers that have analog filters (instead of digital emulations), the filter cutoff will be very loud, but you can still hear the stuff under it, however you'll probably be tempted to turn the volume down some if your synthesizer is like this because this can get loud. The final possibility happens on some analog synthesizers (like the Minimoog), and this is "self oscillation", where the filter will actually start to feed back and CONSTANTLY create the harmonic at the input whether or not there is sound coming from the oscillators. However, not many synthesizers do this and you probably are not on your first synthesizer if you have one where this happens.

Another thing that's worth mentioning is key tracking. Most modern synthesizers offer variable key tracking. When the key tracking is set at 100% or a 1:1 ratio, that means that the cutoff rate will rise or decrease at the same rate the notes change. This means that the patch will sound exactly the same no matter what note you play. The only difference will be the pitch. On acoustic instruments this really does not happen because as the string, pipe, head, or whatever grows shorter, it becomes harder and harder for it to make the higher harmonics. Wind instruments don't experience this nearly as drastically as percussive and string instruments do, so don't automatically assume that you should have total or no keyboard tracking. I'll go into more detail on this one later.

An example of how to use a lowpass filter is to once again look at our patch that consists of the two saw waves and the triangle wave below them. Currently this has a very bright edge to it, but we will be taking off that edge with a 24db/oct lowpass filter. So since the general sound we're going for here is probably most likely to be used as a bass sound, we want the filter cutoff pretty low (but not too low, or as stated earlier it will sound like you're beating a large dead animal). We'll go ahead and set the cutoff at somewhere around 1300Hz. It is not important that you get the filter cutoff on a harmonic or octave. Filters are a gradual decline so it doesn't make TOO much of a difference if you aren't totally exact. There is a difference, but you don't have to be Adolf Filter about it.Also, if your synthesizer doesn't offer exact values for the cutoffs, just set it to something that sounds pretty low but doesn't make your patch totally bassy.

If you're hell bent to find close to the frequency I said turn off every oscillator except a saw wave, turn the filter cutoff all the way down, turn the resonance all the way up, and start slowly turning the cutoff knob up. You will start to hear a frequency grow really loud, and then you will hear another frequency fading in as the previously loud frequency begins to fade out, and the same thing will happen after passing the second harmonic. Once the third harmonic has reached it's peak, you're there. Also, turn the resonance back down to a rational amount after doing this and turn your other oscillators back on. This is useful if you're on an analog and for some reason or another want the cutoff dead on a harmonic.

OK, so at 1300Hz our 220Hz triangle wave is untouched until the 6th harmonic, and our 440Hz saw waves start to experience cutoff near thier third harmonic. Since this is a 24db/oct filter, that means that the cutoff will be pretty drastic, so it won't be a very bright sound (keep in mind that you don't want to use a 24db lowpass at a low frequency on every sound, because if you do that your track will be a bunch of muddy lowpass shit). So now we have a relatively dark bassy sound that has a tad of dissonance from one of the saw wave oscillators being slightly detuned from the others. Just for fun, lets add a tad of resonance, only about 10-15%. Normally resonance in a bass makes you sound like a techno weenie, but the reason we are adding resonance here is to make something that comes later a little more noticable. Try to avoid abusing resonance, but if by the end of the article you're starting to think of weird things to do with it feel free to experiement with higher resonance levels. Just don't release it unless you think you've done something pretty unusual with it.


Filters are a gradual decline so it doesn't make TOO much of a difference if you aren't totally exact. There is a difference, but you don't have to be Adolf Filter about it.


Amps and Modulations:

The amp section is simple. It turns the sound into something audible. Amazing.. However, this is a very good turning point for going from the basic sound crafting to manipulation of the static sound, known as modulation, because when you combine the amp with envelopes, LFOs, and other things, it can quickly become the single most drastic factor on what you sound turns out to be.

