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Synthesizing The Rest Of The Hammond Organ: Part 2 |
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As with so much surrounding the Hammond organ, there's much more to the Leslie rotary speaker than meets the eye, and synthesizing its effects involves considerably more than just adding vibrato, as we find out this month... Gordon Reid Photo: Richard Ecclestone  |
For three months, we've been investigating the sound of the Hammond organ, spending two of those months recreating the sound of the tonewheel generator, and a third attempting somewhat less successfully to emulate the onboard effects provided by 'the real thing'. But, as we all know, the classic jazz/rock/pop organ sound is as much a consequence of a rotary speaker as it is of the organ itself. So, in this fourth article dedicated to understanding and synthesizing the organ, we're going to concentrate on the physics and sound of the 'Leslie' speaker.
A Brief Description What we now recognise as the rotary speaker did not materialise as a fully developed concept overnight. In an effort to animate the sound of the Hammond electromechanical organ, Don Leslie had been experimenting with all manner of systems before he alighted upon what he called a 'Vibratone Speaker', but which is what we now call the classic, twin-rotor 'Leslie'. One of his early experiments was a monstrosity with 14 speakers mounted inside a rotating drum. Fortunately, while paring his ideas down to a manageable size and complexity, Leslie found that just two speakers (mounted inside a cabinet, as shown above) generated the most pleasing sound. One of these was a treble unit that produced the frequencies above 800Hz, and which played upward into what looks like two rotating horns (although one of these is a dummy, provided only to stop the whole assembly from shaking itself to bits). The second was a bass speaker reproducing frequencies below 800Hz, played downwards into the single rotating 'rotor' (see Figure 1, below). Leslie provided each speaker assembly with two rotation speeds — one slow and one fast — that he called 'chorale' and 'tremolo', respectively. The rotor's chorale speed was different from the horn's, as was its tremolo speed, and the transition rates between slow and fast (and vice versa) were different for the two assemblies. The result of playing a sound through this device was, therefore, a complex effect that combined pitch modulation, amplitude modulation, tone modulation, and reverberation (ie. the effect of the enclosed cabinet), with the high frequencies and low frequencies swirling around independently to create a very pleasing and expansive sound. What's more, Leslie found that, by placing the cabinet close to a wall or to the corner of a room, he could use the additional reflections from those surfaces to obtain a stereo field from a single, monophonic source. Nowadays, there are dozens of models of Leslie speaker, and numerous physical as well as electronic imitations. Some Leslies have single rotors, but the sound produced by these is inferior to that offered by the larger, dual-rotor models characterised in Figure 1. Others are built into their host organs; a common example is the single-rotor unit found within the Hammond T500-series organs from the mid-1970s. And, of course, no modern organ emulation could be considered complete without the inclusion of a digital recreation of the Leslie speaker effect. But how many of us fully understand how the Leslie creates its instantly recognisable sound? Ask many keyboard players what makes the device so special, and they will usually offer an answer that includes the words 'Doppler effect'. They are right to do so — the Doppler effect can explain a significant element of the sound generated by the Leslie. However, if you then ask what the Doppler effect is, you will often be met with a blank stare. What's more, this is only part of the story, as we shall now see...
The Doppler Effect Christian Johann Doppler was a scientist who died as long ago as 1853, yet he explained something that we all experience; the fact that, when something emitting a sound is moving towards us, we perceive a higher pitch than when the same sound is moving away from us. To understand why this is the case, we'll start by following Doppler's line of thinking, and consider an archetypically 19th-century mode of transport: a ship.  Figure 1: Don Leslie's twin-rotor speaker cabinet.  Figure 2: Observing the waves from a stationary ship.  Figure 3: Moving into the waves increases the perceived frequency.  Figure 4: Running from the waves reduces the perceived frequency.  Figure 5: The pitch of an approaching ambulance siren is higher than if stationary.  Figure 6: The pitch of a receding ambulance siren is lower than if stationary.  Figure 7: How the pitch changes as the ambulance passes.  Figure 8: The observed pitch when the ambulance is stuck on a roundabout.  Figure 9: The perceived pitch shift of a rotating horn speaker.  Figure 10: The sound from the horn exhibits both tremolo and vibrato, out of phase with each other.  Figure 11: Recreating the phase and modulation characteristics of Figure 9.  Figure 12: Adding tone modulation to Figure 11.  Figure 13: Reflecting the sound off an office block.  Figure 14: Considering the phase and amplitude of the reflected sound.  Figure 15: Synthesizing the direct 'rotary' sound plus one reflection.  Figure 16: Bouncing the sound inside a quad of office blocks.  Figure 17: Four signal paths: the direct sound plus three reflections. |
Imagine, if you will, a docked liner floating in a harbour with the tide coming in. If this is facing into the direction of the tide, the waves will be breaking against the bow once every few seconds. Let's say — for the sake of argument — that the peak of each successive wave is reaching the bow five seconds after the previous one, as shown in Figure 2 (above). Now let's imagine that the ship is surging through the seas, with the bow cutting through the waves like... well, like a million tonnes of cruise liner cutting through the waves. If the direction of the tide is unchanged and the ship is still pointing in the same direction, the time between wave crests will be much reduced — say, to one crest every three seconds (see Figure 3 above). Finally, let's imagine that the ship has swung right around and is heading back the way it came. As you would expect, the wave crests are now reaching the stern at a slower rate than before — say, once every seven seconds, as shown in Figure 4 (above). The frequency of the waves hasn't changed, but by moving in the same direction as the waves, or in the opposite direction to them, we have demonstrated that the frequency at which we observe a waveform is relative to our motion with respect to it. This is the effect that Doppler not only observed but also quantified, so history has seen fit to call it the Doppler effect. Now, you don't need to be standing on an ocean liner to experience the Doppler effect. An equivalent shift in pitch occurs when you are stationary and something emitting a wave — say, the siren mounted on top of an ambulance — is moving toward you or away from you. In the first instance, the vehicle has moved a little closer to you as its siren emits each subsequent peak in the waveform, so the wavelength is shorter than it would otherwise be, and therefore higher in pitch (see Figure 5, above). The reverse occurs when the ambulance is moving away from you, with the siren a little further away each time it emits a peak. In this case, the waveform is lengthened, and the pitch is lowered (see Figure 6, above). Matters are complicated slightly when the ambulance is not travelling directly towards or away from you. Consider the case where you are standing on the pavement as it goes by. At the exact moment it passes you, it will neither be approaching or receding, and you will hear the true pitch emitted by its siren. So it should be intuitively clear that the change in pitch describes some sort of curve as the ambulance passes. This is the case illustrated in Figure 7 (above).
