Synthesiser Basics: Part 2 – Filters

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In Part 1 of Synthesiser Basics we looked at the way in which a synth generates tones. In this next part we look at the process of subtractive synthesis and the role of filters in shaping and defining sound.

Subtractive Synthesis and Filters

Different synthesisers may employ different methods of synthesis. A few of these methods include additive synthesis, wavetable synthesis and FM synthesis – you can read more about these here. However, the most commonly employed method is that of subtractive synthesis. In essence, unwanted frequencies are subtracted from the original waveforms (generated by the oscillator) in order to achieve a certain timbre. An easy way to understand this method is to liken it to a stonemason carving a sculpture from a slab of rock.

Filters form the backbone of subtractive synthesis. Like a stonemason’s chisel they are the primary tool used to carve out the sound. The filter section of a synthesiser modifies timbre by attenuating certain frequencies in the waveform and letting others through. This is where things may get a little confusing. If an oscillator generates a waveform at one particular frequency and a filter simply removes/attenuates certain frequencies, how can a filter modify the timbre of a tone? The filter would either just let frequency through or it wouldn’t right? Well, not exactly.

Waveforms and Harmonics

In order to properly understand how a filter defines the character of a sound it is important to firstly discuss the concept of harmonics. The basic building block for all sounds is the humble sine wave. Every sound imaginable can be broken down into combinations of multiple sine waves at different pitches and volume levels. This means that even basic waveforms such as square, triangle and sawtooth waves are, at their core, made up of a series of sine waves. The loudest sine wave in a tone is known as the fundamental. It is the fundamental that defines the actual pitch of a tone. The additional sine waves that make up the tone are known as harmonics. Harmonics are always higher in pitch and exponentially decrease in volume relative to the fundamental.

Pure sine waves do not contain any harmonics; they are only made up of the fundamental frequency.

A triangle wave is made up of the fundamental frequency and all odd harmonics. Odd harmonics are those 3x, 5x, 7x, etc. above the fundamental. For example, a triangle wave played at 100 Hz will be made up of the 100 Hz fundamental frequency and harmonics at 300 Hz, 500 Hz, 700 Hz etc. Relative to the fundamental, these harmonics are considerably lower in volume and quickly decay to nothing. Because it contains harmonics (albeit at low volumes) it sounds somewhat higher, richer, and louder then a sine wave.

A square wave is also made up of the fundamental frequency and all odd harmonics above the fundamental. However, compared to a triangle wave, the harmonics are much louder. Because of the increased impact of these harmonics square waves sound richer and fatter than triangle waves. As a point of reference, old Nintendo game soundtracks were made almost exclusively from square waves.

Sawtooth waves are the most complex of the basic wave shapes. They have a distinct ramp shape combining the front end of a triangle wave with the back end of a square wave. The wave is made up of the fundamental frequency and all harmonics at gradually decreasing levels. For example, a sawtooth wave played at 100 Hz will be made up of the 100 Hz fundamental frequency and harmonics at 200 Hz, 300 Hz, 400 Hz, 500 Hz etc. Sawtooth waves can be easily identified by their distinct sharp buzzing sound.

For harmonic-rich waves like square, triangle and sawtooth, filters can have a dramatic impact on the timbre by selectively removing certain harmonics.

Synthesizer Basics: Part 2 – Filters
Example of a LPF curve via Wikipedia
Synthesizer Basics: Part 2 – Filters
Synthesizer Basics: Part 2 – Filters
Synthesizer Basics: Part 2 – Filters
Triangle, square and sawtooth wave harmonics via http://beausievers.com/synth/synthbasics/

How filters work

There are three fundamental components that define the impact of a filter: the type of filter, the cutoff and the resonance. The most common type of filter in subtractive synthesis is the low-pass filter (LPF). Other types of filters include the high pass, band pass and notch. A LPF, filters out everything above the cut-off frequency and lets everything below it pass. The cut-off frequency therefore determines the point where the filter starts attenuating frequencies. This point is not a fixed value and subsequently may be moved around the frequency spectrum. In a LPF, moving the filter down the frequency spectrum results in more frequencies being filtered out; the opposite occurs when it is moved up the frequency spectrum.

It is important to note that the cut-off does not operate as a brick wall. Frequencies are not hard stopped at the cut-off point. Instead they are attenuated at a rate defined by the slope or roll-off of the filter. The filter slope is measured in decibels per octave. A filter with a slope of 12 dB/octave means that for each successive doubling of frequencies above the cutoff frequency, the response falls 12dB. Likewise, a 24dB/octave results in a steeper 24dB decrease. Most synths will implement 12dB or 24dB filter designs, referred to as 2-pole and 4-pole filters respectively.

Resonance is another essential aspect that allows filters to colour and give character to the original sound. Resonance (also referred to as Q) boosts the volume of the frequency at the cutoff point. On its own resonance is useful for giving a sound a little more high-end, or can be used to dramatically boost the upper harmonics of a sound, giving it more edge and bite. Some filters can be driven into ‘self-oscillation’,effectively giving the user another oscillator to play with – when a filter self-oscillates it create it’s own sine wave, the pitch of which can be controlled by changing the filter frequency. While using the resonance alone can have interesting results, it really shines when used in conjunction with envelopes and LFOs.

The type of filter and the way in which it is implemented varies widely between synthesisers. This comes as no surprise; given the filter is the sound-defining centrepiece of any subtractive synthesiser. A classic example of a 2-pole LPF design can be found in the Korg MS-20 LPF. This type of filter design is often described as a ‘bright and bitey’. In contrast the iconic Moog ladder filter is a classic 4-pole design, delivering a sound that is often described as ‘warm and full’. Each type of filter has its pros and cons depending on the type of sound you are trying to achieve. There is often a trade-off between bass retention and ‘warmth’. While 4-pole often providing a fat warm sound, the bottom end can sometimes seem to ‘disappear’ on these designs compared to 2-pole equivalents. To try and cover all bases, the original Arp Odyssey came in 3 revisions, each with a differing filter model: a 2-pole, a 4-pole and a special 4-pole design, which attempts to retains bass (The Arp re-release by Korg combines all three filter models in the one unit). Other synths, such as the Korg Minilogue allow you to switch between 2-pole and 4-pole modes, giving the user the best of both worlds. Recently, insanely flexible and feature packed Arturia Matrixbrute has taken filter implementation to the next level, combining a switchable 2/4 pole ladder filter and a switchable 2/4pole steiner-parker filter in the one synth.

Synthesizer Basics: Part 2 – Filters
The unique filter section of the Arturia Matrixbrute

To summarise so far…

An Oscillator produces a waveform, either sine, square, triangle or sawtooth. This waveform is fed into a filter, usually a low pass filter, which modifies the oscillators “raw” sound by attenuating the higher frequency harmonics of a sound while passing the lower harmonics. The slope of a filter’s cutoff, how it reacts at different frequencies and the different ways it can resonate or drive a signal all contribute to giving a unique character to a synths sounds.

Synthesiser Basics: Part 3 – LFOs & Envelopes

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