Sound Synthesis: Part 1

Though sound synthesis has a relatively short history, its progress has been rapid, with the result that the basic concepts of synthesis are now becoming lost in the mists of time — yet to effectively programme current synths, it really helps to know them.

[Regrettably the diagrams are not available for this article, due to archive DVDs being lost.]

Synthesis has been a musician's dream since the early days of music concrete — an era when electronic compositions were assembled from cut lengths of recording tape using simple electronic oscillators and 'found sounds' as sources. The original Doctor Who theme was one of the most widely heard examples of music concrete, but creating music in that way is very time consuming and laborious — and has many inherent limitations. What the more forward‑looking musician of the time wanted was a keyboard instrument that could emulate any known instrument, produce an infinite range of new sounds and respond to the player's touch like a 'real' musical instrument. To the best of my knowledge, such an instrument has never been built — but in the course of their endeavours, electronic designers have spawned a varied range of complex and fascinating instruments, all of which come under the generic heading of synthesizers. But before we can approach synthesis in a meaningful way, we need to know a little about the fundamental principles of sound itself.

Sound

Sound is produced by airborne vibrations which impinge on the human ear and are translated into the sensation we know as hearing by the human brain — you all know that, so I'll skip the stone, pond and ripples analogy. Most of you will also be familiar with the fact that the higher the frequency of vibration that causes the sound, the higher the perceived musical pitch. But there's a lot more to sound than mere pitch — what gives a sound its unique character?

The simplest sound is a pure tone, and if we were to plot out the changes in air pressure on a piece of graph paper, we'd get a sine wave, as shown in Figure 1. The electrical output of a microphone 'listening' to this signal would also be a sine wave. A continuous sine wave sounds like a whistle or test tone — every cycle of the waveform is identical, there's no variation in level, and as a sound, it's musically uninspiring. Our continuous, pure tone posseses a fundamental pitch but nothing else. However, the vast majority of real life sounds are infinitely more complex. Rather than being made up of a single pure tone, they are made up of a whole series of tones known as harmonics. In the case of a musically meaningful sound, there will be a strong fundamental frequency (which determines the musical pitch), accompanied by a series of harmonics that are higher in frequency (pitch), and usually lower in level, than the fundamental. Harmonics occur at exact multiples of the fundamental frequency; if they are even multiples they are called even harmonics, whereas if they are odd multiples, they are called odd harmonics. Figure 2 shows how the harmonic series is constructed. Sounds may also contain frequencies that aren't directly related to the fundamental frequency and these are known as non‑harmonic overtones. Sounds such as bells contain many such complex overtones.

The character of a sound is determined by two key factors: the harmonics (and non‑harmonic overtones) that make up that sound, and the way that these change in both level and pitch as the sound evolves. In other words, most sounds can be viewed as dynamic events, not as continuous or constant.

The way in which the levels of the different harmonics and overtones change with time determines the envelope of the sound, and this has a profound bearing on how we interpret what we hear. For example, a percussive sound starts very suddenly and then the vibrational energy dies away because no new energy is being applied to sustain the sound. It follows, then, that a typical percussive sound will start suddenly and then decay, as shown in Figure 3a.

A bowed sound, on the other hand, may build up relatively slowly as the energy driving the sound is being applied over a period of time, not in one hit. When the driving energy, in this case the bow, is removed, the string vibration will decay in much the same way as a percussive sound. Figure 3b shows a typical bowed string envelope. Interestingly, when most natural sounds (which includes acoustic instruments) decay, the higher frequency harmonics decay faster than the low frequency components (it's the laws of physics, Jim!). This knowledge can be useful when it comes to synthesizing natural sounds.

To accurately synthesize a 'real' sound, we'd need to recreate all the harmonics and overtones of the sound in question, set their relative levels, apply a separate envelope to each harmonic and vary the frequency of each of them to emulate the way they behave in the real sound. Building a sound from scratch in this way is known as additive synthesis, but in practice, it is extremely difficult to implement — though modern resynthesis methods are getting very close. However, we can 'paint' sounds using much broader strokes and still produce a fair imitation of the real thing, though most types of synthesizer are better at emulating some types of sounds than others. No one instrument yet built satisfies all needs, and it can be argued that the relative strengths and weaknesses of modern instruments is also what makes them interesting.