Analysing The Rotary Speaker Cabinet Everything I've described so far is relatively straightforward, but it doesn't explain the sound of the rotary speaker cabinet, so please bear with me while I extend the 'ambulance' analogy somewhat further, whereupon all will become clear. Instead of considering the ambulance siren moving toward or away from you in a straight line as shown in the diagram above, imagine that the vehicle is stuck on a roundabout, forever circling as it fails to find an exit. Clearly, the siren's pitch will appear to be raised when the vehicle is moving towards an observer on the roundabout, and lowered when it is moving away. There will also be two instances — when the ambulance is neither moving toward nor away from the observer — when the pitch is heard unaltered by the Doppler Effect. Without going into the trigonometry of the situation (which would involve a little mathematics and no doubt elicit yelps of pain on the SOS Readers' Forum) I can tell you that — provided that the speed of the ambulance is constant — the change in perceived pitch is described by a sine wave (see Figure 8, below left). Now, if we replace the ambulance and siren in Figure 8 with the aperture of a horn speaker, we can see that the analogy explains the first element in the rotary speaker effect. As the horn aperture moves toward you, the perceived pitch of the sound it is radiating is raised; when the aperture moves away from you, the perceived pitch is lowered; and the nature of the pitch-shift is again described by a sine wave (see Figure 9, below left). Many writers have stopped at this point, claiming that this explains the sound of the Leslie speaker. But this can't be right; all we've described so far is a mechanical method for generating a simple vibrato. So let's think about the situation a little more deeply... Looking again at Figure 9, it should be obvious that the pitch of the note is not the only thing affected by the rotation of the horn. In particular, the perceived sound is going to be much louder when the horn is pointing towards you than it is when the horn is pointing away from you. What's more, it's going to have some intermediate loudness when the horn is pointing sideways. It doesn't take a genius to realise that the perceived loudness curve is also going to be a sine wave, or something very similar. This means that the motion of the horn aperture is generating not one, but two sonic effects. The first is vibrato, with its peak occurring when the horn is moving fastest toward you (when it is pointing to the right in Figure 9), while the second is an amplitude modulation — or tremolo — with its peak occurring when the horn is pointing straight at you. This means that the vibrato is 90 degrees out of phase with the tremolo (see Figure 10, on the next page). Although this may seem a little complex, it's very simple to synthesize if we use an oscillator as the sound source. It requires just four modules to generate the effect; the VCO generates the initial sound, a sine wave LFO emulates the rotary motion of the horn, and a delay line connected to a VCA introduces the phase-shift between the frequency modulation and the amplitude modulation. Hooked together as in Figure 11 (below), these would generate a waveform exhibiting both vibrato and tremolo, but with the two 90 degrees (or some other desired amount) out of phase with one another. Unfortunately, this is still not a complete description of the effects imparted by the rotating horn, because the tone of the sound will also change throughout the cycle. The manner in which it does so is not intuitively clear. It is certainly not straightforward, because to understand this we would need to analyse such nasties as the backward projection from the horn driver, introduce some fluid dynamics to determine how sound is propagated 'backwards' through the air, and look into the refractive edge effects of the horn itself. Trust me... these are matters best left alone unless you fancy studying acoustics for a PhD. Nonetheless, we can say with some confidence that, whatever other changes take place, the sound will be brighter when the horn is pointing towards us, and duller when it points away. This suggests that the tonal modulation lies in phase with the loudness modulation, and that we can synthesize this — to a first approximation — by adding a low-pass filter modulated by the delayed LFO signal that is driving the VCA in Figure 11. The result looks like Figure 12 (see below).
Cabinet Reflections However, even this is far from a description of a rotary speaker, because neither the horn nor the rotor in Figure 1 are rotating in free space. So let me return for a moment to the analogy of an ambulance stuck on a roundabout. Imagine that, on the opposite side of the roundabout, there's a large, reflective surface of some sort... say, a large office block (see Figure 13, above right). This will reflect back some of the siren's sound that would otherwise travel forever away from you, and you'll hear this mixed in with the direct sound. If you consider what is happening to the reflected signal, you'll appreciate that — due to the Doppler effect — the pitch of the sound is at its highest when the ambulance is moving toward the office block, and its loudness and brightness are greatest when the ambulance is alongside the office block (ie. at its point furthest from you). If we ignore, for a moment, the finite speed of sound, this means that the pitch, loudness, and brightness modulations of the reflected signal are 180 degrees out of phase with those of the direct signal. However, we can't ignore the finite speed of sound, so what we hear is delayed by an additional amount proportional to the greater distance that the reflected sound must travel. This means that the phase change of the effects is not 180 degrees, but some other amount, as illustrated in Figure 14 (on the next page). But this still isn't the end of the story, because we have not yet taken into account the additional changes in tone that occur as the sound is reflected off the surface, and as it is absorbed by the air. Experience teaches us that, if the original signal occupies a broad band of frequencies, the direct sound will be brighter than the reflected sound. I think that it's safe to adopt this as an accepted — if unproven — part of our analysis because firstly, the reflected sound travels further, so more high frequencies are absorbed by the air, and secondly, the building will reflect lower frequencies better than others, thus imparting a duller tone to the sound. In addition to this, the delayed signal is going to interfere with the direct signal, resulting in constructive and destructive interference, which in turn will result in comb filtering of the sound that you hear. We can synthesize Figure 13 in block-diagram terms as shown in Figure 15 (below). In this, I have added a second set of delay lines, filters and VCAs to Figure 12, thus creating a second signal path that provides the delayed, lower-amplitude 'reflected' signal. In an attempt to be as accurate as possible, I have also added a gentle low-pass filter in the second signal path, which emulates the additional loss of high frequencies in the reflected signal. Clearly, placing just one reflector in the system complicates matters hugely, but that is as nothing compared to the complexities of a real rotary speaker cabinet which (ignoring the top and bottom) has four sides. If I may use my analogy one last time, this would be like placing three more office blocks on the remaining sides of the roundabout, such that the sound source is surrounded by reflective surfaces (see Figure 16, on the next page). It's pretty clear that the interactions between the enormous number of signal paths thus created are going to become very complex, very quickly.
