Synth School: Part 1

After all the political talk in recent years about a return to traditional values, Paul Wiffen kicks off a major new series on synth programming by arguing the Analogue Fundamentalist Party case — that an understanding of the basic elements of traditional analogue synths is essential to fully exploit the various types of synthesis available today. This is the first article in a 12‑part series.

Back when I wrote my first series on the basics of synthesis (longer ago than I care to remember), there was really no need to mention the word analogue, as it was the only type of synthesis commercially available (except for the odd bit of harmonic addition on prohibitively expensive computer systems like the Fairlight). As a result, anyone who knew anything at all about synthesis would be familiar with the basic building blocks of waveforms, filters and envelopes. This meant that when a new synthesis technique came along, some of the elements in it would be familiar, even if it didn't use all the same components to build up a sound. So FM synthesis (or Frequency Modulation, which will be covered in a future part of this series), for example, might not have filters, but it used sine waves and envelopes. Sampling might not use regular waveforms, but most samplers had filters and envelopes on them — and so on.

While I may sound like a right‑wing politician attempting to claim the moral high ground, I still maintain that anyone who has a good grounding in the principles of analogue synthesis will not take long to get their heads around any new system that comes along, simply because several of its elements will probably be familiar to them, so all they need to do is spot how the unfamiliar elements are used to do the job of the missing analogue stages.

While experienced analogue synthesists can get into the right ballpark when imitating acoustic sounds, it's clear that this way lies considerable frustration.

Five years ago, such an insistence on starting with analogue might have been greeted with scorn, as few people were using analogue synths for music making. Now, though, whether through the use of original analogue instruments bought on the second‑hand market, authentic recreations of the way the sound was made (like the Novation Bass Station), hurriedly adapted PCM‑based systems like the Yamaha CS1x and MC303, or even the computational muscle of DSP‑based physical models of analogue such as the Korg Prophecy and recently released Roland JP8000 and Yamaha AN1x, the analogue sound and programming style are back in a big way. Perhaps it's the pre‑millenium retro vein in all forms of music, from techno to straight rock. But it does mean that starting this series with analogue makes me hipper now than I've ever been accused of being in my life. Even if analogue synthesis hadn't made a huge comeback, I'd still be starting with it. I just wouldn't look so cool!

Another side benefit is that those of you buying brand new physical models of analogue synthesis (three of which will ship this year to swell the growing numbers already out there) need not worry about how the sound is achieved internally (any more than those of you using the genuine article or PCM‑based copies). The controls still use the same terminology, the very terminology we will be exploring in these first few articles.

Subtraction — That's The Name Of The Game

Most other forms of synthesis are additive in nature — they take simple elements and add them together to build up the more complex sounds which our ears find interesting. The most obvious example of this is additive synthesis, which takes sine waves (possibly the most uninteresting sound of all) and sums them to imitate the harmonic series found in nature. Even FM synthesis, which multiplies sine waves together in an attempt to generate complex waveforms more quickly, tends to add several of these products together to get to its more effective results (which is why 6‑operator FM sounds better than 4‑operator FM, because you can add more products together).

Analogue, or subtractive, synthesis (as it is sometimes called in academic circles) does the opposite. It starts with more than you need, and you take away bits until you're left with the sound you want. This makes it more analogous to sculpture (where the sculptor knocks lumps off a big block until the shape he wants is revealed) than painting (where the image is built up from individual brush strokes).

To continue the sculpture analogy, where do we get our sonic block of stone and what form does the audio chisel take? Let's take the block first. If we're to remove frequencies from sound, presumably we need to start with a sound that has more frequencies than we need. There are two possibilities here. Firstly, we could take a sound with all the audible frequencies contained in it, and many analogue synths do have the ability to generate this sound, the technical term for which is... noise. It should be reassuring to any absolute beginners that they are already familiar with this term, even if they would normally associate it with a generic description of non‑musical sound. Indeed, if you just listen to the noise setting on an analogue synth, without any filtering or enveloping, it is a fairly unmusical sound. Usually referred to as white noise (meaning that it contains all frequencies at equal volume), it takes a fairly severe amount of processing to remove enough frequencies from this to leave you with a musical sound (although, as we will see next month, it can be done, by using resonance).

