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Synth School: Part 4

Additive Synthesis By Paul Wiffen
Published October 1997

Throughout the '80s, additive synthesis was the Holy Grail for synth purists; many machines aspired to it, but only one achieved it successfully. Paul Wiffen explains how additive works and looks at the various implementations, including the newly updated Kawai version.

In previous instalments of this feature, I've used various analogies from the visual arts to help illustrate how different types of sound generation work. Analogue or subtractive synthesis I likened to sculpture, where artists starts with more 'stuff' than they ultimately need and remove large chunks of it until they are left with what they actually want. Sampling is more like photography, with a snapshot of the required timbre being taken; in PCM‑based machines (often known as sample + synthesis) that snapshot is tweaked for the final result in much the same way that a photograph is manipulated during development and printing. It can be altered a little, but it will always be a photograph of the same subject.

To continue in this vein, additive methods of synthesis are closest to the oldest of the visual arts, painting. The sound is built up from its constituent parts, just as a painter mixes together different hues to achieve the required colour, and then lots of different colours are used to create the final picture. Additive synthesis uses combinations of harmonics to create the basic tone colours or 'timbres' and on more sophisticated systems several of these timbres can be combined to make the overall sound. On later additive synths it's not uncommon to find filters, borrowed from subtractive synthesis (just as you find them on many PCM‑based machines), used to highlight the unique harmonic content of the waveforms that additive can create.

All‑Artificial Additives

When we looked at the basic waveforms used in subtractive synthesis (see SOS June '97), we found that certain common electronically generated waveshapes — square, sawtooth, sine, and so on — could be described in terms of their harmonic content. A sawtooth contains all harmonics in inverse proportion to their number, a square wave all the odd harmonics in the same ratio, a sine wave only the fundamental or first harmonic. Additive synthesis turns this arrangement on its head and uses those very harmonics as the building blocks for much more complex waveforms. Where real‑time timbral changes are possible, these are achieved by varying the levels of individual harmonics or groups of harmonics, often using devices we have come across before, such as envelopes and LFOs.

Because the sine wave is the purest waveform, in that it only contains the fundamental, and because it is the easiest to generate electronically, being very simple to describe mathematically, the sine wave is used as the basic building block of additive synthesis. A whole series of sine waves (whose frequencies are related to each other in exact correspondence with the harmonic series we used to analyse analogue waveforms previously) are 'summed', or mixed together. The second sine wave is double the frequency of the first, the third three times that of the fundamental, and so on. This makes it very easy to know the frequency of the harmonic in relation to the fundamental — for example, if your fundamental is good ol' A440, then the frequency of its fifth harmonic is 2200Hz.

One of the measures of power in an additive synth is how many harmonics are available per note of polyphony. Although in natural and synthesized sound the greater proportion of the harmonics present are the lower ones, if the upper harmonics (normally only present in very small amounts) are not there at all, a the sound is perceived as dull or distant, because distance and obstacles remove the higher frequencies first. This is why, when that flash car masquerading as a mobile disco pulls up next to you at the lights, all you can hear through your closed windows is the bottom end of whatever dubious taste in music the occupant has decided to share with you. Open your windows and the full glory of the unvarying hi‑hat pattern becomes clear.

So, in order to create bright, interesting sounds, an additive synthesizer must be able to produce more than just the lower harmonics. This is particularly true in the lower ranges, where more and more of the harmonics of a sound are brought down into the audio spectrum. On higher fundamental frequencies, the higher harmonics quickly move into ranges which can only be appreciated by dogs.

Any self‑respecting additive synth should be able to manage a minimum of 32 harmonics. Any less and the proper term for it is 'an organ'. In fact, strictly speaking, the tonewheel organ is the first additive synthesizer, allowing you to mix ten or more sine waves at related harmonic frequencies via the drawbars. Of course, if the tonewheels are creating pure sine waves, the sound will be very thin and uninteresting. Those organs which tend to sound the most pleasing to the ear are those where, through age or deliberate design, the tonewheels are putting out more complex waveforms, augmented by percussion, overdrive and a rotary speaker. Ten sine waves on their own (whatever unique mix of levels you come up with) do not a full sound make. In fact, 32 harmonics is an absolute minimum, and many additive synths provide 64. On the really well‑specified machines, it is often possible to go to 128 by halving polyphony (ie. the second voice is used to create harmonics 65‑128).