Synthesizing Some More Reflections Contrived though this analogy may seem, it's a surprisingly good description of the physics of a rotating speaker. The only difference in the geometry is that, instead of escaping through gaps in office developments, the sound of a rotary speaker escapes through holes cut into the sides of the cabinet. This means that we can use this model of pitch-shifts, amplitude-shifts, tone modulations, and reflections to develop ways of synthesizing the Leslie itself. But be warned... the solutions are far from trivial. Indeed, the fact that there was never a convincing 'analogue' Leslie effect is a dead giveaway. Consider this: Figure 15 is already starting to look rather complex, but we now have to imagine what happens when we add all four walls of a Leslie cabinet (ie. the multiple reflective surfaces in Figure 16) and try to synthesize all of the signal paths thus generated. The result is completely impractical, both in terms of the number of analogue synth modules required, and in the amount of paper that we would need to represent them. Figure 17 (also on the next page) shows the modules required to model just three reflections, and this is already becoming a nightmare. When you consider that wherever you may stand in space, the sound you hear coming from a Leslie comprises many thousands of such paths, you can appreciate the size of the problem. What's more, sophisticated though Figure 17 appears to be, it is in fact rather inelegant, with all of its individual VCFs, multiple delay lines, and all the signal paths' low-pass filters set to different cutoff frequencies. However, there's a bigger problem. In Figures 12, 15 and 17, we have been modulating the pitch of the sound source (the VCO) directly, rather than modulating any possible sound that we might want to affect. While this might be satisfactory for some organ sounds (for which we can modulate multiple VCOs to create a tonewheel/Leslie effect) it is unsuitable for synthesizing the complexities of, say, a guitar or human voice played through a Leslie speaker. To do this, we need to be able to input an external signal and effect this. Fortunately, there is a way, and we can use a particular analogue device to modulate the pitch of any input signal. This will then give us a creditable chance of imitating the effect imparted upon any sound source played through a Leslie cabinet. Figure 17 even contains some of the information that we need to do this. Unfortunately, we have run out of space for this month, so next time we'll begin looking at some practical methods for synthesizing rotary speakers. Until then... Source: SOS |
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Synthesizing Hammond Organ Effects: Part1 |
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So, you can synthesize a Hammond's tonewheel generator — but what about its all-important effects? This month, we look at recreating the Hammond's percussion, vibrato, overdrive, and reverb — and find that it's harder than you might think... Gordon Reid Original photo: Richard Ecclestone  |
I find that my relationships with my synths can be much like any other romantic entanglements... fun and frustration in turns. When you're lucky, everything comes naturally, and you attain what you crave both easily and quickly. On other occasions, you have to work hard at things, and sometimes you just have to give up, pretending that you weren't that interested in the first place. For the past two months, I think that it's fair to say that this series has been dishing up a good deal of the former, with the basis for some fine tonewheel organ patches being produced on some unlikely synths. But, as I wrote when I left you last time, what these have all lacked is the excitement introduced by the Hammond's effects and side-effects; percussion, chorus/vibrato, leakage, and overdrive. So now, we're going to attempt to spice things up still further. Unfortunately, as in real life, some relationships start out as fun, but lead to frustration, although you usually learn some important lessons on the way. In this case, even though we don't necessarily achieve everything we set out to do, there's plenty to be learned about how a tonewheel organ creates its distinctive sound along the way.
Matching Registrations Just across the room from where I'm writing, there sits one of greatest organs ever crafted by human hands: a Hammond A100, an instrument every bit the equal of the B3 and C3. If you're unacquainted with Hammond genealogy, let me explain... For many decades, the company had a policy that its 'spinet' organs (those with four-octave keyboards) had built-in speaker systems, while the larger 'console' organs (those with five-octave keyboards) required external speakers, or 'tone cabinets'. Sometime after the launch of the B3 and C3 in 1955, Hammond's customers made it clear that they wanted a self-contained organ with the wonderful sound of the new flagships, but also the reverb and internal speakers of the less expensive spinets. Thus was the A100 born: a B3/C3 tonewheel generator and controls mounted inside a smaller case that nonetheless includes a spring reverb, dual valve amplifiers and three chunky speakers.  Figure 1: Returning to the Juno 6 Hammond patch. 
Figure 2: The Juno patch lacks the depth of 88 8000 000, lying closer to 67 8000 000. 
Figure 3: Increasing the resonance of most filters reduces the low-frequency amplitudes of low-frequency signals passing through them. 
Figure 4: The registration 67 8321 000 is much like the Juno patch. 
Figure 5 (left): The percussive 'blip'. 
Figure 6 (below): Creating second-harmonic and third-harmonic percussion using modules. 
Figure 7: Adding a percussive shape to the amplitude contour. 
Figure 8: Using the ADSR to create a blip at the start of the note. 
Figure 9: The Hammond percussion sound. 
Figure 10: A useable percussion patch — but it won't fool you. 
Figure 11: Using one of the Prophet 10's filters to create a far more accurate percussion sound. 
Figure 12: Creating a percussive 'blip' using the Upper filter envelope. 
Figure 13: Hammond percussion recreated on the Prophet 10. 
Figure 14: Three levels of simple vibrato. 
Figure 15: Three levels of chorus. 
Figure 16: Adding 'Hammondesque' vibrato. 
Figure 17: Adding distortion. 
Figure 18: The conventional use of a reverb unit. 
Figure 19: A simplified schematic of the Hammond A100. 
Figure 20: The affected Juno 60 'Hammond' patch. |
So close is the relationship between the B3, C3 and A100 that there is nothing to stop you from sliding the tonewheel generator out of one and wiring it into the others (well, nothing other than a few hundred wires!). This means that the A100 is the superior of the three organs, because it sacrifices nothing, but takes up less room and adds the reverb and speaker system. This superiority is not borne out by the second-hand prices of these models, which baffles me, but there it is. Anyway, having the Hammond sitting just a few feet from my Juno 60 makes it simple to investigate and resynthesize each of the Hammond's effects. So, to start, I'm going to match the sounds of the two instruments such that applying the same effect to each should yield the same result. I do this by switching off the percussion and chorus/vibrato effects on the A100, limiting the volume somewhat, and making sure that I don't play the result through the attached Leslie rotary-speaker system. Now, if I play the Juno patch that I developed two months ago (see Figure 1) through a high-quality amplifier/speaker combo, while simultaneously playing the Hammond through its own speakers, the similarity is almost uncanny, provided that I match the Hammond's registration to imitate the Juno. the synthesizer patch is not quite a true emulation of 88 8000 000. Most obviously, the amplitudes of the three primary harmonics lie closer to a Hammond registration of 67 8000 000, with the 8' pitch most audible, and lesser contributions from the 5 2/3' and 16' pitches, as shown in Figure 2 (above). This result suggests that, by using the filter to synthesize the 5 2/3' drawbar, we are sacrificing some of the amplitude of the sub-oscillator. This is not altogether surprising. In fact, it is exactly what we would expect from most analogue filters, because high filter resonance usually suppresses lower frequencies, as shown in Figure 3, above. Listening more closely reveals that the Juno not only lacks the low-frequency 'oomph' of the Hammond's 88 8000 000 registration, but is also a tad brighter. As a result, a touch of the next two or three Hammond drawbars makes the two instruments sound even more similar. After a few minutes' comparison, I found the registration 67 8321 000 to be about right (see Figure 4, below). Again, this is not surprising. After all, we would not expect the Juno filter to eliminate everything above the cutoff frequency, even when oscillating. This explains the need for the low-level signals injected by the 4', 2 2/3' and 2' drawbars. Anyway, having matched the sounds of the two instruments, we're now in a position to move on to...