It is the variable nature of the pulse wave which makes it my favourite as a starting point for analogue synth sounds.

Fortunately, there are other sound sources which contain lots of frequencies suitable for selective removal, but which also sound more musical to begin with. Although the sine wave we mentioned earlier in conjunction with additive and FM synthesis contains only a single frequency, other commonly recognised regular waveforms — square, sawtooth and pulse — contain whole families of frequencies in mathematical relationships to each other, known as harmonic series. In lay terms, this means that the human ear perceives them as a single pitch whose tonal quality is determined by the exact mix of related harmonics present.

This is because these harmonic series are naturally occurring and are produced by traditional 'pitched' musical instruments. What we hear as a single note from a flute, piano or violin is actually a whole series of sounds which are related to each other. The actual pitch we hear in musical sounds is known as the fundamental and this is usually the lowest and loudest frequency present (although not necessarily so). The other frequencies present in the aforementioned waveforms (and many natural sounds) are all multiples of the fundamental's frequency (two times, three times, four times, and so on). These are referred to as the first harmonic, second harmonic and so on, making up the harmonic series. Guitar (and other stringed instrument) players actually use these harmonics as a part of their repertoire of timbres. By touching the string halfway, or a third or quarter of the way, along its length they cause it to vibrate in two, three or four sections, at twice, three times or four times the frequency respectively. Many wind instruments achieve the higher octaves in their range by a similar technique, blowing harder to split the vibrating column of air into sections. Indeed, brass instruments before the introduction of valves could only play the pitches in the harmonic series (hence the reason why standard military bugle calls are variations on the higher harmonics).

Of course, all these acoustically produced 'harmonics' actually contain their own harmonic series, from the new fundamental that has replaced the original. Few sounds in nature consist of a single frequency, as the energy used to create any particular frequency usually spills over into creating its related harmonics at lower volumes. The closest sound you might get to a sine wave produced acoustically is wetting your finger and running it round the rim of a wine glass till it begins to resonate (a great way to liven up a dull dinner party).

Unfortunately, the 'pure' sound of a sine soon bores the ear (unless combined together by additive synthesis or FM — see future episodes), so what are your waveform choices if you want a whole raft of related frequencies instead of a single one?

Meet The Candidates

Fortunately for subtractive synthesis, waveforms such as sawtooth, square and pulse, which are easily produced by electronic oscillators, contain a whole heap of harmonics which determine their characteristic timbres. Indeed, the sawtooth waveform (so called because the slow rise/fast fall of the cycle when traced out resembles the teeth of a saw) contains all the harmonics within the human hearing range, although not in the same quantities. In fact, the loudness of each harmonic is inversely proportional to its frequency. So the harmonic with double the frequency of the fundamental is at half the volume, three times the frequency is at a third the volume, and so on. This makes this waveform ideal for producing fuller sounds, as it contains all the frequencies related to the fundamental.

The square wave (so called because the trace it makes looks like square blocks — or the tops of castle walls) is the one electronic waveform which has always produced a murmur of recognition on first hearing. It contains only all the odd‑numbered harmonics (ie. every other one) again in inverse proportion to their frequency, and the 'hollow' sound this produces is extremely reminiscent of the clarinet. Presumably this is because the resonant characteristics of the body of the clarinet accentuate the odd‑numbered harmonics and mute the even‑numbered harmonics. The patch charts supplied with old analogue synths always had a clarinet patch (square wave with wide open filter), and this was also a common preset when technology became available to recall synth settings instantly.