It's an interesting exercise (and proof that the theory I have been spouting is based in fact) to use additive synthesis to recreate the standard waveform timbres of analogue synths (although if this is all you ever plan to do with additive you will be drastically under‑using its potential and should give up now!). By setting the second harmonic to half the level of the first, the third to a third of the level, the fourth to a quarter, and so on up the series, you will soon hear the familiar timbre of the sawtooth wave emerging as if a filter were being opened up slowly on it. In fact, as long as you're able to set the levels precisely enough, this will probably give you a more accurate sawtooth than most analogue synths. If you don't recognise the sawtooth timbre from your analogue synth, it's probably because the synth is only producing an approximation, with a bunch of extra frequencies not technically supposed to be present adding the extra character (just like the more interesting organs I referred to earlier).

Herein lies an early warning of one of the main dangers of additive synthesis. Without care it can sound weak and thin, and on simple implementations the best you can hope for is some pure tones with a glass‑like transparency. If you're looking to additive for rip‑roaring sounds which cut through everything else and grab the ear, you'd better make sure that your additive synth offers enough complexity and real‑time operation to vary the harmonic content enough to demand the ear's attention (or that it 'cheats' by adding subtractive filters or PCM snippets to its sonic arsenal). I actually think there's little point in additive synthesis if you're going to stick to imitations of waveforms which are produced in analogue synths, or — worse still — attempt to recreate 'real' sounds. Having said this, theoretically speaking, any sound can be broken down into its constituent sine waves and therefore could be recreated by a sufficiently powerful additive synth. This theory was often advanced by many of the hobbit‑like academics who lurked in the aisles of smaller stands at '80s trade shows, waiting to ensnare innocent journalists who weren't forewarned by previous encounters of this type. The real problem was that, after expounding half an hour of theory along these lines, when you finally persuaded them to play you a sound from this system of theirs (which was going to change the history of synthesis forever), it was always the same thin‑sounding pipe organ patch they came up with (hardly surprising, since the pipe organ was the first additive system).

On many of the computer music systems of the early '80s which offered multiple methods of sound generation, additive synthesis was the poor relation, the 'also ran'. The Fairlight had its sampling, the PPG its wavetables, the Synclavier its FM, and these were the glamorous aspects of these machines. They all also had some form of additive capability, yet somehow this was rarely mentioned, and used even less often. There were two reasons for this. The first was that the other means of sound production offered by a given system was more or less unique to the system (in the early days, at least) and therefore its promoters would always emphasise that side. Secondly, the other ways of working offered far more in terms of instant gratification than the additive side, which suffered from what I always refer to as the 'Compute' syndrome.

Stone‑Age Additive

Early implementations of additive synthesis were not real‑time implementations. The actual computational power in these computer music systems was pretty puny by today's standards (the current average PC with a soundcard outstrips the sonic potential of the original Fairlight by several powers of 10). As a result, they couldn't perform the level changes you might make to different harmonic components in real time, but had to go off‑line to compute the new waveform. So, when adjusting the relative levels of the harmonics, you would be flying blind in terms of what the result would be. Actually, deaf is probably a better term than blind, as most of these systems had some pretty fancy graphics to show you what you were doing; my favourite was the PPG Waveterm, which superimposed the waveforms for new harmonics on top of the current waveform, complete with amplitude representation of level. Then, when you pressed 'Compute', it merged these together (eventually) into a single new waveform. However, no matter how pretty these displays were, unless you were very experienced they told you little about how the final product would sound. As a result, the process of creating an additive waveform could be very long‑winded, unless you just went for the serendipitous approach of bunging in a load of harmonics with random levels, pressing Compute and hoping for a gem sooner or later.