Hammond Effects — Percussion A Hammond's percussion has nothing to do built-in rhythm units. That is, there are Hammonds with such units built in, but when I say Hammond percussion, I'm not talking about them. No, the four percussion controls on an A100 allow you to add a greater or lesser amount of either the second or third harmonic of the 8' pitch — ie. of the 4' or 2 2/3' drawbar — as an accent at the start of the note. The amplitude 'shape' of the result is therefore as shown in Figure 5. It's worth pointing out that adding percussion also reduces the loudness of the sustained part of the note, but we're going to overlook this. Likewise, Hammond percussion is polyphonic, but of the single-triggering variety, so if a previous note is held, the percussion does not sound. Again, we'll overlook this, because trying to recreate it would take us into areas best not trodden in an article of this length. Returning to the four percussion controls on the A100, the On/Off switch is self-explanatory, as is the Second/Third selector. This leaves just the Normal/Soft and Fast/Slow switches that control the loudness and decay rate of the effect. Simple though these seem, to emulate all their combinations would stress the resources of any analogue synth. Nonetheless, if we had the resources of a suitably expansive synth to hand, we could set up a patch to produce just one organ note, imitating the percussion by diverting part of the 4' or 2 2/3' signal through a VCA controlled by an AD contour generator. I have shown a stylised representation of this (using 88 8000 000 as the basic registration and omitting unused footages) in Figure 6. Complex, isn't it? Unfortunately, the Juno does not offer the complexity needed to imitate the structure in the diagram. Faced with these limitations, many synth programmers attempt to give the impression of percussion by modulating the audio VCA to create the amplitude blip shown in Figure 5. On the Juno, you would obtain this by flipping the VCA switch from 'Gate' to 'Env', and by adding a little Decay to the ADSR contour. I have shown these changes in Figure 7 (below). This creates the audio effect shown in Figure 8, which is far removed from the true percussion effect represented by Figure 9 (both at the top of the next page). What's more, the patch in Figure 1 creates key-click by using the ADSR to modulate the VCF cutoff frequency. The extended decay in Figure 7 changes this click into a completely un-Hammond-like soggy squelch. So, if we want to use this idea, we must disconnect the filter from the envelope generator and retune the cutoff frequency so that it again gives us the 5 2/3' drawbar pitch (see Figure 10 overleaf). Of course, our failure to synthesize even a basic percussion effect is not indicative of a limitation of analogue synthesis in general, and things are much more promising if we move away from the Juno, and consider a more complex synth with multiple signal paths. You may remember that the Sequential Prophet 10 introduced last month offers two paths that we could use to generate any four drawbar footages of our choosing. For example, we could use the Lower synth to produce the 16' and 2 2/3' pitches, and the Upper synth to produce the 8' and 5 2/3' pitches. This allows us to use the Lower filter to create a percussive 'blip' at the front of notes, controlling the loudness of the 2 2/3' pitch without affecting the amplitude of the other pitches (see Figure 11, below). Figures 12 and 13 (overleaf) demonstrate why this works so well; the 5 2/3' and 8' pitches are not passing through the Lower filter, and the 16' pitch is far enough removed from the cutoff frequency to be unaffected by the changes. OK, I'm cheating, because the Prophet 10 cannot produce the sine waves needed to make this picture strictly accurate, but the result nonetheless sounds surprisingly authentic. Neat, huh?
Hammond Effects — Chorus/Vibrato Given that there's no way to emulate the Prophet's percussion settings on the Juno, let's now ignore this effect, throw a temper tantrum, and — as suggested at the start of this article — decide that we never wanted it, anyway. Instead, let's move on to the wonderful chorus/vibrato provided on the larger Hammond organs. Chorus was not a feature of Laurens Hammond's earliest instruments, but he soon decided that the sound of his tonewheel generator was too pure, and that it needed something to impart life and movement. Some of his earliest production organs used two ranks of tonewheels detuned by a small amount to create what was possibly the world's first example of 'polyphonic oscillator detune', while some of his 'X-series' speaker cabinets had a rotor at the top of the assembly that added amplitude modulation. But Hammond wanted something with more animation, and in 1945 he designed an electromechanical device that created the pitch modulation he wanted. He called it a 'scanner' vibrato. This uses a tapped delay line which, if we look closely at the electronics, is a type of phase-shifter constructed from low-pass filters. The signal generated by the tonewheels is applied to the input of the delay line, and a rotating pickup driven by the tonewheel generator picks the signal off the delay line at each of the tap points, one at a time. The scanner is wired so that it moves from one end of the delay line to the other, and back again, during each rotation. As it does so, the pitch shifts up and down... which is, of course, vibrato. Careful analysis shows there is also a small amount of amplitude modulation as the scanner sweeps round the taps, but we should be able to ignore this. If you select one of the 'V' settings on the Hammond, all of the audio is routed through the scanner, and the signal suffers unadulterated pitch modulation at one of three depths called V-1, V-2 and V-3 (see Figure 14 on the next page). If you select a 'C' setting (C-1, C-2 or C-3), the output from the scanner unit is mixed with the unaffected output from the tonewheel generator, and the result is what we call 'chorus' (see Figure 15, also overleaf). This is the key to the best Hammond sounds yet, despite its apparent simplicity, only a couple of Hammond emulators manage to get it right. So, what hope do we have of getting the Juno's onboard chorus unit to imitate the C-3 setting favoured by many organists? None, I'm afraid. The Hammond chorus mixes the straight-through signal with just a single instance of the pitch-modulated signal, so the Roland's three-stage chorus/ensemble is far too lush. It's little consolation that we can use the Juno's LFO to create vibrato of an appropriate depth and speed... it doesn't sound the same as the Hammond's. If you want to try this, you must select the LFO rate very carefully — I find that 'six and a bit' is correct on my Juno 60 — and set the LFO depth in the DCO to create the correct amount of modulation. But this is only half the story. The 5 2/3' pitch is being generated by the VCF, so you must also raise the LFO depth in the filter section, and try to ensure that identical amounts of modulation are applied to the DCO and the VCF. If you don't, the 16' and 8' pitches will deviate more (or less) than the 5 2/3' pitch, which leads to some very unconvincing effects. I have shown the modified parts of the patch in Figure 16 (below). To be honest, I think that these changes have turned my original Hammond patch from prime steak into dairy produce. In other words, a patch that was previously meaty now sounds cheesy. It may be theoretically accurate, but that doesn't mean that I have to like it. In fact, I never use any of my A100's 'V' settings, so I'm going to abandon the changes in Figure 16 and return, yet again, to Figure 1.
Hammond Effects — Leakage Another characteristic of the tonewheel generator (which, like key-click, Laurens Hammond considered to be a fault) is 'leakage', a mixture of drawbar pitches and noise that gives the A100 a characteristic, throaty quality. On some synths, adding the tiniest amount of noise helps to create this impression. On the Juno, however, the noise passes through the self-oscillating filter, and emerges tuned to the 5 2/3' pitch. Bah! Because its filters are not oscillating (indeed, have zero resonance), adding noise works far better on the Prophet 10. But on consideration, I think that I'll leave well alone. Back to square one (or, to be precise, Figure 1) again!
