Synth School: Part 3

Having completed his study of analogue synthesis last month, Paul Wiffen takes a look at FM and its related digital synthesis types, which rocked the synth world throughout the 1980s. This is the third article in a 12‑part series.

Incredible as it now seems, 10 years ago, Frequency Modulation (or FM) synthesis ruled the world — well, the musical world at least. Having already sold a phenomenal number of FM‑driven DX7s, Yamaha were in the process of creating cheaper and cheaper FM synths (with increasingly large model numbers) so that even the most impoverished musos could have their own. A couple of years after this, Yamaha launched their (in my opinion) best‑ever synths with the hybrid SY series, which combined 16 FM voices with 16 PCM sample‑based voices. My treasured SY99 is actually my favourite Yamaha product of all time (for reasons which will become clear elsewhere — see the 'Which FM Synth Is Best?' box).

These days, from a synth player or programmer's point of view, you could almost be forgiven for thinking that FM had never existed, and that Yamaha had discreetly drawn a curtain over that whole period of synth history (they dropped FM from the SY85 a few years back, and then quietly discontinued the synth itself); in short, the profile of FM keyboard synths on the market is at an all‑time low. But, in fact, FM synthesis is more widespread than ever; hidden in the bowels of every IBM‑compatible computer now being sold is a miniature FM synth. Back in the days when PCM‑based synthesis (or wavetable synthesis, as the computer industry incorrectly refer to it) was still too expensive to put on soundcards, Yamaha sold their FM technology to Creative Labs as the sonic engine on the original SoundBlaster, in the form of the OPL chip. Due to the phenomenal success of this soundcard and its descendants, the OPL chip is now part of the ubiquitous SoundBlaster spec which games and other multimedia applications alike use for their sonic accompaniement. So every SoundBlaster‑compatible card now produced has to have the OPL chip (even if it also features a high‑quality PCM sample‑based synth as well) — and these days you can't sell a PC without a SoundBlaster card built in. This means that there are actually more FM synthesizers out there than ever, although they no longer sport Yamaha's unique combination of brown and green, nor the label DX. In fact, the huge numbers of FM synths sold in the '80s has probably now been eclipsed by the number included in the PCs that have been sold worldwide!

Capital FM

As the FM sound engines on PC soundcards use a less sophisticated version of FM, we will concentrate on the implementation of FM first made available on Yamaha's DX7 (and their much more expensive DX1). If you are serious about using FM in your sonic arsenal, try to get your hands on an FM machine with the same implementation as this, because the scope of what you can achieve with the less complex implementation, sonically speaking, is rather more limited. In addition to the thousands of DX7s out there (including 1988's DX7 MkII), there are also TX802 and TX816 racks, SY77 & SY99 workstations, all now going second‑hand for a fraction of their original asking price, and all with the 'more evolved' version of FM. This implementation is generally referred to as 6‑operator FM (as opposed to 4‑operator FM on the DXs with higher model numbers and, of course, their OPL chip descendants in PC soundcards). Straight away, we've run into our first piece of FM‑related jargon; operator. However, there is no need to worry about this, as when I tell you that all operators do is produce sine waves, you will (hopefully) recognise them from the previous two parts of this series as being closely akin to the oscillators in an analogue synth. What's different in FM synthesis is the way these sine‑wave generators interact to create sounds.

Don't expect to master FM synthesis as quickly as you did analogue.

So, why are they called operators? The answer lies in history... Unlike analogue synthesis, which was developed and refined in parallel by several different individuals and companies over some years (Bob Moog of Moog Electronics, Dave Cockerell of EMS, Dave Smith of Sequential Circuits, and Dave Rossem of Emu, to name but a few), FM has a much more singular parentage. In the early '80s, a team at Stanford University in California, led by Dr John Chowning, discovered a pure synthesis application for Frequency Modulation, which had been in use as a high‑quality audio broadcast transmission system for some years. The new form of synthesis allowed the creation of sounds which had previously been beyond the ability of most analogue synths (for example, reasonably realistic brass, electric piano, and bell sounds, as well as other 'metallic‑sounding' timbres); and so, emphasising this particular strong point of the new discovery, Chowning shopped FM synthesis around several manufacturers, and, after a few refusals from American companies (who must have later felt like the man at Decca who turned down the Beatles), signed an exclusive agreement with Yamaha for them to develop the new method and bring it to the market. As a result, Chowning and Yamaha were able to develop their own jargon, and decided that operator, rather than oscillator, was the term for them. Actually, it wasn't a bad decision, as it meant that nobody expected to use operators in the same way as oscillators on an analogue synth.