But the amount of time taken by these early systems to create an additive waveform wasn't the only drawback. Because they were computed rather than generated in real time, these waveforms were set in stone when it came to playing them back. In fact, they were just like samples — indeed, the additive waveform the Fairlight created was loaded into the sample RAM for playback, in exactly the same way as a sample. Even when you used a merge facility to move from one additive waveshape to another, the result was still a fixed calculated product and the speed of the transition would increase as you went up the keyboard and decrease as you descended. When an additive capability was provided really cheaply by Digidesign's Turbosynth software for the Mac and Atari, the same restrictions applied. The resulting sound could only really be played effectively by MIDI sample‑dumping it across to a sampler, with all the restrictions that implies. Of all the first generation of additive‑capable systems, the sounds generated on the PPG Waveterm were probably the most useful, as they could be played back with real‑time movement between different waveshapes in the wavetable (if you had the time to create several and then compute the transitions between them) or analogue filtering (if you didn't).

I'm proud to say that the first commercially available synth with the capability to alter additive waveforms in real time was British, and the present author had the honour (if not the financial reward, for there never was any) of being the midwife at the birth. The OSCar, which was mentioned in a previous instalment of this series for the flexibility of its filtering system, also had the capability to generate new waveforms using additive principles. What was unique at the time was that you could actually hear the harmonics being added or removed in real time. I vaguely remember saying to Chris Huggett, during the OSCar gestation period, that if he was going to put additive capability on the OSCar, it had better be more usable than on other machines I had tried. I had clearly been traumatised by my singular lack of success in coaxing something interesting in the additive vein out of Oxford University Music Department's Fairlight on my sole encounter with it, making a mockery of the lengths of bribery and corruption I had gone to in order to gain access to it.

Although the system Chris came up with for defining the mix of harmonics was perhaps a little unscientific (each key on the keyboard represented a harmonic, and pressing it repeatedly in additive waveform creation mode increased its proportion in the overall result), it was fairly intuitive and gave you real‑time feedback. If you didn't like the immediate change in timbre when you added a new harmonic in, you could just take it out again, without all that tedious mucking about with computing. The actual process of building up a waveform was so pleasing to the ear (as harmonics came and went) that several artists used it unadorned as intros to tracks. You can hear a clear example of this on Jarre's Revolutions (perhaps the most OSCar‑intensive album ever made, although Ultravox's Lament comes a close second and their 'Love's Great Adventure' takes the award for most OSCar‑laden single).

Unfortunately, this real‑time change in harmonics during waveform creation could not be reproduced during playback, but two waveforms created like this could be played back at once, and then mixed or filtered to create real‑time timbral change. I always found the mixture of an additive waveform with a conventional analogue one to be most useful in imparting a little bite and unique character to the traditional analogue synth sound.

Other real‑time additive implementations started to appear, mainly from the realms of academe, and they were usually lamentable both in terms of sound quality and of playability — not to mention the poor appearance and hygiene of the member of the design team who had been let out of the lab to do the demo at the trade show where they were previewing. Mercifully, very few of these systems made it to commercial release, but one of the few that did (and proved to be one of the more successful implementations) was the Technos Axcel shown above. Of French‑Canadian origins, it had a splendid multi‑LED touch‑sensitive user interface which made it possible to draw harmonic levels, waveforms and envelopes with a single sweep of the hand. This made it terrifically easy to use but also horrendously expensive (probably the main factor in its short life — a little over a year of intermittent commercial availability).

It also had the capability to load a sample, analyse it and produce an approximation to it built up from sine waves. While this was not very close in terms of fidelity, it made a great starting point for new sound creation (another of additive's traditional drawbacks is the amount of time it takes you to set all the harmonic levels and envelopes to get an interesting sound going — this made for a great shortcut). However, the Axcel's main strength was that it could set the amplitude envelope separately for each harmonic (or vary the level from other controllers), so you could get really interesting timbral changes in a sound in real time, and in this respect it pointed the way forward. The Axcel's weakness was that the more harmonics you used (ie. the more complex the sound), the more polyphony suffered (the best sounds were monophonic or duophonic), and this, coupled with its high price, led to its early extinction.

