Harness the power of additive synthesis
Additive synthesis hasn’t gained the popularity enjoyed by other forms, but behind its apparent simplicity lies a whole world of innovative sound design. Robert Alan adds it all up.
Before we begin, you should note that we will be using Native Instruments’ Reaktor to explore the possibilities of additive synthesis. A modular synthesis environment such as Max, Reaktor, Pure Data or SynthEdit is a useful tool for exploring additive synthesis as you will need lots of oscillators. If you don’t already have such software, you can download Pure Data for free from www.puredata.info
First, let’s define exactly what we mean by the term ‘additive synthesis’. Additive synthesis is the collective name for a range of synthesis methods that add together a number of basic waveforms to create a more complex waveform. And that’s it! It sounds simple enough, but underlying that simplistic facade lies a complexity of infinite detail.
In some respects, additive synthesis pre-dates what we now know as the synthesizer. Indeed, the first implementation of additive synthesis can be found on the Hammond organ. The Hammond produces an electrical current that is close to a sinusoidal (sine wave) and a drawbar system enables you to add or remove harmonics to create different sounds. With only one drawbar extended the organ will produce a pure (ish!) sine wave. If the player then extends the second drawbar, a second sine wave will be added to the sound. The third drawbar adds a third sine wave and so on. Each of the sine waves is harmonically related and you can combine these at different amplitudes, giving you a whole range of possible tones.
In the 1960s, Jean-Claude Risset analysed and resynthesised trumpet tones at Bell Laboratories using additive synthesis. These experiments eventually led to the first true digital implementation of additive synthesis, the Bell Labs Digital Synthesizer (or the Alles Machine).
It was during the 1980s that additive synthesis became viable for the commercial market, with synths such as the NED Synclavier, DK Synergy and the Kurzweil K150, which was built like a tank and featured a massive 240 oscillators. Unfortunately, though, additive synthesis was a long, labourious process in the early days and many of these early additives also featured other synthesis methods, such as FM or wavetable synthesis, which offered much more in terms of instant gratification. One of the first synths to bring a real-time, intuitive approach to additive synthesis was the British-made OSCar.
Science and synthesis
The OSCar’s approach to additive synthesis was fairly simple and quite unscientific: players simply used the keyboard to alter the level of each harmonic. Importantly, however, the custom additive waveforms could be combined with the ‘traditional’ waveforms, offering new sound-design possibilities without overcomplicating the process.
The invention of the OSCar paved the way for yet more real-time additive synthesizers. Arguably the most notable synthesizer to follow the OSCar was the Kawai K5 (for more details see www.vintagesynth.com/kawai/kawaik5.php). Offering 64 harmonics per voice, ingenious methods for rapidly programming the synth, numerous modulation sources and digital filters, the K5 was one of the greatest hardware additive synthesizers of all time. The K5 was followed by the K5000, released almost ten years later.
Recently, interest in additive synthesis has increased ten-fold as sound designers are drawn to the undiscovered world of sound that additive synthesis can offer. Rapidly increasing computing power has played a large part in this, but what’s more, software additive synthesis simply makes much more sense. Ultimately, additive synthesis demands a highly customisable interface, which enables the user to alter the harmonics in whichever way they see fit. Having this degree of control allows users to create new and previously unheard sounds.
Subtractive versus additive
These days, we have many different synthesis types to explore, including subtractive, additive, frequency/amplitude modulation, granular and physical modelling. Techniques can vary greatly in their approach to generating sound, and most modern synthesizers are hybrids, combining several elements from each type. However, at a rudimentary level there are two ways of performing ‘classic’ synthesis, taking either a subtractive or additive approach.
In subtractive synthesis (also known as analogue synthesis), sound design begins with a basic waveform with lots of harmonics. Filters are then used to remove or subtract harmonics and shape the sound to create the desired tone or timbre. Subtractive synthesis is by far the most common approach – most DAWs have at least one subtractive synthesizer included: Logic’s ES-1 and ES-2, Reason’s Subtractor and FL Studio’s Wasp all make use of subtractive techniques. There is also a range of third-party plug ins that utilise subtractive techniqes, such as LinPlug’s Albino and FXpansion’s Cypher.
While subtractive synthesis begins with a waveform containing lots of harmonics, additive synthesis makes use of the most basic waveform, which has only one harmonic –the sine wave. Rather than remove harmonics, the user combines lots of different sine waves to gradually build up a complex waveform. Additive synthesis is much less common than subtractive synthesis; to get a taste of additive techniques there are some synthesizers that offer additive features, such as the G-Media ImpOSCar, which emulates the basic additive tone-generation techniques of the original OSCar synth. Then there are the more complex additive synths – such as U-He’s Zebra and Camel Audio’s Alchemy – that boast a mind-boggling array of features.