Envelopes:

We will start with envelopes. The most common type of envelope is ADSR, which means that it allows you to set how fast something goes from unchanged to it's largest change (A: Attack), the change starting to wear off (D: Decay), what level it will remain at a level that is still different from the starting point (S: Sustain), and how long it takes for the sound to go from wherever it's at back to the starting point after you release the key (R: Release). The most common use of envelopes is to change the amp's output level. So lets take our patch once again, and set an envelope to have an instant attack (if you synthesizer is digital or even VA, nudge this up slightly. Digital synths usually don't take well to instant attacks and will have a "pop" near the beginning of the sound on the fastest attack, so nudge this up a value or two), a moderate decay (around 1/4 of a second is good), a sustain of about 1/2, and a pretty fast release (not instant, because that sounds extremely unnatural. Not even palm muting a guitar cuts off the sound as fast as an envelope with an instant release). Now you have a pretty punchy bass. Now lets assign this envelope to change the filter cutoff as well. Change the ammount of the effect according to taste, but due to the resonance that we added you will hear an initial punch and then the brightness of the sound dropping (listening to the resonance you can hear it better). You can also assign an envelope to pitch (there should be a way to route it to the pitch of all of the oscillators. so just to prove a point take a second envelope (or if you only have one, just use it for now and set it back), and go ahead and set the attack rate to the fastest possible, have the decay just slightly above instant, no sustain level, and a release time of zero. Assign this envelope to the pitch and go ahead and make it have as much of a positive (meaning that the envelope raises the pitch instead of lowering it, which can be done too) effect as possible. When you hit a key with an envelope assigned like this, you will hear the pitch of the patch start somewhere extremely high and quickly shoot down to the proper pitch.

LFOs:

LFOs are totally useless for this patch as it currently works, so for the purposes of establishing how LFOs work set the attack time to something pretty slow (perhaps 1/4th to 1/2 a second) and play higher on the keyboard. LFO waves are generally pretty similar to oscillator waves, but they are slower and therefore the harmonic content of an LFO doesn't matter at all, the waveform does. Lets go ahead and take a triangle waveform and have it mildly effect pitch, and set it to something around 6Hz (6 cycles a second in case you don't know) Now when you hit the key, the pitch of the sound will move up and down and you'll have vibrato. If you don't hear anything different, turn up the amount the LFO effects the pitch until you do. If you were to do this to the filter cutoff (crank the resonance up to 30-40%, have the LFO have a moderate effect on the cutoff, and slow the LFO down some), you'll have a slow "wah" effect. If you don't turn the resonance up, it will sound sort of like tremolo, which will be described now. If you set the LFO speed back up to 6Hz or so and assign it to the amp, the volume will move up and down, creating tremolo.

A Comment on Effects and Other Goodies:

Since all synthesizers have different features (effects, different oscillator waveforms, various filter types and so on and so on), I cannot give any sort of valid commentary on them. However, with minimal research on the internet you can probably find out all you really ever wanted to know about them.


There you have it, the basics of subtractive synthesis. While this document explains why synthesizers work and to some extent how, you'll have to read your synthesizer's manual to know the exact process for how to make a change (most manuals will give you all the "how" you need to know). As for what you make, that can only be done by your own experimentation. Everything about the basics of subtractive synthesis has been explained here, but in order to truly understand it you have to work with it. Explore this whole "slow attack" concept some more. Assign a square wave LFO to change the pitch 2 octaves, use waves other than triangle and saw, see what happens when you mix a square wave and a two sine waves tuned to an octave and three octaves above, experiment with different filter types and cutoffs (contrary to the ideas of many, 24db/oct lowpass is not the only filter in the world). Also, not all synthesizers follow this exact signal path. Synthesizers like the Ensoniq ESQ-1 have volume envelopes available for all three oscillators before the filter and have a final volume envelope at the amp stage, and some synths like the Access Virus have multiple filters. The concepts explained here will still work on these synths. Now that you know why your shiny new synth works and your manual should tell you how to use it, go see what you can make.
-Mister Bill

 
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