So, how does FM synthesis use operators to create sound? (Warning: more incoming jargon, albeit slightly more familiar!) Firstly, it is important to note that on any FM synth, each operator is known as either a Carrier or a Modulator, depending on the role that the sine wave produced plays in the creation of your FM sound. Those of you who know something about the way radio transmissions work may recognise the terms Carrier and Modulator. In broadcasting, it was discovered that if you modulated the frequency of a waveform instead of its amplitude (as in the earlier method of radio broadcasting, Amplitude Modulation, or AM), you could encode more audio information more accurately for transmission, which resulted in better reception, and a greater bandwidth and dynamic range. Those of you reading this in the Shires will be capable of listening to Mr Branson's fine radio station in hissy old AM (if you haven't given up on it because it's too much like listening down an old telephone), while us Greater London types have it in glorious FM stereo (although I can assure you that Michael Bolton's bleatings do sound worse on FM). The frequency of the carrier, in the case of Virgin Radio FM, is 105.8 MHz (ie. what you tune your radio to — or away from if Mr Bolton is playing) and that of the modulator varies according to the audio signal being transmitted. When we then tune into an FM radio signal, the carrier signal is taken out and we listen to the modulator.

However, in FM synthesis, it is the carrier we listen to (although with the effect of the modulator still present). In other words, we are actually interested in the interaction of the carrier and modulator, rather than using one as a means to get the other from A to B.

In fact, those of you who remember the difference between audio oscillators and low‑frequency oscillators (LFOs) from the first two parts of this series should now be able to understand exactly the relationship between the carrier and modulator. A carrier is like an audio oscillator; its modulated output is sent to the mixer and thence to the speakers. The modulator is more like an LFO. You don't actually hear it, but you do hear the effect it has on the carrier.

The main difference between the modulator and an analogue synth's LFO is the speed of operation. As implied in its name, an LFO operates at low frequencies, nearly always below the audio range. There is no such restriction placed on a modulator; it may operate at frequencies considerably higher than audio, within the audio range, or below it. In this respect, the way it is used is similar to the way analogue synth oscillators can be employed to create ring modulator‑style effects, where you set up one oscillator to modulate the pitch of another (this was covered in more detail at the end of the last instalment in this series). The frequencies produced by this analogue cross‑modulation are ideal for bell‑type sounds and other metallic timbres — exactly the timbres which FM later became famous for. This is no big surprise when you consider that pitch is merely the musical way of referring to frequency.

So, what's the difference between cross‑modulation as practised on an analogue synth and the frequency modulation in the Chowning/Yamaha implementation? Well, to start with, FM operators can only ever produce sine waves, unlike an analogue oscillator. At first, this may seem a bit limiting when you remember that a sine wave only produces a fundamental frequency, but in fact the interaction of just two sine waves can produce incredibly complex timbres. This is because in FM, you don't simply mix two frequencies. Frequency Modulation actually produces multiple frequencies based on the sum and the difference of the original frequencies. The greater the modulation depth, the louder these new frequencies are in relation to the original frequency of the carrier. When you also consider that in Yamaha's FM, modulated carriers can be further modulated or themselves used as modulators, you should see that it is possible to quickly build up large numbers of frequencies in harmonically‑related and/or harmonically‑unrelated series. In general, the former will give the purer tones, and the latter the more complex, more enharmonic sounds, until all at last becomes noise if the relationships get too complex.

This also explains why 6‑operator FM is more versatile than its lesser, 4‑operator relative.If you think about it, there are so many more ways you can configure six operators as carriers, modulators, modulated carriers, carrying modulators, re‑modulated modulators, and so on, than you can four. This brings us neatly to the pretty pictures screen‑printed on the front panel of the DX7 (or on illuminated displays if you are the proud owner of a DX1), which tell you how the operators are currently configured. These configurations are known (jargon alert!) as Algorithms.