Additive synthesis is a complicated topic, so it helps to understand the underlying theory before diving in head-first. This will also give you an idea of exactly what you’re up against. Let’s start at the top…
Sound can be defined in two domains: the time domain and the frequency domain. Both domains represent the same information, we are just looking at the information in a different way. So, when you import a sound sample into your audio editor or DAW and you see the shape of the waveform, this is the sound being displayed in the time domain; when you open up the frequency analyser you will see a graphical display showing the amplitudes of the various frequencies, this information represents the same sound in the frequency domain.
A core principle of our understanding of sound is that any soundwave can be broken down into a sum of simple sinusoids (sine waves). This process is called Fourier Analysis, after the French mathemetician who discovered it, Joseph Fourier. To understand this better, let’s consider an example. You examine a sound in the frequency analyser and see that there are five frequencies present, positioned at 100Hz, 200Hz, 300Hz, 400Hz and 500Hz. Another way to interpret this information would be to say that the sound is made up of five individual partials (or sine waves).
So, if a sound can be ‘broken down’ into its constituent sine waves then it is reasonable to assume that the reverse is also true: that a sound can be ‘built up’ by generating the appropriate sine waves. This is indeed true, and you could re-create this sound by generating five sine waves at 100Hz, 200Hz, 300Hz, 400Hz and 500Hz.
In fact, this principle is the basis of how the frequency analyser works. The frequency analyser takes a complex sound and breaks it down into a number of different sine waves using the FFT (Fast Fourier Transform), then displays the relative amplitudes of each of the sine waves in a graph. We are performing the opposite process in additive synthesis, using a number of different sine waves to build up a more complex sound.
Now, consider putting a snare drum sound through the frequency analyser and looking at the resulting graph. You will see thousands of different sine waves present. In additive synthesis, it is this level of complexity that we are dealing with. We are working with the finest level of detail in the frequency domain, constructing sound from the atom upwards. This level of detail can seem daunting – it’s certainly no walk in the park! However, the real advantage of additive synthesis is in the level of control it offers.
Taking control
So far we have discussed only defining the frequency of our sine waves. This is fine as a starting point, but unless we change our sound in some way we are not really making use of the full potential of additive synthesis. The next step, then, is to consider the amplitude of our sine waves, putting particular focus on how the amplitude changes over time.
Sounds that do not change as time progresses are considered to be static. Static sounds seem flat and never develop into anything more than a basic tone, such as an organ. By contrast, most real sounds have a complex evolution, whereby individual frequencies or groups of frequencies follow a detailed envelope, fading in and out of prominence as the sound develops. This is what we must imitate in our setup in order to access the range of sounds that additive synthesis offers.
To clarify this point further, let’s consider the evolution of a plucked string sound and how we might go about imitating it. We know from experience that a plucked string sound begins loud and bright and gradually fades to become quieter and darker. In other words, the higher frequencies lose amplitude at a faster rate, leaving only the lower frequencies towards the end of the sound, resulting in a ‘duller’ or ‘darker’ tone.
Let’s consider how we might go about imitating this using additive synthesis. Let’s assume that we have numerous oscillators and we set their frequencies to imitate the harmonic nature of a string. Oscillator 1 produces a sine wave at the first harmonic (the fundamental), oscillator 2 produces a sine wave at the second harmonic and so on. For each oscillator we also have an envelope that determines how quickly the amplitude decays. Oscillator 1 decays over one second, oscillator 2 decays over half that time (0.5s), oscillator 3 decays over a quarter of that time (0.25s) and so on. This setup would produce a sound that begins bright and fades to a much duller sound, leaving only the fundamental frequency present in the final stages of its progression. This evolution is much like that of a plucked string.
In fairness, this sound could be created much more easily by using subtractive synthesis, employing a sawtooth waveform and a low-pass filter. However, what if we wanted to adjust this sound in a more unusual way? Let’s imagine that we wanted our mid frequencies to begin to decay, as before, then rapidly increase until the end of the sound, when they shot down to silence in an instant. This type of evolution would simply not be possible with your typical subtractive setup.
In these days of complex hybrid virtual analogue synthesizers, it’s perfectly feasible that you could approximate the previous example using complicated routing and multi-stage envelopes. However, this is only a very simple example. In reality you’ll be controlling hundreds of individual oscillators at the same time and you would not think of modulation in terms of basic groups, such as low/mid/high frequencies. For example, you may decide that harmonics 1–20 have a ripple-like modulation effect, that all odd harmonics are detuned by an amount realtive to their frequency, and that higher harmonics become stretched as they gradually decay. It is at this level of control that additive synthesis really begins to shine.
The next step
All this talk of Fourier analysis and spectral modelling can seem a little daunting but don’t despair: you don’t have to dive in at the deep end to get started with additive synthesis. Anyone who has combined tunable oscillators to build up new tones has already started on the path towards additive experimentation. The next step is to add some more oscillators and explore the new control possibilities that are on offer.
Start with the basic examples, as described above, and familiarise yourself with the results of changing groups of frequencies in different ways. You’ll be exploring new sonic territory in no time and finding some gems along the way. MTM
This feature first appeared in Music Tech Magazine issue 103
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