The other common waveform on analogue synths is the pulse wave and this is a bit of a chameleon. You can't describe its timbre, nor even list the waveform's harmonic content, as this varies with the width of the pulse. Yes folks, unlike the staid old sawtooth waveform, which is unvarying in its harmonic content, you can change the harmonics and their proportion in the dynamic go‑ahead pulse waveform by changing the width of the pulse. Indeed, the aforementioned square wave is actually a special case pulse wave, where the negative and positive sections of the cycle are of equal length.

It is the variable nature of the pulse wave which makes it my favourite as a starting point for analogue synth sounds. This enduring love affair started on the day when I twisted the width control on a Wasp for the first time with a pulse waveform selected on the oscillators (before that I had assumed that the width control must be broken, because it didn't seem to do anything). The moving harmonic spectrum which greeted my ears really transformed my interest in synthesis from a cerebral one to an emotional one. In that brief sweep many different harmonic spectra came and went, and I realised that analogue synthesis could hold as much sonic interest as any naturally produced sound. While the human ear cannot always pick out the static presence of particular harmonics, it's extremely sensitive to changes in their levels (as we'll see when we come to additive synthesis in a later article). The fantastic thing about the pulse wave is that not only are there thousands of variations of harmonic spectra available as starting points for sounds, at the tweak of the width knob, but also, most analogue synths will let you automate the moving of the pulse width. This technique is referred to, unsurprisingly, as Pulse Width Modulation, or PWM for short.

Why should we limit ourselves on electronic instruments to things that occur in the real world?

The width parameter actually refers to the duration of the positive component in proportion to that of the complete cycle. So a 10% pulse wave means that the positive segment only lasts one tenth of the cycle length before dropping to the negative segment. A 50% pulse wave (aka square wave) means that the positive and negative segments are of the same duration.

We've already looked at the harmonic content of the square wave (all the odd harmonics decrease in volume as they go up, in case you weren't paying attention earlier) and whilst it's not feasible to describe the spectra at every possible width setting, the fundamental and lower harmonics become weaker the further from the central setting you venture. This leads to a bright but thin sound which, at the extremes, starts to sound as if it is moving up several octaves before disappearing altogether. Some analogue synths prevent this from happening, by restricting the width control to between 5% and 95% or even 10% and 90%, providing a sort of set of 'training wheels' for fledgling synthesists, but on other machines you can completely silence the oscillator by turning the width control too far.

Later analogue synths (usually those with presets) feature width knobs which only vary between 0 or 5% at one end of their range and 50% (square) at the other, as their designers started listening to the result and noticed that a 30% pulse wave sounds the same as a 70%. So if the analogue synth you have access to doesn't have graphics or numbers next to the width knob to indicate the width at that position, try the following procedure to find out which range you have. Move the width knob (with pulse wave selected on at least one oscillator, unless you want to repeat my error of all those years ago) until you hear the signature 'hollow' sound of the square wave (you may even have a preset square wave to compare it to). This will probably be either the central position or the maximum.

Oscillators: The Other Use

Pulse width modulation, the automatic movement of pulse width by the synth in a repeated cycle, is as good a way as any of being introduced to the other type of oscillator used in analogue synthesis: the Low Frequency Oscillator. The LFO is one of the many tools first invented for analogue synthesis which have found their way into other synthesis styles, just because they're so useful. The low frequency at which this type of oscillator cycles is below the range of human hearing, so it's no use routing an LFO through the audio pathway of the synth. Instead we use an LFO to control the regular, repeated change of settings on the synth (the jargon term for this is modulation, because 'change' would just be too easy to understand!). The LFO can be routed to control, amongst other things, the pitch of the audio oscillators (for vibrato), or as here, the width of the pulse wave. Hardy souls may prefer to move the width control for their pulse wave themselves, but for the busy player (using all 10 fingers on the keyboard) and the lazy (more my style), LFO control of PWM (aren't all these three‑letter abbreviations great?) is the best thing since sliced bread (no, actually, it's more satisfying than that!).

Minimoog Model D: The third audio oscillator (a luxury few analogue synths boast, whatever their price point) can be set to operate as an LFO.