Hammond Effects — Overdrive & Compression The next thing we need to consider is overdrive; our ability to cause the valve preamplifier and amplifier(s) in the Hammond to distort. Laurens Hammond was an engineer, not a musician, and reputedly tone-deaf. Yet he had very strong views regarding the tone that he wanted from his organs, and gave explicit instructions to his factory and service centres that the amplifiers were to be adjusted so that there was no overdrive or distortion. Nowadays, we think that Hammond was wrong, and overdrive and distortion have become invaluable in all forms of non-classical music. To be fair to Mr Hammond, it was only in the 1950s that keyboard players and guitarists started to experiment with overdrive seriously, and it took another decade for distortion to emerge as a fundamental building block of modern popular music. Nowadays, many synths feature digital overdrive/distortion effects, but the Juno predates such enhancements. Nonetheless, all is not lost, because with the high internal signal levels generated by the DCO, the sub-oscillator and the self-oscillating filter, it is easy to overdrive the Juno's VCA by raising its Level toward +5 (see Figure 17, left). The result can be anything from a mild distortion to a full-throated crackle. It's not the same as the warm burr of a 30-year-old valve on the edge of break-up, but produces some very useable results, plus an unexpected side-benefit. A Hammond exhibits mild compression when you add notes to a chord and, coincidentally, an overdriven VCA exhibits exactly the same quality when you exceed the limit of its abilities to amplify and drive it into clipping distortion. Unfortunately, you can't employ this trick on many synths, because the majority are factory-calibrated to stop you from clipping the signal. This is understandable; for most sounds, the results would be inappropriate and unpleasant. Still, it would be nice if the option existed, as on the Juno.
Hammond Effects — Reverb In some low-cost Hammonds, the next element in the signal path is a spring reverb unit. You would think that it would be a doddle to imitate this... why not just plug a suitable spring reverb or digital imitation between the Juno and the amplifier/speaker system, as shown in Figure 18? However, this is not quite right, because the overdrive generated by the overdriven VCA occurs before the reverb unit, and this is the opposite of what happens in the Hammond. Nonetheless, many modern reverb units offer suitable effects, provided that you disable all the extra stuff that they tend to offer. Things become more complex when you consider the A100, which has a separate amplifier and speaker to handle the output from the reverb unit (see Figure 19). However, this is easily recreated, because many digital reverb units allow you to send a treated signal to one channel while directing the original to another. This means that I can draw Figure 20, with a modified Juno patch providing optional vibrato and overdrive, played through two channels; one clean, the other reverberated. So... how does it all sound? The truth is, not great. I don't like the vibrato effect, we've been unable to synthesize percussion or chorus, and while the distortion effect is quite pleasing, sticking a digital reverb after a patch doesn't count as 'real' synthesis. Sure, we've learned a great deal simply by attempting to recreate the Hammond effects, but it would have been nice to achieve something more satisfying. Fortunately, this isn't the end of the story, because I've left the most important — and by far the best — organ effect out of this discussion. I'm referring, of course, to that generated by the rotary speaker or 'Leslie' attached to almost all A-, B- and C-series Hammonds. So, next month, we're going to wrap up our synthesis of the Hammond organ by getting ourselves into a bit of a spin. Source: SOS |
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Synthesizing Tonewheel Organs: Part2 |
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By: Gordon Reid Original Photo: Richard Ecclestone  |
You may recall that last month, I described how, many years ago, I embarked upon a quest to find an affordable and manageable synthesizer to replace my ageing Crumar Organiser and Korg BX3. I left you with the solution I found, a Hammond patch created on a Roland Juno 6 (shown here as Figure 1 below). If you refer back to last month's article, you'll remember that the harmonic spectrum of this patch is as shown in Figure 2, where the three red squares represent the amplitudes of the first — and only — three harmonics present in the sound; the basis for a fine emulation of the 88 8000 000 registration. (For an explanation of the curious axes on the graph in Figure 2, and why they are particularly well suited to depicting the harmonic spectrum of the output from a tonewheel organ, I again refer you back to last month's instalment of this series). Now, you might think that these diagrams reveal the secret for synthesizing all manner of Hammond registrations on the Juno. After all, the self-oscillating VCF — which is responsible for the presence of the third harmonic — can be tuned to any frequency, so in theory, we should be able to create any patch that uses three drawbars, provided that two of them, those generated by the sub-oscillator and the main DCO, are an octave apart. For example, if we slide the VCF cutoff up to the next drawbar frequency (the fourth harmonic of the fundamental, which is the 4' drawbar) we obtain strong components at the first, second and fourth harmonics, with a reduced contribution from the third harmonic; maybe something along the lines of an 82 8800 000 registration. But when we try this, something doesn't sound quite right. While the basic tonality is much as you might expect, the patch is too bright, and lacks the character of half a hundredweight of pickups, valve preamps, and rotating steel. To explain this, I've calculated the amplitudes of the frequencies present in the new patch, and shown the results in Figure 3 (above). As you can see, the first four harmonics are present in the expected amounts, but three more — which I have shown in orange — are also present, albeit at lower amplitudes. We might be able to excuse the rightmost of these because it lies on the eighth harmonic, and therefore represents a bit of leakage from the 2' drawbar. But the contributions from the fifth and seventh harmonics are not so welcome. They don't sound 'wrong' exactly — after all, they lie in their correct positions in a perfect harmonic series — but their contributions are inappropriate, and it is these that make the patch sound too bright (the 6th harmonic is entirely absent, but I'll leave you to work out why). The situation deteriorates further if we raise the cutoff frequency any more. There are two reasons for this. Firstly, the filter passes all the harmonics that lie below the cutoff frequency. This is no good because, as shown last month, the idealised spectrum generated by the Hammond tonewheel engine — which goes as high as the 16th harmonic of the 16' drawbar — does not include the fifth, seventh, ninth, 11th, 13th, 14th or 15th harmonics. Secondly, the densely packed higher harmonics are not attenuated as rapidly as the widely spaced lower harmonics, so we hear many overtones above the cutoff frequency of the self-oscillating filter. To demonstrate this dramatically, I have calculated 80 8000 008 as recreated by the 'Juno method' as described last month. This is a perfectly acceptable Hammond registration which, when patched on the synth, is a sonic mess. Again, the desired harmonics are shown in red (see Figure 4, above), and the unwanted ones in orange. As you can imagine, it sounds nothing like the real thing. If this weren't bad enough, the tracking of the Juno's filter becomes very unstable at higher frequencies. It is superb at low multiples of the fundamental because it 'locks onto' the strong second, third and (just about) fourth harmonics, producing a pure, stable tone at pitches that relate precisely to the 8', 5 2/3' and 4' drawbars. But as the harmonic number rises, its ability to lock on diminishes, and it starts to float around. The result is a strange, tuned noise that is interesting, but nothing whatsoever to do with the sound of a Hammond organ. When it comes to the crunch, the 'Juno method' is capable only of synthesizing the 88 8000 000 registration with any degree of realism. So perhaps we should now look elsewhere to synthesize a more flexible imitation of the Hammond.  Figure 1: Last month's Juno 6 Hammond 88 8000 000 patch. |
Another Method Of Hammond Synthesis In 1981 and 1982, Genesis were on tour promoting their Abacab album. For keyboard player Tony Banks, this must have been a very different experience compared with the tours of the 1970s. Gone was his Mellotron, gone was his RMI Electrapiano, and gone was his ARP Pro Soloist. And, most relevant to this month's discussion, gone was his Hammond T-series organ, to be replaced by a dual-manual Sequential Circuits Prophet 10.  Figure 2: The harmonic spectrum of the patch shown in Figure 1.
 Figure 3: Trying to synthesize 80 8800 000.
 Figure 4: Failing to synthesize 80 8000 008.
 Figure 5: The voicing of the Prophet 10.
 Figure 6: Setting up the Prophet 10's dual oscillators.
