Pioneered and refined by Bob Moog through the '60s and '70s, subtractive synthesis remains the approach taken by the vast majority of hard and software synthesisers available today. While modern synths are awash with preset patches, any producer worth his salt knows that building new, original sounds is half the battle when it comes to forging a unique sonic personality. So, through this piece, we're going to look beyond the presets to understand the basics of subtractive synthesis, in the hope that it will encourage you to start designing your own sounds from the ground up.

Sonic Basics

All musical instruments are capable of altering three separate elements of the sounds they produce: pitch, tone and volume. At the same time, every instrument you can imagine is governed by its physical properties. In other words, while the range of sounds each instrument can produce is varied (think of violins when bowed or plucked, for instance), a violin could never sound like a trumpet, as the instrument is constructed and played entirely differently.

The concept behind subtractive synthesis is that synths can be almost endlessly flexible, as the way they build sounds isn't tied to physical construction. To understand this we need to think for a moment about acoustics—the way we hear sound and the way it's produced by musical instruments in particular. When you sit at a piano and play a single note, the loudest thing you hear is the note you strike, which explains how you're able to identify it as a C or a G#, for instance. However, in addition to this main note, or "fundamental frequency," a whole range of other notes sound too, called harmonics. Pitch and frequency (measured in Hertz, or 'Hz' for short) mean the same thing but whereas musicians tend to refer to pitches via their note names, in this instance it's better to do some math to understand how harmonics are produced. The note A just above C3 has a full technical name of A440, which contains both its note name and its frequency. Harmonics are produced whenever that frequency is multiplied, so the loudest harmonics you'll hear are those at 880Hz, 1760Hz, 3520Hz and so on. The 440 times table isn't the most friendly, so let's imagine a note which has a frequency at 100Hz. Its harmonics will occur at 200Hz, 300Hz, 400Hz and so on, with each new harmonic quieter than the previous one in the case of most instruments.

Acoustic instruments are capable of producing thousands of harmonics whenever they play a single note which is just as well; after all, if you could strip any instrument of its harmonics to leave just the fundamental frequency, every instrument would sound exactly the same. Thinking about this another way, it's the harmonic content of a sound which provides its characteristic tone. The reason violins don't and can't sound like trumpets, then, is because the range of harmonics produced by each instrument is radically different. Of course, no two violins sound quite the same either but they share enough harmonic content to be identifiable as both being violins.

Man-Made Sound: The Oscillator stage

So how does all of this relate to synthesis? Well, the building blocks of any synthesised sound are called oscillators and what these do is to provide pre-determined groups of harmonics. You'll probably have heard of sawtooth, square or triangle oscillators and each of these is simply a combination of a fundamental frequency and a different package of associated harmonics.

Synthesis provides waveforms that don't exist in nature, however. Acoustic instruments offer harmonic content which is much less ordered than the combinations you'll find in subtractive synthesisers and this is a crucial point, as it explains why synthesisers are so poor at producing real instrument emulations. Think about this another way too—if you want the sound of a violin, either find a violinist or use sample libraries. If you want to enter a realm where an infinite number of new sounds can be produced which don't exist in nature already, however, read on.

To simplify the process of understanding how a subtractive synthesiser works, conjure up a seemingly unrelated image; that of the Olympic rings. There are five main sections or "modules" which make up a subtractive synthesiser with the three essential ones to control pitch, tone and volume at the top and two additional, "optional" ones below which we'll look at shortly. As you might already have guessed, the oscillator stage comes first in the top left-hand ring as oscillators control and produce pitch. Every time you play a note, its fundamental and harmonics are produced as a single packaged sound and the differing oscillator types allow you to hear what those different packages might be.

Sonically, the most basic oscillator choice is a sine wave, which is a fundamental frequency without any harmonics at all (a sound no acoustic instrument can produce) but the other choices will all provide harmonics on top of a fundamental frequency. Subtractive synthesisers often allow you to combine two or more oscillators to produce bigger, thicker sounds. Now that you know what an oscillator is this should make sense—if you add one waveform which contains a certain group of harmonics to another with its own harmonic set, you'll end up with more harmonics present in the combined, richer sound.

Logic's ES1 is a classic subtractive synth and you can see below how each section matches the Olympic rings analogy with Oscillator, Filter and Amplifier sections across the top, the LFO in the bottom left-hand corner and two envelopes in the bottom right.

1. The ES1 features two Oscillators, labelled Wave and Sub. Both have their own waveforms to choose from and their balance can be blended via the Mix slider.

2. The filter features four variations on a low-pass filter, with different strength amounts. Above you'll find the Cutoff dial to control tone and below is Resonance, which boosts the volume of frequencies at the cutoff point.

3. The split output Level slider lets you decide the volume of both the quietest velocities you play and the loudest ones too.

4. Choose your modulation waveform on the left and then its speed on the right. Pick a target parameter from the ladder of options and then move the green slider up to select the amount of LFO effect you'll hear.