Slave To The Algorithm

On modular analogue synths, you could create your own audio signal routings, allowing you to plumb the most bizarre signal paths together. Most analogue synth manufacturers preferred to set the possible paths in stone to some extent, so that you didn't end up with routings which produced no noise or led to the direst rackets (both of which tended to trigger lots of calls to modular manufacturers complaining of "broken" machines). Yamaha saw this problem coming a mile off, and quite sensibly chose to limit how the six available operators on the DX1 and DX7 could be hooked together, permitting only those algorithms liable to produce the most musical results, and thus giving the end user reasonable flexibility without the suffering. 6‑operator FM offered 32 algorithms (its 4‑operator junior had just eight — another plus point for 6‑operator FM). Most DX owners complained that the synths were too complicated, but can you imagine the complexity if all routings had been freely user‑definable? Or what the user interface would have been like? The mind boggles!

The conventions Yamaha use in the diagrams of these algorithms are fairly simple once they are explained. Whilst we do not have the room to reproduce the layout of all 32 algorithms in this article, 11 are pictured in Figure 1, on the first page of this article, as examples, which will allow you to visualise some of the ways DX operators can be arranged.

Algorithms are 'read' from top to bottom, and the operators on the bottom row of any algorithm are the carriers. These are what actually produce the sound you hear coming from the machine, mixed together like the signals from analogue oscillators before they enter their synth's filter. Anything above the bottom row is a modulator, and the lines joining them to the carriers show which is modulating which. You will see from Figure 1 that in many of the first few algorithms, one carrier is being modulated by two or even three modulators. In the final 16 algorithms on the DX7 (numbers 17 to 32), one modulator is able to modulate several carriers. Of course, some algorithms (numbers 3 and 4, for example) have a third row on top, and this is where you find the modulators modulating modulators (stay awake at the back there, please). Algorithms 1, 2 and 16 (in the diagram) even have a fourth level to re‑modulate a modulated modulator. In case I have failed to lose you so far, I must also mention that each algorithm has an feedback loop somewhere, with which one or several operators can be set to modulate itself/themselves. As an example of the latter type, take a look at algorithm numbers 6 and 4 (again, see Figure 1) where a chain of two and three operators respectively are fed back on themselves).

I hope you can now see that the algorithm selected has the most fundamental role to play in terms of the sound the DX produces. Randomly switching the algorithm on any of the preset sounds will soon convince you of this. In fact, if you are not careful, you can end up removing all the FM from your sound!

DX In Not‑All‑FM Horror Shock

Now it's time to let you in on a big secret. Some of the algorithms on a DX7 have hardly any FM in them at all, which you might feel is a bit like finding out the Pope is not Catholic after all. Algorithm 32 has no modulators at all (except that operator 6 can modulate itself, thanks to the feedback loop) and is actually more like additive synthesis (next month's topic of investigation) in that it just mixes together the sine wave audio output of all six operators, a bit like drawbars on an organ. Algorithm 31 is little better, with one modulator tacked on to carrier 5 like an afterthought. If you are scared of getting lost in over‑complicated modulation paths, I suggest you start your experimentation with algorithms 31 or 32. The more adventurous among you should dive straight in on the triple modulation loop of algorithm 4.

Incredible as it now seems, 10 years ago, Frequency Modulation (or FM) synthesis ruled the world...

By the way, not all the operators featured in an algorithm are necessarily being used. Firstly, whenever you are in Voice Edit Mode on the DX, you will see what looks like a 6‑bit binary number in the upper half of the display. This actually shows the status for each operator (1 for On, 0 for Off). These can be toggled using the first six of the 32 green switches on the right‑hand side of the machine. Clearly, if a carrier or modulator is switched off, its sound (in the case of carriers) or effect (in the case of modulators) will not be heard.

Secondly, if the modulation depth of a particular modulator is set to zero, its effect will also not be heard. To check this, first use the Operator Select switch to step through to the operator you want to check. The various parameters for controlling the modulation amount (initial depth, envelope, velocity, aftertouch, LFO, and so on) will then all be available under their respective switches to the right.