 Figure 7: Setting up the filter.
 Figure 8: Creating the 'key-click' sound using the filter cutoff frequency contour.
 Figure 9: The 'organ' amplitude envelope settings.
 Figure 10: The amplitude contour.
 Figure 11: The Prophet 10's four voice-allocation modes.
 Figure 12: Using four oscillators to emulate four drawbars.
 Figure 13: The filter and amplifier settings for a four-oscillator Hammond emulation. |
As well as being hideously expensive, the Prophet was, and is, a large and heavy synthesizer, which means that it is just as much a pain in the posterior as an organ. Given that it is not particularly reliable, it seems odd that Tony should have adopted it in this fashion. Indeed, he told me many years ago that he carted two of them around on tour (with one as a spare), although he preferred not to use the second instrument because it sounded different from his favoured one. I'm not surprised... the tuning of the 20 oscillators and the 10 low-pass filters on the Prophet 10 is not what you would call 'precise'. Nonetheless, Tony produced a fine organ sound on that tour, and the method he used illustrates a useful principle, so I thought that it would be interesting to recreate his patch. Figure 5, which is shown on the next couple of pages, and will cause the graphics department at Sound On Sound to stick large pins into little Gordon effigies, shows the voice structure of a Prophet 10. It's huge, even though I've omitted the patch selection and housekeeping section of each of its two control panels for the sake of practical representation. Hang on a second... two panels? Of course, the Prophet 10 has only one physical panel, but it really is two synths, each similar to a Prophet 5. Each has a dedicated keyboard, and each offers dual oscillators per voice, a 24dB-per-octave low-pass filter, dual ADSR contour generators per voice, an LFO, plus the Prophet 5's renowned Poly-Mod section. In Normal mode, the Upper synth is played from the upper manual, while the Lower synth is played from, well... the lower one. This means that we can take either one, and patch it using the 'Juno method'. We'll start with the VCOs. Figure 6 (below) shows that I have selected a pulse wave for Oscillator B, and set the pulse width to '5', which is the setting at which it produces a square wave. You'll also see that I have tuned it to the lowest pitch available, with no fine tuning offset, and that the 'Keyboard' LED is lit, which shows that the oscillator will track the keyboard in a conventional manner. Oscillator B is, therefore, performing the same task as the sub-oscillator in the Juno patch. Oscillator A is also programmed to produce a pulse wave, but on this occasion, the pulse width is 33.33 percent, just as it was last month. The Frequency knob is tuned by ear to produce a pitch that is precisely one octave above Oscillator B. Once this is set correctly, we can adjust the relative amplitudes of the oscillators (which are, in effect, the drawbar settings of the 16' and 8' pitches) in the Mixer. Next comes the filter section (shown in Figure 7, left). Firstly, the 'Keyboard' switch must be on (ie. with the red LED lit) so that the filter tracks the keyboard. Then, as with the Juno patch, we set the cutoff frequency so that it lies precisely on the 5 2/3' pitch, and increase the resonance until the filter begins to oscillate and produces a sine wave. The Prophet 10 has a dedicated ADSR contour generator for the filter, and I have set all its knobs to zero. This is because the P10's envelopes are not the snappiest in the world, and we need to use the minimum settings to obtain the 'key-click' sound (see Figure 8, above) at the start of each note, as explained last month. You determine the amount of click by adjusting the Envelope Amount knob to taste. The next part of the patch is easy. We want an 'organ' envelope, so we can set the amplitude ADSR as shown in Figure 9, with instantaneous Attack, maximum Sustain level, and no Release. The Decay segment of this contour is, of course, irrelevant (see Figure 10, below). And there you have it: defeat all the modulation sources and you have programmed the wonderful Prophet 10 organ patch, a gorgeous sound from one of the greatest synthesizers ever built. Fantastic! Or is it? For one thing, the Prophet 10 hardly answers to my required description, 'affordable'. And then there's the sound itself. Sure, it's nice, and has a warmth and presence that you would be proud to use, especially if you use the onboard EQ section to boost the middle frequencies. But, just as I suggested last month, for this purpose the Prophet is still the inferior of the vastly cheaper Juno. Why? The answer lies in the aforementioned instabilities of the Prophet 10. Despite the microprocessor that lies at its heart, it is a truly analogue synth, and you can press the Tune button until you get blisters, but you still won't get its oscillators in perfect tune, much less its filters. What's more, the quantisation of the controls is very apparent, and this makes it impossible to use the 'Juno method' effectively. Back in Part 21 of this series (see SOS January 2001, or surf to www.soundonsound.com/sos/jan01/articles/synthsec.asp), we discussed the reasons why analogue synths with memories must have quantised controls. So, while you might be able to tune any one of the Prophet's filters to precisely the correct pitch, the one in the next voice might be far enough removed that, when you turn the filter knob a tiny amount to bring it into line, the cutoff frequency jumps so far that the situation is worse than before. On my Prophet 10, one of the filters on the Upper keyboard is always a few cents out of tune, and, while it tracks correctly, the voice that contains it sounds significantly different from the other four. You may choose to call this 'analogue warmth', but it's not. It's just plain wrong.
Two Is Better Than One So how can we overcome this? The old Genesis videos demonstrate that Tony's Prophet 10 was capable of a much better likeness to the old Hammond, so there must be a way... And there is. The secret lies in the 'two synths in a box' nature of the big Prophet, and the four keyboard modes that it offers. Up until now, I've been assuming that we've been in Normal mode which, if the 'Juno method' had been successful, would have allowed me to create different patches for each keyboard, and to play the Prophet 10 as a dual-manual organ, or as a single-manual organ plus a string ensemble, or brass section, or whatever. But the method was not successful, so now I'm going to place the synth in Double mode (see Figure 11, below). This allocates Upper Voice 1 and Lower Voice 1 to the first note you play, Upper Voice 2 and Lower Voice 2 to the second note you play... and so on. In other words, I have placed both synths under the control of one keyboard (the Prophet 10 was one of the first instruments to offer layering). This makes it possible for us to patch registrations containing four pitches, and without having to use the filter as an oscillator. Consider Figure 12 (above). This shows the Upper and Lower Oscillator and Mixer sections simultaneously, with Double mode selected, and all four oscillators tuned and balanced to produce the 88 8800 000 registration. The Lower section is identical to Figure 6, with one exception: I have switched off the square waveform in Oscillator B (the oscillator producing the 16' pitch) and selected the triangle wave instead. This is as close as the Prophet will come to emulating the (near) sine wave produced by a tonewheel generator. The Upper section is set up using the same waveforms, but tuned so that oscillators B and A produce the pitches of the 5 2/3' and 4' drawbars respectively. Of course, there's nothing forcing us to use these pitches, and we no longer have to use the self-oscillating filter to produce the 5 2/3' pitch. So, in this way, the Prophet 10 patch is superior to the Juno's. Now we must reprogram the filter sections for both synths, eliminating the resonance, but keeping the cutoff low enough to attenuate the unwanted harmonics generated by the triangle and pulse waveforms (see Figure 13, right). The amplifier ADSRs should, of course, be identical to each other and to that shown in Figure 9, and all modulation should be defeated. Having set all of this, we should now be able to create and play any registration, provided that it uses only four drawbars at a time. Nevertheless, the Juno still sounds the better of the two. Far from being the millstone that some anoraks would have you believe, the precision offered by its digitally controlled oscillators and its superb filter tracking ensures consistency across all the notes played, and this is exactly what a Hammond patch requires.