5. Attack, Decay, Sustain and Release sliders which, by default, control volume over time.

6. On the left, choose a parameter from the Matrix of options and then either select Attack or Decay to bend up or down into your parameter of choice.

Tone Control

Why is synthesis of this kind called subtractive? Surely if you're adding oscillators together its sound is getting larger rather than anything being taken away. That's right. But the term refers to what happens after the oscillator stage rather than during it. The second Olympic ring, in the middle at the top, is the filter, whose job it is to control tone, and this is where the sound begins to get smaller.

The most common type of filter in a subtractive synthesiser is a low-pass filter and its job is to remove upper harmonic content. Imagine the stack of harmonics coming out of the oscillator as a deck of cards, with the fundamental at the bottom. A low-pass filter splits the deck using its cut-off dial or slider, with more upper harmonics removed the lower the cut-off dial is. You might be wondering why the filter is necessary at all; after all, if you want a sound with fewer harmonics, why not just choose an oscillator combination which features less? Well, tone change is a huge part of record making and the only way you can switch a sound from dull to bright and back again is to have all of those harmonics present. The cut-off point then decides how many of them can be heard at any one time. So, you'll find that sweeping the cut-off point up and down will change your sound as described.

Frequently, filters in subtractive synthesisers are multi-mode which means that low-pass filtering is only one of the available options. Additionally, you might well find high-pass and band-pass modes. High-pass filtering lets through high frequency harmonics above the cut-off point, whereas band-pass filtering allows frequencies around the cut-off point to be heard but removes both those below and those above.

All three options provide huge flexibility to shape a sound's tone but they're also aided by the resonance control. Resonance does something fairly unnatural, in that it boosts the volume of frequencies at the cut-off point. Remember, the cut-off dial has to be somewhere—it's either towards the bottom, in the middle or pointing at frequencies at the top. Wherever it's pointing, resonance will boost the frequency being targeted and with high resonance settings, this will be really apparent. Resonance can either make bright sounds much "fizzier" or warm up frequencies just above the fundamental to give richer, rounder bass sounds, as two examples.

To hear it in action, select a low-pass filter, set resonance to zero and sweep the cut-off dial from top to bottom. Then do exactly the same thing, having turned resonance up to about 70%. You'll hear the fizziness straight away, as well as the warmer bass as the cut-off travels towards the bottom.

Logic's ES M is a single-oscillator synth with basic filter and amp controls and is an example of a great synth to practice synthesis with. Here you can see an automated filter sweep which controls the sound's tone.

Amplify and Modulate

The third circle in the top section of our Olympic Rings is the amplifier section. Early analogue synthesisers were electric instruments whose output could only be heard via amplification, so it makes sense that everything to do with volume would be housed within the amplifier module. Modern synthesisers tend to pack other features into this section too, such as effects processing and distortion capabilities, for instance. Additionally, this is where Velocity control is targeted, to ensure that note volume varies depending on how strongly keys are played. All that matters is that, if you're controlling the volume of a sound in some way, it's the amplifier module you're affecting.

That deals with the three essential elements of oscillator, filter and amplifier, and basic sounds can be constructed with these three components alone. However, remember that synthesisers were designed to echo the capabilities of real instruments. With that in mind, these three components alone miss out some of the performance features that players of acoustic instruments take for granted. For instance, if you want a sound which starts quietly and grows in volume (crescendo) every time a note plays, there's no capability for this control with these three modules alone. Similarly, let's suppose you want to create a vibrato effect where the sound bends from sharp to flat quickly, as a violinist might play. Again, there's no way to achieve this with a basic oscillator, filter and amplifier combination. To provide these facilities, subtractive synths offer two additional modules in the form of LFO (Low Frequency Oscillator) and envelope sections, which occupy the bottom two rings of our diagram.

NI's Prophet 5 emulation provides twin oscillators, flexible LFO routing and independent envelopes for filter and amplifier sections, among many other features.

LFOs

We know what oscillators are now. They're combinations of fundamental frequencies and associated harmonics, with each bundle of harmonics producing a different wave shape. LFOs are no different, except that rather than being designed to be heard like regular oscillators, the sound LFOs produce isn't connected directly to the amplifier. In other words, these wave shapes are silent. You might be wondering why on earth this would be of benefit; after all, what's the point of a sound you can't hear? To understand LFOs, we need another analogy. The most useful one is the wind. If you stand outside on a windy day, you can't actually see the wind, as it's just a bunch of air molecules being pushed around. However, you can see the effect the wind has on things—leaves and tree branches swaying, or ripples on water.

LFOs are like this, as they're inaudible as waveforms in their own right but perfectly audible when they're connected to interrupt the oscillator, filter or amplifier stages. Imagine an LFO with a sawtooth wave shape which ramps up and down. As we know, the oscillator's job is to control pitch so if we were to plug our LFO into the oscillator, its pitch would receive the LFO wave as a control source, so that each note would bend up and down in time with the LFO, producing a vibrato effect.