The Land Of The Rising Synth

It fell almost inevitably to Japan to produce the first implementation of additive synthesis which was both real‑time and affordable without sacrificing polyphony. The Kawai K5, when I first came across it in 1987, was a revelation, and its sound and facilities still stand up pretty well today. Offering 8‑note polyphony (only the DX series had ever offered more at the time), it nevertheless managed up to 64 harmonics per note (128 if you used two notes per voice) and, most important of all, real‑time control of the levels of various harmonic groupings. I fell in love with it for its speed and flexibility, and for the fact that I had always known that there must be something in this additive synthesis business — I just hadn't managed to find it until then. If you can find one of these wonderful machines on the second‑hand market (it also came in rackmount form as the K5M), it's well worth the paltry sum you will probably have to pay to make it yours. It makes a fine introduction to additive synthesis and is only bettered by Kawai's current K5000 range.

Also worth looking out for is the Dr T's Atari program which took Akai S900 samples and analysed them, for subsequent downloading, via MIDI, into the K5 as additive impressions. First seen on the Axcel, this capability would never fool anything but the most untrained ear, but it made for excellent sounds and a great starting point for new sound development.

Let's look at how the K5 allowed the individual level of harmonics to be controlled in real time, as this synth is one of the best models for successful additive synthesis (and one Kawai have expanded on in the K5000 series). As I mentioned earlier, one of the drawbacks of additive synthesis can be how long it takes to make a sound, simply because of the sheer number of parameters that needs to be set. There's the starting volume level of each harmonic, to begin with (in the earlier non‑real‑time systems, this was all you could do, because, having been computed, those levels then couldn't be changed). Just setting the level of each of 64 harmonics could take 20 minutes (more if you decided you didn't like the original level you had set). The K5 cut out a lot of the donkey work, by first showing you all harmonics at once, with a bar representing the level of each in the LCD display and then allowing you to select groups of harmonics whose values could be adjusted simultaneously. These groupings include Odd, Even, Octaves (2, 4, 8, 16, and so on) or 5th intervals (3, 6, 12, 24, and so on) or a user‑definable Range specifying the lowest and highest harmonics you want to affect. Once these are selected, turning the increment dial raises or lowers the level of those harmonics in proportion. This may seem simple enough, but before the K5, no‑one had streamlined the process to this extent. The Axcel's touch‑sensitive interface made it quick to set the levels individually, but grouping harmonics was Kawai's innovation.

Of course, this is only the beginning of making an additive sound on the K5. To actually change the harmonic levels over time, we return to our old friend the envelope. It would have been possible to make do with the traditional ADSR‑type envelope, but Kawai opted for the more flexible rate/level style, with six stages, and the settings of these rates and levels are all visible at once, which saves flipping between screens all the time. Each harmonic (or group of harmonics) can be assigned to one of the four envelopes. There are even short‑cuts for the programming of these envelopes, to speed up the process of setting them up. Higher‑numbered envelopes can 'shadow' or take on the settings of the lower‑numbered envelopes. So you can set up the first envelope and then tweak the higher‑numbered ones using the settings of the first envelope as your starting point, rather than having to do each one from scratch.

In addition to the four harmonic level envelopes, there are three more: one for the overall level of the sound, one for its pitch, and one for the filter. To the additive purist, this last word is probably the equivalent of blasphemy, but Kawai realised that sometimes there is just no substitute for the sheer speed of using a filter. Having said that, the filter is a very accurate digital one, with a unique set of parameters to control it. In addition to the normal cutoff frequency, the point around which the filter operates, you can specify the 'flat level' (ie. the amount of signal that is passed below the cutoff frequency). By reducing this to zero you can acheive the same sort of result as a band‑pass filter; with it set to maximum you get a normal filter response without resonance; and in between, the frequencies immediately around the cutoff are passed at a higher level (very similar to the effect of resonance). The final parameter, Slope, actually gives a degree of control over how steep the transition is between the cutoff frequency point and the flat level. This is equivalent to changing the number of poles in an analogue filter (ie. increasing the dB/octave cut), and at very steep settings gives a similar result to high resonance settings.