On the Minimoog and Memorymoog, the third audio oscillator (a luxury few analogue synths boast, whatever their price point) can be set to operate as an LFO, but this example of switching between audio device and modulation device is fairly rare. Normally audio oscillators are audio oscillators and LFOs are LFOs and ne'er the twain shall meet. Audio oscillators are usually labelled as OSC 1, OSC 2, and so on, and LFOs as LFO 1, LFO 2, and so on. The waveforms these low‑frequency oscillators can adopt vary slightly from those used by their audio cousins. The sine wave, for example, often eschewed by analogue audio oscillators because of its rather thin, single‑frequency sound, really comes into its own on an LFO because of its gentle undulating nature.

Most of the time you want LFO changes to be gradual and without sudden jumps. Sudden or instant movement of parameters tends to introduce an 'event' into a sound which the ear often perceives as a new note. Gradual changes, such as those brought about by the smooth cycle of a sine wave, maintain an interest in the sound without demanding the full attention of the listener, as abrupt changes do. Thus it is that the classic pulse width modulation effect uses a sine wave on a slow LFO to vary the width setting. Particularly on low bass notes or string ensemble sounds, this makes for the most sensual sound an analogue synth can produce, with the slow ebb and flow of the harmonic content making for a subtle but intoxicating effect. The best‑known example of this is the original Moog Taurus pedals, which featured a special preset with this effect hardwired in. Beloved of many a prog‑rock band, this sound has yet to re‑surface in the analogue vocabulary of dance music, probably because there is more interest in the real sub‑bass end, which is somewhat concealed by the PWM movement higher up the harmonic series. However, anyone who has heard Taurus pedals through a big arena PA cannot doubt for a second that the real low end is definitely present. If you want to try out this effect for yourself at home, it's fairly simple to set up.

• Route a slow LFO (no more than one cycle per second) to the pulse width of your oscillator, and crank the depth of the modulation up.
• Play a low note and you should hear a continuous movement in the sound as the harmonics come and go.
• If you want to use the sound higher up, you may find the effect a little lost, as many of the harmonics will have moved out of the audio range, but you can compensate for this by speeding up the LFO a little (not too fast, though, or it can end up sounding out of tune).

While I would always rather have other types available, if your analogue synth only has low‑pass filtering, you will still be able to get the majority of 'standard' analogue sounds

One word of caution when setting up your own PWM effect: just as you can set the static width of a pulse wave to be so narrow that the sound disappears altogether, so an LFO set to too great a modulation depth can take the pulse width in and out of the same territory, so that the sound temporarily disappears. If you hear this happening, just back off the LFO depth a little. Sometimes this can happen just once every few minutes, but in that case, you can be sure it will happen right in the middle of your best take or the highlight of your solo. Here's one solution I've found which avoids the need to decrease the amount of PWM in your sound.

If both slightly detuned oscillators of an analogue synth are set to pulse wave and their widths are modulated by different LFOs, set to slightly different speeds, then not only does the richness of the PWM effect increase as the two shifting harmonic patterns interact, but the chances of your sound going AWOL at the critical moment are less than you winning the lottery jackpot. Of course, there are some who might describe this technique as over‑egging the pudding (usually insensitive producers trying to get some other instrument to fight its way past my overblown synth sound), but I've never subscribed to the 'less is more' philosophy (being more of a 'too much is never enough' kind of guy!).

Other uses for the LFO, such as vibrato (modulating the pitch) and tremolo (modulating the volume) are also best used with the sine wave settings (indeed some synths don't offer a choice, their LFO waveform being fixed to sine wave). Its near‑relative, the triangle wave, sometimes available as an alternative, is subtly different, making the variations linear instead of exponential (straight up and down instead of slowing towards the extremes before going back to the centre). If you've got both on your synth, see if you can hear the difference. Even with a slow LFO speed, it's a subtlety easily lost in a mix. If you don't have it, don't feel too hard done by. It's a bit like New Labour and the Conservatives: 9 out of 10 voters can't tell the difference.