A Better Mousetrap? I don't know about you, but I feel decidedly uneasy that the Juno has outshone the mighty Prophet. Nevertheless, this set me thinking... there must be a synth that's not too expensive, but which combines the stability and tuning accuracy of the Juno's DCOs and filter, and also offers the flexibility of four oscillators and dual signal paths. Of course there is! It's the Roland JX10, which has a the 'two synths in a box' architecture, but is digitally controlled. Surely this is the best of both worlds, and must sound superb? Well... no, it doesn't. I used a JX10 as my main stage keyboard/controller for more than a decade, and after numerous abortive attempts, I never again attempted to use it for organ patches. Experience showed that JX10 organ patches are at best unconvincing, and that's perhaps the reason that my Juno 60 survived as a gigging instrument for as long as it did. Hmm... what other affordable analogue synths can we try? The Oberheim OB-series? Far too inaccurate. A Memorymoog? You've got to be joking... How about the Prophet 600, or the Korg PS3200, or the Crumar Bit One, or the Akai AX60, or the... Stop it Gordon, take a deep breath, and relax. None of these fit the bill. When it comes down to it, the Junos really are remarkable little synths, and it is no wonder that they often sound superior to instruments worth many times as much. Nonetheless, there is at least one low-cost analogue/digital hybrid does an even better Hammond emulation. The sound quality is superb, and it is completely flexible, being capable of any of the 387,420,489 registrations that you care to name (did anybody check my maths?). Yet its second-hand value is close to zero, and you would probably walk past one if you saw it in a car-boot sale. It's one of my favourite synths of all time. It's the Kawai K3 (shown above right). | HARMONIC NUMBER | 1 | 2 | 3 | 4 | 5 | 6 | ... up to 128 | | VALUE | 31 | 31 | 31 | 0 | 0 | 0 | ... all zero |
| KAWAI K3: HAMMOND 88 8000 000 REGISTRATION | | OSC 1 |  1 | Wave | 32 | The additive wave | | 2 | Range | 16' | | 3 | Portamento Speed | 0 | No portamento | | 4 | Balance | -15 | Only OSC1 used | | 5 | Pitch Bend | 0 | | 6 | Auto Bend | 0 | | OSC2 | | 7 | Wave | n/a | | | 8 | Coarse Freq | n/a | | | 9 | Fine Freq | n/a | | | FILTER | | 10 | Cutoff | 65 | Sounds about right | | 11 | Resonance | 0 | | | 12 | Low Cut (HPF) | 0 | No high-pass filtering | | 13 | Env Amount | 31 | Maximum amount | | 14 | Attack | 0 | | | 15 | Decay | 0 | A fast key-click 'blip' | | 16 Not used | | 17 | Sustain | 0 | | | 18 | Release | 0 | | | AMPLIFIER | | 19 | Level | 31 | Maximum amplitude | | 20 | Attack | 0 | | | 21 | Decay | 0 | | | 22 | Not used | | | | 23 | Sustain | 31 | A 'square' amplitude contour | | 24 | Release | 0 | | | LFO | | 25 | Shape | n/a | | | 26 | Speed | n/a | | | 27 | Delay | n/a | | | 28 | Oscillator Amount | 0 | | | 29 | VCF Amount | 0 | | | 30 | VCA Amount | 0 | | | TOUCH SENSITIVITY | | 31 | Velocity -> VCF | 0 | | | 32 | Velocity -> VCA | 0 | | | 33 | Pressure -> OSC Balance | 0 | | | 34 | Pressure -> VCF | 0 | | | 35 | Pressure -> VCA | 0 | | | 36 | Pressure -> LFO OSC Amount | 0 | | | KEYBOARD TRACKING | | 37 | VCF | 9 | Approximately 100-percent tracking | | 38 | VCA | 0 | | | CHORUS | | | | | 39 | Chorus | 0 | Off |
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It All Adds Up Last month, I mentioned that dedicated additive instruments such as the Kurzweil 150, Kawai K5 and Kawai K5000 were capable of some fine Hammond sounds, as are the larger DX-series FM synths. But the thing that makes the K3 special is its combination of a primitive form of additive synthesis plus one of the scrummiest analogue filters ever designed by man, the SSM2044. Unlike the dedicated additive instruments mentioned above, the additive section in the K3 allows you to create just one spectrum (and, therefore, waveform) at a time, but this comprises up to 32 partials distributed anywhere among the first 128 harmonics of the pitch. Setting this up is a doddle; you just select the harmonic number and dial in an amplitude between zero and 31. Simple! This means that we can construct any conventional registration using the first, second, third, fourth, sixth, eighth, 10th, 12th and 16th harmonics, or reproduce the extended drawbar set offered by a handful of rare Hammonds, or even imitate the 'EX' mode of the new, DSP-driven Korg CX3 and BX3 emulators. Think about it; we no longer need to resort to trickery to obtain the spectrum in Figure 2. We simply select harmonic #1 and give it an amplitude of 31, select harmonic #2 and give it an amplitude of 31, select harmonic #3 and give it an amplitude of 31, and then press the 'Write' button to calculate the waveform, as shown in the smaller value table opposite. We then reduce the filter cutoff frequency a little to remove some stray upper frequencies that, in a perfect additive world, wouldn't be there in the first place, and the result is...? Superb.  |
We construct the rest of the patch exactly as before, with a 'spitty' filter contour as shown in Figure 8. We do this by setting the ADSR values for the filter (parameters 14, 15, 17 and 18) to be 0, 0, 0, 0... which is the same as the Prophet 10 knobs shown in Figure 7, but represented in numerical form in the K3's 'digital parameter access' user interface. Likewise, the amplitude ADSR (parameters 20, 21, 23 and 24) is set to 0, 0, 31, 0... the same as the knobs in Figure 9, and therefore defining the 'square' amplitude envelope of Figure 10. Next, we defeat the velocity sensitivity and pressure sensitivity (neither of which are appropriate for a Hammond patch), reduce all the modulation amounts to zero, and... bingo! The complete patch is shown in the large table opposite. So there we have it... We started with the little Juno, which is cheap and cheerful, and synthesizes just one Hammond registration extremely well. We then graduated onto the mighty Prophet 10, which is far from cheap, but is limited to four 'drawbars' and — unless every voice is tuned absolutely precisely — produces no meaningful Hammond registrations well. Finally, we ended up programming an almost unknown, valueless analogue/digital hybrid. Yet it is this that is best suited to Hammond emulation, which proves to be the most flexible, and which has produced the most satisfying result. You might think that I've cheated by introducing additive synthesis (and you would probably be right) but given that my original aim was to program convincing registrations on something that was cheap and physically light, but sounded as good as a Korg BX3, I'm happy. The answer, ladies and gentlemen, is the Kawai K3.