Not content with that filter, Kawai also added a digital formant filter, which works on 11 bands set an octave apart. Although a full examination of formant filtering is really a subject for a future Synth School, the effect of this filter is very similar to that of a graphic equaliser, where the amount by which each octave of frequency range is boosted can be independently set. This dovetails very nicely with additive synthesis, because the harmonics are also related to the octaves above the fundamental — so you know, for example, that boosting the third octave will affect the harmonics centered around number 8 (if you play the lowest C). Kawai rounded off their real‑time implementation of additive by making sure that it was not only the envelopes which could affect the harmonic levels, but also parameters such as keyboard scaling and velocity, giving additive an expressive feel for the first time ever.

Adding It All Up

Reading this piece might leave you with the impression that you're actually in the middle of a review (or a eulogy) of Kawai synths. But to talk about additive synthesis without mentioning Kawai would be like covering FM without reference to Yamaha, or analogue synthesis without Bob Moog. Yes, other people made FM synths, and analogue synthesis existed before Bob came along, but the DX7 and the Minimoog produced the most cost‑effective and manageable versions of those types of synthesis, and for me the K5 is in the same league. It took a previously interesting but unwieldy type of synthesis and made it available in a form that was quick and easy to use. Sadly, no other manufacturer has picked up this ball and run with it. For 10 years the K5 has really been the only additive synth to sell in any quantity, and only Kawai's recent re‑investigation of the concept has saved additive synthesis from being consigned to the history books (see 'Current Additive Possibilities' box).

The great thing about additive synthesis is that, unlike many of the other methods we have covered in these Synth School pieces, it has not been done to death. It is perhaps one of the most flexible types of synthesis, and is particularly well suited to the creation of abstract sounds rather than imitative ones. In terms of its usage in commercial music, the surface of what additive can do has hardly been scratched, and now that there is a new generation of additive synthesis on the market, I'm optimistic that we may see a revival in its fortunes. If you're looking to add a bit of originality to your music, whatever the style, additive will enable you to depart from the fixed sounds of PCM and the well‑trodden timbres of analogue. You certainly won't exhaust its potential in a hurry.

Current Additive Possibilities

Until late last year (that is, when Kawai re‑entered the additive arena with a totally updated additive synth, the K5000W, which I had the pleasure of reviewing in January's SOS), it looked as though the Kawai K5 might be the final full stop in the history of additive. You should refer to the K5000W review if you want precise details of how Kawai have used the extra processing power available in the late '90s to update their concept, but let me just broadly cover how the additive synth's potential has been expanded by the K5000 series:

  • There are now individual envelopes for each of the 64 harmonics.
  • The formant filter has 128 bands (adjusted on a semitone rather than an octave basis) and can be swept using the LFO or envelope.
  • The more standard filters now allow high‑ or low‑pass configuration.
  • Envelopes can now be looped to cycle complex harmonic changes.
  • It is now possible to morph between harmonic snapshots in real time (an updated version of the old Merge capability on the Fairlight, which was so interesting but unfulfilling because it was frozen into a sample format).
  • The last major addition is the ability to add DSP effects to the sounds, something no modern synth can afford to be without.

Since looking at the K5000W, which featured some other facilities in the auto‑accompaniment vein which I felt were of peripheral interest to synth aficionados, my excitement at Kawai's development of the additive strain has further increased with the release of the K5000S and K5000R. These two units forgo auto‑accompaniment in favour of the real added value of an arpeggiator and — joy of joys — hard‑wired and assignable knobs for real‑time manual performance‑parameter control. Having a dedicated knob to tweak the balance between Odd and Even Harmonics, adjust the Low and High Harmonics, move the Bias (centre frequency) and LFO speed and amount of the Formant Filter, not to mention the Cutoff and Resonance of the standard Filter and the main envelope parameters is, for me, the icing on the cake that Kawai have been baking for ten years now. Those of a more scientific frame of mind will appreciate the ability to assign the four user knobs to the parameters of their choice, and additive sounds are ideal for triggering from an arpeggiator.

If this article has whetted your appetite for the (largely) unexplored area of additive synthesis, you can do no better than to get your hands on the K5000S or R for experimentation. If this exceeds your budget, a second‑hand K5 will give you an excellent start (especially if you can track down the Dr. T's editor to go with it).

Thanks to Arbiter Music Technology for the loan of a Kawai K5000S for the purposes of this article.