Real‑Time Timbre Change

Without going into more detail than we have room for here, this last sentence has quietly summed up one of the real strengths of Yamaha's FM synthesis implementation, and also explains why it had such a massive impact on the synth market of the mid‑'80s. Up until then, most analogue synths had not been velocity sensitive, and those that were tended to be very expensive. The Prophet T8 first shipped around the same time as the DX7 (some two years after it was first shown), and its eight (admittedly very big) voices set one back a not‑so‑cool £5000, compared to the DX7's much less wallet‑savaging release price of £1549. Even when a manufacturer managed to produce a more cost‑effective machine, the limited number of voices was still a problem — at the same Frankfurt show where I first saw the DX7, Siel launched the velocity‑sensitive Opera 6 for slightly less money, but as its name implies, it still only had six voices.

Not only did the DX have 16 voices (the first affordable synth with more voices than people have fingers), but on each, velocity and aftertouch could be routed to control some or all frequency modulation depths. This brought pianists (many of whom had sneered at the limited polyphony and real‑time expression of synths for years) flocking in droves to hand over their hard‑earned for a DX, particularly those jazz players for whom a chord is not a chord unless it has a dozen notes on top of those in the straight major or minor triad.

Suddenly, voices on a synth could change quite radically, depending on how hard you hit them and whether you leant on the note afterwards. This meant that you could keep your left hand (previously needed to push the mod wheel up every time you wanted a bit of vibrato or other form of expression) free to play basslines or a further five/six notes of jazz harmony (or, as we classical types like to refer to it, dissonance!). Previously, polyphonic synthesis had been an exclusive club, firstly thanks to its price, and secondly because you had needed to learn new ways to introduce expression into your playing. Suddenly, you could use all the techniques learnt in those years of piano lessons without modification. The sustain pedal could even be used unsparingly, as you had enough notes to ring on while you flourished up and down the keyboard (so to speak). Suddenly, all the real players wanted a DX7 — or a DX1, if they had money to burn.

Meanwhile, die‑hard synthesists were still reeling from the shock. Of course, the drawback was that even the most experienced analogue programmer had to learn how to program a DX from scratch, and for many, unfamiliar terms like operator, feedback and algorithm proved a hefty culture shock. Fortunately, there were a couple of familiar terms amongst the alien parameters on the front panel.

It's Ok — FM Has LFOs & EGs Too

Certainly, when my eyes first fell on the DX's front‑panel EG label, I breathed a sigh of relief. OK, so the DX had no filters, but at least it had envelope generators... and an LFO as well. Phew. Everything I had previously learnt about analogue synthesis had not gone out of the window. In your first close encounters with FM, I suggest you keep this thought in mind, as FM synthesis can seem like another universe after the familiarity of analogue, particularly when the envelopes don't seem to have the familiar Attack, Decay, Sustain and Release phases. We will look at how DX envelopes work, but first let's look at the altogether more familiar use of the LFO. The DX7's LFO parameters, Wave, Speed and Delay, should be self‑explanatory (what waveform you want, how fast it cycles and when it comes in), and PMD and AMD are just abbreviations for pitch modulation depth (vibrato) and amplitude modulation depth (tremolo). Of course, if the operator to which these two are applied is a modulator, the audible effect will not be vibrato and tremolo, but instead a variation in the modulation frequency or depth, the end result of which will be changes in the harmonic content of your sound. Despite these differences, the DX7's LFO section will be fairly familiar territory to the average analogue programmer. If you have access to a DX7, try setting up fairly radical LFO modulations (for radical read unmusical) on operators 2, 4 and 6, with algorithm 32 selected (where all six operators are behaving as unmodulated carriers), and then switch to algorithm 5 or 6; you will be surprised at how much more interesting (and musical) the timbre will suddenly become as these wild audio sweeps are converted into frequency modulations. Switching algorithms really is the fastest way to sonically, rather than intellectually, appreciate the relationship between carrier and modulator. As you get more proficient, you can try using the more radical algorithms, like numbers 16, 17 or 18.

Pushing The Envelope — Rates & Levels

A similar technique can be applied as you find your way around the DX's initially unfamilar envelopes. These allow a greater degree of fine‑tuning of the operator level than the simple analogue ADSR type, but they are fundamentally the same. If it helps at first, try thinking of a carrier's EG as an amplifier envelope which changes the volume in real time (because that's what it is), and a modulator's EG as a filter envelope which changes the harmonic content over time (because that is the closest analogy). It is by increasing the level of the modulator with its envelope that you can simulate the changes in brightness which occur in real plucked or blown sounds.

