What is additive synthesis?
>Unlike subtractive synthesis – ie, that found on most analogue synths, where you start with a harmonically rich waveform and remove frequencies using filters – additive synthesis builds from the ground up.
It uses Fast Fourier Transform theory, which says that any audio signal, no matter how complex, can break down to a series of sine waves; you can recreate any waveform with the right combo of sine ‘building blocks’. Pile up sine waves (ie, harmonics) at related harmonic integers at different amplitudes, and you get familiar waveforms.
For example, start with a simple 100Hz sine as the fundamental frequency, then stack up more sine waves at odd-integer harmonic intervals from the fundamental (ie, one at 300Hz, another at 500Hz) to create a basic square wave. Take that same initial 100Hz sine and add sines at odd- and even-integer multiples of the fundamental (200Hz, 300Hz, 500Hz, etc) and you’ve created a sawtooth wave.
This process of adding together so-called ‘partials’ to create more complex waveforms is the basis of additive synthesis. Things get more timbrally interesting once you mix in additional sine waves at inharmonic intervals from the fundamental, modulate the amplitudes of these harmonics over time, alter the phase of individual sines in relation to each other, and mix in noise for more bite.
Sounds technical, but it’s essentially the same concept at work in many classic organs, where pipes or drawbars stack simple sounds, altering the instrument’s timbre.
>Frequency modulation synthesis is notoriously complicated, and for those more used to working with analoguestyle subtractive instruments, it’s easy to be put off by jargon such as ‘operators’, ‘algorithms’, ‘carriers’ and ‘modulators’. When you break the concept down to its fundamentals, however, it’s not actually as impenetrable as you may think.
The basic principles behind FM are actually common in the analogue realm. Essentially, FM involves taking a simple waveshape – typically a sine wave – and altering its timbre by modulating it. If you’ve ever used an LFO to create vibrato by applying it to an oscillator’s pitch, then you’ve encountered a basic form of FM. The difference is that FM synths use audio-rate oscillators as opposed to the lower frequencies of an LFO. This audio-rate modulation is fairly common in the analogue realm too; synths like Arturia’s MiniBrutes, Moog DFAM or the IK UNO Synth Pro all let users create a simple form of FM by using one analogue oscillator to modulate the pitch of another.
So if FM is common to analogue synths in one form or another, why do we associate FM synthesis with digital instruments? Well, instruments that we’d typically call true ‘FM synths’ take this concept and run with it, using more complex routings as well as dedicated envelopes in order to finely adjust the relationship between each oscillator. Because of the precise, stable tuning and complex processes required to make this work, it’s usually only possible with DSPpowered instruments.
Let’s tackle some of that jargon. ‘Operators’ are essentially FM-speak for oscillators. In classic FM synths, these are usually sine waves, and the key difference between FM operators and analogue-style oscillators is that each operator has its own amp envelope, meaning it can be individually shaped before being routed to an output or to modulate another operator.
Operators divide into categories of ‘carriers’ and ‘modulators’. Carriers are operators routed to an output, meaning they’re heard in the finished sound, modulators are routed to modulate the pitch of a carrier, so we only hear the effect of their modulation, not an output from the modulator itself. The arrangement of these operators is controlled by something known as an ‘algorithm’, which is essentially a map indicating which operators are assigned as carriers or modulators and where each is routed.
The other key difference between operators and their analogue counterparts is that their tuning is usually labelled as a ratio. These are harmonic ratios – ie, multiplying the incoming pitch by a certain number. Tuning an FM operator to ‘2:1’ equates to ‘2x’ the pitch, meaning it’ll be an octave above an operator tuned to ‘1’. An operator tuned to 3:1 will be pitched an octave and a fifth above the original note; 4:1 gives you two octaves, and 5:1 gives you two octaves and a third.
These ratios, combined with the individual envelopes, are key to FM sound design. Modulate a carrier tuned to 1:1 by a modulator with a higher ratio and hear it add high frequency harmonic content. Use the modulator’s envelope to introduce a slow fading attack or short decay, to hear how this creates changes to the sound over time.
WHEN TO USE IT…
FM synthesis is often associated with metallic or ‘glassy’ sounds: eerie pads, bells and mallets. It’s great for bass too – the stability and wide-tuning range of FM synths mean they can create seriously powerful low end. It’s an underrated tool for percussion too though. The fact that each operator has its own envelope gives lots of control over the attack and decay elements of percussive sounds, which can be great for creating kicks, hats or metallic perc tones.