Filter Tips

Once you've selected the waveforms that give you the mix of harmonic content you want to represent your virgin sculptor's block, you need the sonic equivalent of a hammer and chisel to 'chip away' the unwanted bits. This is the filter which, as its name implies, removes unwanted frequencies and also allows you to boost certain frequencies if required (a capability not implied in its name, admittedly). Which frequencies are removed and which are left depends on the type of filter used. Most analogue synths only have one filter per voice (except modular designs, of course) and a good many of those are limited to the low‑pass type. Others may have a switchable type, but even then it will be the low‑pass setting which gets most use.

The low‑pass filter attenuates (lowers the volume) of the frequencies above its cutoff point (the frequency at which it is set to work either manually or automatically). It lets frequencies lower than this cutoff pass through to the audio output (hence its name). The reason why this is the most commonly used type of filter is that for most musical purposes we need to hear the fundamental frequency of the oscillator, and a low‑pass filter will not remove this until it is closed down nearly all the way (ie. until the cutoff frequency is moved to the bottom of its range). So even when some pretty drastic filtering is going on, we can still hear the fundamental pitch. That's why many manufacturers decided it was the only filter type needed. While I would always rather have other types available, if your analogue synth only has low‑pass filtering, you will still be able to get the majority of 'standard' analogue sounds. It may limit your ability to venture into the weird and wonderful, but it shouldn't restrict your mainstream analogue palette too much.

The cutoff frequency of the filter is perhaps a slightly misleading term, as it actually refers to the frequency at which the filter starts to do its job of attenuation. However, analogue filters can only gradually reduce frequencies in proportion to the distance from the cutoff. Slope‑off might actually be a more accurate term, if it didn't imply someone leaving work early. Indeed the measurement of how quickly a filter attenuates is known as the slope or gradient of the filter. On conventional analogue synths (and many modern ones) this is either 12 or 24dB per octave — so each time the frequency doubles, anything at that frequency is reduced by another 12 or 24dB.

If you're interested in making new sounds, you'd do well to look for analogue synths with high‑pass and band‑pass filters.

The characteristics of a filter change subtly, depending on the degree of attenuation it offers. Aficionados of the more drastic slopes (those on the Minimoog or ARP Odyssey, for example) praise the punchiness of the resulting sound, whilst those who favour the gentler gradient filters (on Roland instruments, for example) speak of a smoother, rounder sound. It's all a matter of taste, and you'll have to compare analogue synths to see which suits yours, if these vague descriptions don't immediately strike a chord with you.

You may come across another way of referring to a filter's attenuation capabilities: the terms 2‑pole and 4‑pole. These refer to the number of circuits the filters originally used to do the job — each pole represented 6dB of attenuation. Don't worry too much about this, though (if you're buying second‑hand the information may not even be available); just listen to the sound as you move the filter about and see if you like it. Those who need scientific accuracy in the description of their filters may do better to look at some more modern DSP models of filters, which are very precisely documented.

By this point the more perceptive of the uninitiated will be saying to themselves "Never mind all this dB/oct stuff; why use waveforms full of harmonics if all you're going to do is take half of them out again?" Why indeed? The answer lies in the fact that the filter's cutoff frequency can be controlled in real time, either manually or via devices like the LFO (which we have already looked at) or the envelopes (which we will cover next month, as they're used in all types of synthesis). So you can start with all the frequencies present but close down the filter quickly, taking out progressively more frequencies as you go, so that the tail end of the sound is much duller, lacking the top end. This is a fair approximation of how plucked strings act in the real world. As the string is struck, much of the harmonic series is generated, giving a very bright attack. But as the energy present in the system dissipates, it's the higher frequencies which die away fastest, leaving the lower harmonics to ring on until only the fundamental is left.