The way to approach rate/level envelopes is to see them as a customisable ADSR for the DIY enthusiast. The level is the point at which each segment of the envelope changes to the next and the rate is the time it takes to make this transition. Yamaha thoughtfully provided a diagram of the envelope on the front panel to the left of the algorithms (see Figure 2 on the previous page), and if you take a look at this, you should see straight away that rate 1 and level 1 provide the equivalent of the ADSR's Attack phase. The only difference is that the attack does not necessarily have to go to the maximum level available, as with an ADSR. By making level 2 higher than level 1, you can have a secondary attack phase, whereas making it lower would put you into a more conventional decay situation (sorry if this is starting to sound like strategic military jargon!). The third phase of the envelope can be another increasing or decreasing segment, depending on whether level 3 is higher or lower than level 2. Care must be taken with level 3, however, as it is also the sustain level — that is, once this level has been reached, you're stuck with it until the key is released. Rate 4 gives you the equivalent of an ADSR's release time, but again this need not necessarily go to zero (just as rate 1 need not necessarily go to maximum). This is ideal on a modulator if you want to keep the harmonic complexity as your sound fades out, but be careful when using this on a carrier, or the note may go on forever (or until you change the sound, at least!).

Don't expect to master FM synthesis as quickly as you did analogue. If using analogue synthesis is like learning Spanish, with a simple structure and warm to the ear, then FM is more like German or Russian, complicated and often harsh‑sounding (anyone spotted what I studied at university yet?). Some people never feel confident that they know what parameter changes to make with FM, and just busk it, or give up altogether. But don't be put off. Investing time pays dividends with FM, and it is possible to achieve an expressivity rare in the world of synthesis, especially if you are a jazz player and need to create the sort of sounds that don't over‑fill the frequency spectrum when you play a dozen notes at once. Some people I know claim that they are still getting new sounds from FM (although when I've heard them, 'new' is perhaps a little strong). Techno/industrialist enthusiasts will love some of the metallic 'klangs' you can produce, and it is the only type of synthesis to appeal to bell‑ringers (pun intended).

Yamaha's SY‑series of synths contained, to my mind, the ultimate implementation of FM...

Those of you whose appetite for knowledge has been whetted by this all‑too‑brief resumé of Yamaha's FM can find much more detail, programming advice and exhaustive analysis in my colleague Martin Russ' series on FM programming which ran from May to October 1988 in the pages of this fine publication. There are also many fine books on the subject, including the excellent tome by Howard Massey, The Complete DX7. Those of you who like a more surreal approach should try the alternative DX7 manual from Rittor Music, translated rather literally from the Japanese (if it's still available) which features several pages on operators which produce a POOOsound and a section on what happens to a 'tickled' operator when it is being 'tickled' by the 'tickler' (presumably the carrier modulated by the modulator). I was reduced to tears of laughter by this Ken Dodd approach to FM synthesis.

Casio, Pd & The Cz Range

For several years, Yamaha had the digital synthesis field all to themselves, until competition came from the most unlikely source. I can still remember driving round the North Circular Road to Casio (yes, they of digital watch, calculator and VL‑TONE fame), wondering what I had done to so upset the Editor of a certain now‑long‑deceased hi‑tech music and recording publication that he would send me on a punitive mission to look at a Casio mini‑keyboard. I came away a total Casio CZ‑series convert, due in no small part to the enthusiasm of Richard Young, who persuaded me to 'listen without prejudice' to the CZ101 and its grown‑up equivalent, the CZ1000. What I heard was reminiscent of FM in its clarity and expressivity, but it had the warmth I felt the DX lacked (I was fairly anti‑FM at the time). I ended up writing a book with Dave Crombie on the CZ range and the Phase Distortion (or PD) system it used, and I still use IPD sounds (the later, advanced version of Phase Distortion) in my Casio PG MIDI Guitar — it works really well for plucked timbres.