LFOs provide control of three main parameters; the wave shape, its rate (speed) and its amount. With these controls, you can radically change your vibrato effect. Whereas a saw wave will ramp up and down, a square wave would jump from one pitch to another with no intermediate pitches heard. The rate control is self-explanatory, as it controls how fast the vibrato effect will sound. The amount dial affects how wide the effect will be, with small amounts providing tiny changes sharp or flat of your starting pitch and larger amounts providing more radical bends.

Using a sine wave, it's possible to switch from a natural sounding narrow vibrato to a wide, "police car siren" effect very easily, as you adjust amount and rate. Of course, LFOs don't have to affect pitch. If you've understood the concept, it should make sense that if you plug an LFO into the filter, you'll get tone control, with sounds moving from dark to bright and back again. Similarly, plug an LFO into the amplifier section and the sound will move cyclically from soft to loud. Subtractive synthesisers often provide more than one LFO so that you can control modules with different wave shapes, rates and amounts but the concept is always the same.

The ES2 is a hugely flexible subtractive synth with three oscillators, two filters and range of amp options, two LFOs, three envelopes and a router section which lets you connect a huge range of modulation sources to targets.

Envelopes

The final module contains envelopes with the most common type offering four independent controls: attack, decay, sustain and release. These control how a sound behaves as time goes by. Again, it's easiest to imagine this concept as applied to volume. Think about some acoustic instruments first. A snare drum, when struck, sounds loudly and immediately before dying away fairly quickly. At no stage does its sound sustain. Then think about a violin note bowed gently, starting quietly, growing in volume and then fading away over a second or so once the sound ends. Again, the amplifier section can't control which of these two volume shapes it will produce; by itself, its sound will start and stop as you play a note and release it. So the envelope, like the LFO, is capable of interrupting one of the top three modules to control its behaviour over time.

Three of the controls are self-explanatory when applied to volume. Attack sets how quickly the sound fades in from silent to full volume. Release does the same at the end, determining how quickly a note returns to silence once it has been let go. Sustain sets the level at which a sound will rest at one volume after the attack and decay stages. Decay is the only control which requires a little explanation. Once sound has passed through the attack stage and reached maximum volume, decay controls how long it takes for the sound to fade to the sustain level. So, suppose attack is set to five seconds, decay is set to five seconds and sustain is set to 50%, decay will work as described. However, if sustain is set to maximum (100%), the decay control does nothing; after all, it's not possible to fade from maximum volume to maximum volume.

As with the LFO stage, you're not limited to only applying envelopes to volume. If you want pitch ramps, apply an envelope to interrupt the oscillator stage and if you want tone to change over time, plug an envelope into the filter. Again, higher-spec'd subtractive synthesisers often provide multiple envelopes for added flexibility. Their software synth equivalents often offer a matrix or dedicated routing section, so that you can decide which control source is mapped to which parameter and how strong its effect will be. So there you have it: five modules that allow you to build an infinite array of sounds, with the three essentials at the top and the two optional extras below, ready to make your sound design a whole lot more sophisticated.

LinPlug's MorphoX provides two layers of synth which can be toggled using the mod wheel. A subtractive synth lies at the heart of both layers, though.

Audio: Synthesis technique

1. Logic's basic ES M synth, set to a sawtooth wave, with the filter opened up fully. This is about as basic as synth sounds get.
2. The same sound but with the Oscillator switched to the Square Wave option.
3. This time, the sawtooth bassline has its low-pass filter closed and re-opened using the Cutoff dial, so that its tone changes.
4. The same cutoff sweep, this time with Resonance turned up—notice the much "fizzier" sound.
5. Here's NI's Pro-53 playing a basic sawtooth pad sound.
6. Here's the same joined by a second Oscillator in the form of a square wave. Two separate sets of harmonics are joined together now.
7. The square wave Oscillator has its fine tune dial modified to produce Detune, resulting in a fatter sound. The second set of harmonics are now slightly out of tune now.
8. The Attack dial of the Amplifier Envelope is turned up to soften the start of each note. The Release dial is also turned up so that each note fades at the end. The sound is more pad-like now.
9. Here the LFO is set to a ramp shape and routed into the Oscillator to produce ramping pitch change.
10. This time the LFO targets the low-pass filter's cutoff point, to produce a "wah" effect.
11. This time, all three of the LFO shapes are switched on—ramp, sawtooth and square wave—meaning all three are fighting each other. When routed to both oscillators and the filter, pitch and tone are locked but in a seemingly random way.
12. Let's build a sound from scratch. We're starting with a sawtooth waveform, with its filter wide open.
13. We add Oscillator 2, which provides a square wave.
14. We add the third Oscillator and select a square wave with narrow pulse width, tuned up an octave (12 semitones).
15. We switch on a low-pass filter and slightly increase resonance to darken the sound.
16. We route Envelope 2 into the filter's cutoff point. This makes the tone close as the sound plays and we use the decay time to set this closure to a short period to provide a spiky effect.
17. We increase the Amplifier's Release time to make each note last a little longer.
18. Lastly, we set up an LFO and route it to the filter cutoff so that the sound opens and closes in tone as the sequence plays. It's clocked to a bar in length, so that this movement is in time with the track.