Analogue

Mainstream synthesis started with the analogue synthesizer, so called because it relies entirely on analogue circuitry, where oscillators, filters and envelope shapers are controlled by electrical waveforms and voltages. Analogue circuitry doesn't posses the inherent stability of modern digital designs so parameters such as tuning and filter frequency tend to 'drift' a little, but the subtle detuning effects this causes are thought to contribute to the warm, 'organic' sound of analogue.

Though we shall be covering synthesis in far greater depth in the near future, it is interesting to look at the basic building blocks of a typical analogue synthesizer. Even though the way in which an analogue synth creates and shapes sound is different to the methods used by most current digital synthesizers, there are certain fundamental similarities which will be pointed out as they come to light.

To the musician brought up on modern polyphonic instruments, it might seem strange that the original analogue synths were all monophonic and had no velocity sensitivity. This was due to limitations in technology — even monophonic instruments could be horrendously complex.

Subtractive Synthesis

Analogue synthesis is a form of subtractive synthesis because, instead of attempting to synthesize a sound from its basic elements, we start with a 'harmonically rich' waveform and then, using filters and envelope shapers, trim away what isn't needed. This can be thought of as the electronic equivalent of sculpture, where the artist starts off with a suitable block of stone and then chips away until the finished statue is revealed. Unfortunately, the tools at our disposal, the filters and envelope shapers, are not sufficiently refined to enable us to produce a sculpture that exactly mirrors real life. At best, analogue synthesis produces a caricature of the sound being imitated, though in the case of some types of sounds, the simulation can sometimes be more attractive than the real thing. Again we see a parallel with modern S&S (Sample and Synthesis) instruments which also work on the subtractive principle; sampled waveforms are used as a sound source and are then further modified by filters and envelope shapers.

Any analogue synthesizer can be thought of as a number of quite separate building blocks which can be wired together in a variety of ways, depending on the desired result. Indeed, the early modular systems were exactly that; physical patch cords were used to connect the various modules — and that's where the term synth 'patch' originated. The simplest analogue synthesizer might contain one oscillator followed by one filter and one envelope shaper as shown in Figure 4. The logical starting point is the oscillator because it's here that the raw waves are created prior to shaping.

Oscillators

The basic sound sources for analogue synthesis are voltage controlled oscillators (VCOs) and noise generators. The oscillator provides a tunable sound source with a choice of useful waveforms, while noise generators produce broadband hiss — a random electrical waveform containing all audio frequencies at all times. Noise is useful for simulating breath sounds, wind and surf, percussion and so on.

There are four main oscillator waveforms used in analogue synthesis:

• sine wave
• square/pulse wave
• triangle wave
• sawtooth wave

As touched upon earlier, the sine wave comprises just a fundamental frequency with no harmonics, so no further modification can be made other than to control its pitch and level. Square waves and triangle waves, on the other hand, contain the fundamental plus a series of odd harmonics, the triangle wave having a lower harmonic content than the square wave. Both produce a characteristically hollow, reedy tone; the square wave sounds brighter than the triangle wave. If the mark/space ratio of a square wave is changed, the resulting pulse waveform produces a different harmonic series and is useful for creating reed‑like tones. For a full explanation of square and pulse waves and mark/space ratio, see box.

Though the circuitry is quite different, a modern, sample‑based synth has a very similar signal path to its analogue ancestor.

The sawtooth wave comprises the fundamental plus a series of even harmonics and is used to create string, brass and stereotypical pad sounds. To produce a mix of odd and even harmonics, the oscillator waveforms may be added in different proportions. Figure 5 shows the main waveform types available.

Though it's educational to examine the harmonic structure of both real and electronically generated sound, it's arguable whether a knowledge of the subject is of much practical benefit to the synthesist. Most synthesists work by ear, and even though it can be shown mathematically that a square wave has a very similar harmonic series to a clarinet, the reason you ultimately choose to use the squarewave as the basis for your clarinet patch is because it sounds right.