There is not a huge amount of room left in this slot to explore Phase Distortion fully, but as it's much simpler in structure than FM, we can have a brief look at the principles behind it. Like FM, it eschews the use of subtractive techniques such as filtering, preferring to create its harmonic complexity and real‑time timbral changes with a mathematical process which makes complex sounds by altering simpler waveforms (although not quite as simple as plain old sine waves, as in Yamaha's FM). This is not done by using one waveform to modulate another, as in Yamaha's synths, but rather by changing the speed at which the waveform is read out within the duration of each individual cycle. This has the effect of distorting the phase of the waveform (hence the name) and thereby changing its shape and harmonic content. The greater the amount by which the speed is shifted, the more the waveform changes shape, and the more complex the resulting harmonic content.

There is actually a wider range of raw waveforms on offer for Phase Distortion than in analogue synthesis; there are the old favourites like Square, Sawtooth and Pulse, but also some hybrid forms like double sine, saw pulse and three different resonant waveforms. You can also combine these to produce more complex harmonic structures before you even begin distorting the phase. However, to try and help you understand PD a little better, we will look at what happens to a cosine wave when its phase is distorted (don't worry about the fact that it's a cosine wave — this is simply a sine wave starting from a different point in its cycle, and doesn't actually sound any different). If you look at Figure 3 on the previous page, you will see the cosine waveshape and the corresponding phase angle throughout its cycle.

If we now speed up the readout of this waveform in the first half of the cycle, making a steeper phase angle gradient, and then slow down the readout in the second half, so that the total cycle time does not change (this keeps the pitch constant), the cosine wave will be altered as shown in Figure 4. As you can see, the whole waveshape leans forward, producing a much more complicated set of harmonics than just the fundamental contained in the original cosine. Of course, the wider the variation in the readout speed, the bigger the kink put in the phase angle graph, and the more radical the harmonic content.

By using an envelope to control the amount of phase distortion (Casio refer to this as the DCW ENV, the Digitally Controlled Waveform envelope), you can achieve the kind of real‑time harmonic synthesis changes which all synths must have if they're to produce something more interesting to the ear than organ sounds. As you will see immediately from Figure 5, left, the envelopes Casio used have double the number of Rate and Level components found in Yamaha's FM envelopes (8 instead of 4), but the same basic principles apply, with level 5 being the Sustain component (the one which is maintained while the key is held down). As well as the envelope controlling the Phase Distortion, there are also the DCO ENV for pitch and the DCA ENV for volume.

The main advantage of PD synthesis over FM for the would‑be programmer is the fact that much of the terminology and many of the concepts are closer to traditional analogue synthesis. In fact, if you think of the DCW envelope as akin to the filter envelope on an analogue machine, you will be knocking out your own sounds in no time. However, the principal advantage of PD to the listener is that the sounds have a much warmer quality, without resorting to the kind of chorus detuning of the TX816 or DX‑MAX, or the combination with PCM sounds and effects of Yamaha's SY series. But PD's success in the mid‑'80s was probably due more to the fact that the CZ synths were amongst the first to have a proper implementation of multitimbral operation via MIDI Mono Mode; you could actually trigger different timbres on different MIDI Channels. This led Vince Clarke to use half‑a‑dozen CZ101s hooked up to an old UMI sequencer on the BBC Micro in his late‑'80s setup (before he went right back to analogue stuff triggered from a Roland MC4 at the turn of the '90s).

Casio followed up the success of the CZ models with the VZ range, expanding PD into IPD (Interactive Phase Distortion), which increased the expressivity available through aftertouch and velocity. Although there were far fewer VZ synths made, I would thoroughly recommend them if you are looking for the most developed implementation of Phase Distortion. Those of you wanting to make your way further into the subject can read more in Phil South's two‑part SOS article which ran in the July and August 1987 issues, or even in the book Dave Crombie and I wrote, which rejoiced in the wonderfully imaginative title The Casio CZ Book (if you can still find it).

Having looked at the forms of synthesis based on more complex mathematical operations this month, you may be relieved to hear that next time I will be concentrating on simple addition (so you can put those wet towels and bottles of aspirin away now). We will be looking at the way additive synthesis builds up complex timbres, and will examine the dominance of another Japanese company, namely Kawai, in this field. Till then, happy modulating (or tickling)!