Again, while the imitative role of analogue synthesis is much reduced, the ear still gravitates to sounds which although not exactly the same as naturally‑occuring sounds, nevertheless have some of the same characteristics. So a previously unheard bright sound dying away is more easily assimilated by the ear, as it shares the same overall timbral characteristics as more familiar sounds. In a similar way, sounds whose harmonic content stays roughly the same, or rise and fall more slowly as a means of expression, are also familiar, as the ear recognises these characteristics from bowed strings and wind instruments. Here, too, the player can make a note last as long as (s)he wants (provided they have the stamina) and bow/blow harder or softer for expression. The sound which starts dull and gets brighter/louder is a much rarer phenomenon in nature, and as a result synth sounds like this have that 'backwards tape' character.

We'll look in detail at how envelopes shape these timbral (and other) variations in the sound next month, but to conclude this article, I'd just like to acquaint you with the rarer types of filter, as some of them are in danger of extinction (notwithstanding some brave preservation work being done by the DSP engineers at Emu Systems on the Emulator Operating System). Whilst they will never help you in your search for piano, strings and brass, they are creative tools which should appeal to those interested in less run‑of‑the‑mill sound design (see Figure 3, which illustrates the three types of filter you're likely to encounter).

• The high‑pass filter does the opposite of its more common brother and removes the frequencies below the cutoff point. So a sweep of the filter in the upwards direction will remove the fundamental first and then the lower harmonics, leaving the upper harmonics sounding till last. Again this is a fairly unnatural situation, and may sound strange to the ears, but why should we limit ourselves on electronic instruments to things that occur in the real world? Why not do things which are unusual or impossible in nature, and if we like them, use them? Let's face it: most of the current uses of sampling are hardly naturalistic!
• The band‑pass filter is a combination of the operation of low‑pass and high‑pass, in that it attenuates frequencies both above and below the cutoff (leaving only those around the actual cutoff frequency). In some analogue synths band‑pass operation was actually achieved by running low‑pass and high‑pass filters in parallel (usually splitting the available poles of filtering between them). Some of the more interesting and unique filter configurations were based on this principle. Several ancient Korg solo synths had a great device, called a Traveller, which consisted of two sliders, one of which controlled the low‑pass cutoff and the other the high‑pass cutoff. Although they could be moved apart to widen the frequencies allowed through, they had a physical restraint to prevent the high‑pass going lower than the low‑pass, which would have filtered out all frequencies, leaving no sound.

The OSCar had a similar system, but in band‑pass mode the two cutoff frequencies were swept in tandem from one knob (with two poles of filtering on each, instead of the 4‑pole filtering on high and low pass), with a second knob, labelled Separation, which governed the distance between them. This allowed some interesting vocal effects, as this is a fairly crude model of the way the human vocal system works (those interested in this type of thing should look at Emu's formant filtering on Morpheus, UltraProteus and their samplers, as it is a much more sophisticated version of the same principle!).

However, most band‑pass filters, when available at all, did not offer this degree of control. The single cutoff parameter applied to both high‑pass and low‑pass elements, and frequencies either side were attenuated equally and immediately. Its principal effect was to make the waveform sound as if it were coming down a telephone line (as an analogue phone cannot reproduce lows or highs, it can be considered a primitive band‑pass filter). But clever use of even simple band‑pass filters still produces interesting, if more esoteric, timbral changes. These kind of facilities are what fascinate me most about analogue synthesis, and if you're interested in making new sounds rather than just imitating acoustic ones, you'd do well to look for analogue synths with high‑pass and band‑pass filtering on them.

Next month I'll look at how resonance accentuates a filter's action, and l'll cover the way in which an envelope works and how it can be used to shape a sound's pitch, volume and harmonic content in real time. This is a staple analogue technique, but its application is universal to programming, as it's a standard tool in any type of synthesis. Until then, if you have an analogue synth, experiment with manual tweaking of filtering (especially quick movements of cutoff) as you'll understand the need for automatic control via envelopes better when you've tried to do things manually.