Voltage Control

As VCOs are to be used to create musical notes, some means must exist to control their pitch from a keyboard. In the analogue world, this is done by means of control voltages, and the most common approach was the so‑called 'one volt per octave' system. The keyboard is arranged so that whenever a key is depressed, an electrical voltage is produced which, in effect, is used to tune the oscillator to the required note. In the one volt per octave system, semitones are one twelfth of a volt apart, so as you move up a semitone on the keyboard, the control voltage rises by one twelfth of a volt and the oscillator pitch goes up by one semitone. There's a little more to the circuitry because it's vital the oscillator continues to play the correct pitch, even when the key has been released, otherwise any sustaining sounds would go out of tune as soon as you lifted your finger off the key. To achieve this, a circuit called a keyboard sample and hold is used. Don't let the terminology put you off — it simply 'remembers' the control voltage after the key is released and holds it until a new note is played.

The keyboard also produces a gate signal whenever a key is depressed. This is little more than a simple switch action and is used to control the keyboard sample and hold circuit and also to trigger other building blocks such as envelope generators. In other words, all it really does is tell other parts of the system that a key has been depressed. Figure 6 shows the VCO connected to the keyboard via the sample and hold circuit. If we were to plug this in and listen to the result, we'd hear a fixed level tone but with a different timbre depending on which of the available waveforms we selected. We'd be able to play melodies, but there'd be no pauses between notes; everything would be strictly legato.

Portamento

Before moving on to the filters and envelope shapers that give the sound its form, there's a little more that can be done at the oscillator and keyboard stage. So far we've got a tone up and running that jumps from one musical note to another as we press different keys on the keyboard, but what happens if, instead of the control voltage switching instantly from one value to the next, it is forced to change over, say, a period of one second? Now, when a new key is pressed, the oscillator pitch will slide from the old note to the new note taking a second to do so. This glide or portamento effect was one of the hallmarks of early synthesizer music and most instruments had a portamento rate control that allowed the glide rate to be set anywhere from instantaneous to several seconds. A fairly fast glide is useful in simulating brass sounds, especially trombone, while slow rates are useful in creating special effects.

LFO

You'll probably be familiar with LFOs or Low Frequency Oscillators, as just about every synth ever made has at least one. The simplest LFO is a sine wave oscillator running at just a few cycles per second and the mod wheel on a modern synth usually defaults to using the LFO to create vibrato. On analogue machines, the LFO can be routed to a VCO to create vibrato, but it may also be routed to the filters or envelope generators to modulate the timbre or output level. There'll be more on modulation later, but it is interesting to see how the LFO is used to create vibrato in an analogue synthesizer.

Because everything is voltage controlled, it's easy to control, say, an oscillator from both the keyboard and the LFO simply by adding the two control voltages together using a simple mixer circuit as shown in Figure 7. Because the oscillator has a one volt per octave control law, a one volt LFO signal would cause a vibrato depth of one octave, which would be excessive for most purposes. However, by using the LFO level control, the modulation depth can be set to any value between off and 'well over the top'.

More About Oscillators

Running two oscillators together produces a rich, dynamic sound; a slight degree of detuning allows the phase of one oscillator to drift relative to the other to produce a natural chorus effect. It's also possible to tune one oscillator higher or lower than the other by, for example, an octave or a perfect fifth. This can produce very fat sounds, especially when combined with suitable filtering.

Though the circuitry is quite different, a modern, sample‑based synth has a very similar signal path to its analogue ancestor. Instead of a simple electronic waveform, we start with a sampled sound, but this may still be thought of as an oscillator. This sample is then passed through a filter and finally through an envelope shaper; though the technology involved is entirely digital, and is controlled by numbers rather than voltages, the underlying concept is surprisingly similar.

Progress?

Later incarnations of the analogue synth saw the VCOs being replaced by digitally‑controlled analogue versions (DCOs), and subsequently by completely digital oscillators. Though these had many advantages on paper (such as improved pitch stability), the purists still claim the original low‑tech versions sounded better.

As people demanded more and more polyphony, using analogue oscillators was no longer practical, and it became clear that going completely digital was the only feasible solution. Similarly, the patching systems that worked so well on the old modular synths would be completely unmanageable if the same patch had to be duplicated eight times to obtain 8‑note polyphony. The modern digital equivalent of the old analogue patching system is the button and menu‑driven system with which most of us are so familiar. Digital control systems also made programmable synthesizers possible for the first time, enabling the user to save patches for instant recall. Prior to this, all synth sounds had to be set up from scratch and the only way of storing them was to write the control settings down on a piece of paper.

Next month I'll be looking at the other two main building blocks of analogue synthesis — the filter and the envelope shaper.