Epilogue As with last month's Juno patch, and despite what I've just written, the K3 patch described here doesn't sound all that much like a real Hammond. As I explained last month, this is because these patches make a good fist of synthesizing the sound of an unadorned tonewheel generator — as yet, I've made no attempt to reproduce the chorus/vibrato, percussion, and overdrive effects that really 'make' the Hammond sound. Next month, we'll do what we can to emulate these, and see whether we can use the Juno to produce entirely convincing imitations of the big Hammonds. Until then... enjoy your organ! source: SOS |
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Synthesizing Tonewheel Organs Part 1 |
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Long before Bob Moog built his first synth, there was the Hammond tonewheel organ; effectively an additive synthesizer, albeit electromechanical rather than electronic. So emulating a Hammond with an analogue synth shouldn't be too hard, right? Well... By: Gordon Reid Long before Keith Emerson and Rick Wakeman showed us that keyboard players did not have to be accompanists dressed in black and illuminated by black spotlights, and even longer before musicians began to take to the stage armed with nothing but a laptop computer and a pair of turntables, jazz and blues organists were the hi-tech musicians of their day. So when players such as Jimmy Smith and Earl Grant cast off their sackcloth and made a bee-line for the front of the stage, they did so with nary a Minimoog, ARP 2600, EMS VCS3, chorus unit, phaser, ensemble, or digital reverb in sight — which isn't surprising, as none of these had yet been invented. With no more than a Hammond organ, a bit of spring reverb, and maybe a touch of overdrive, these guys were creating exciting new forms of dance music throughout the middle of the 20th century. In retrospect, it's far from unreasonable to suggest that almost all modern forms of hi-tech music evolved from the 'black' music of the 1940s and 1950s, and it is therefore appropriate to hand the award for most influential keyboard instrument of the 20th Century to the Hammond 'tonewheel' organ. | DRAWBAR | COLOUR | PITCH | TRADITIONAL NAME | HARMONIC NUMBER | | 16' | Brown | Sub-octave | Bass | 1 | | 5 2/3' | Brown | 5th | Quint | 3 | | 8' | White | Unison | Neutral | 2 | | 4' | White | 8th | Octave | 4 | | 2 2/3' | Black | 12th | Nazard | 6 | | 2' | White | 15th | Block-flˆte | 8 | | 1 3/5' | Black | 17th | Tierce | 10 | | 1 1/3' | Black | 19th | Larigot | 12 | | 1' | White | 22nd | Sifflˆte | 16 |
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A Course In Electromechanics Like many brilliant ideas, the basis of Laurens Hammond's tonewheel generator is simple: a knobbly wheel rotates in the presence of a magnet, and the resulting changes in the magnetic field induce a signal in a pickup (see Figure 1, below). The waveform and frequency of the signal is determined by the shape of the wheel and the number of 'bumps' that pass the tip of the magnet every second. Given that in the finished instrument, all the tonewheels are mounted on a single axle, different frequencies are obtained not by using different rotation speeds, but by using tonewheels of different sizes and geometries. Like I said... brilliant! When designing his organ, Hammond decided that each tonewheel should generate a sound as close as possible to a sine wave, so that players could construct timbres using a fundamental and overtones. Building on this idea, he chose a system by which players could mix up to nine sine waves simultaneously, using 'drawbars' (see Figure 2) to give each an amplitude ranging from zero to eight. Some later Hammonds offered more drawbars, and some offered fewer, but nine is the classic configuration.  Figure 1: A single Hammond 'tonewheel' and pickup.
 Figure 2: The nine 'drawbars' fully extended.
 Figure 3: Hammond registration 80 0000 000.
 Figure 4: Hammond registration 88 8000 000.
 Figure 5: Hammond registration 88 8888 888.
 Figure 6: Hammond registration 83 4211 100 (slightly sawtooth-ish?).
 Figure 7: Hammond registration 00 8030 200 (slightly square-ish?).
 Figure 8: You need 20 modules for each note of an additive Hammond emulator!
 Figure 9: The Juno 6 Digitally Controlled Oscillator.
 Figure 10: Representing a sound with three harmonics (the first, second and third) of equal amplitude.
 Figure 11: The sound represented in Figure 10, created using 16', 5 2/3' and 8' drawbars.
 Figure 12: The first 50 harmonics of a mathematically perfect square wave, shown on logarithmic axes.
 Figure 13: Filtering the sub-oscillator from the third harmonic upwards.
 Figure 14: The spectrum of a 33-percent pulse wave.
 Figure 15: The spectrum of the filtered 33-percent pulse wave.
 Figure 16: Adding the filtered sub-oscillator and 33-percent pulse wave.
 Figure 17: The Juno 6 DCO set to produce a Hammond sound.
 Figure 18: Amplifying the third harmonic using filter resonance.
 Figure 19: Four of the six Juno 6 VCF settings.
 Figure 20: The harmonic amplitudes of the signal after programming maximum resonance in the Juno's filter.
 Figure 21: The Juno 6 'Env' settings.
 Figure 22: The resulting VCF contour.
 Figure 23: Raising 'Env' amount to apply the ADSR to the filter cutoff frequency.
 Figure 24: The Juno 6 VCA settings.
 Figure 25: The resulting VCA contour. |
The lowest pitch on a full console Hammond is 16', with drawbars at five and two-thirds feet (5 2/3'), 8', 4', two and two-thirds feet (2 2/3'), 2', one and three-fifths feet (1 3/5'), one and one-third feet (1 1/3'), and 1'. So, despite Hammond's strange decision to call the 8' the fundamental (or 'Unison') and the 16' drawbar the sub-octave, the 16' pitch is the fundamental of a series that includes the first, second, third, fourth, sixth, eighth, 10th, 12th and 16th harmonics, as shown in the table below. Different drawbar configurations are called 'registrations', and (if my maths is correct) there are 387,420,489 of these on each manual. These registrations fall into groups with archaic names such as 'Stopped Flutes', 'Half-covered Flutes', 'Gemshorns', 'Strings', 'Vox Humanae', 'Reeds'... and so on. Within each of these there are anywhere between a few hundred and a few million unique combinations, and each can be represented by a nine-digit number written in the form 'xx xxxx xxx'. So, for example, if the 16' drawbar is fully extended but all the others are pushed home, we can write the resulting registration as 80 0000 000. Now, if each drawbar produces a sine wave, 80 0000 000 will not create a very interesting sound. Depending upon the amount by which you pull out the 16' drawbar, you will simply obtain a sine wave of greater or lesser amplitude (see Figure 3, left). So you add interest by pulling out combinations of drawbars to create complex registrations. Figure 4 shows the waveform generated by one of the simplest but most important of these, beloved of Jimmy Smith, Keith Emerson, and heavy rock players the world over. The registration is 88 8000 000 and, if you are an Hammond aficionado, you will immediately recognise its punchy timbre. In contrast to the simplicity of 88 8000 000, and often deprecated by classical organists, is the registration 88 8888 888 (see Figure 5). This has all nine harmonics present at maximum amplitude, and is very full and bright. More interesting, perhaps, are the registrations shown in Figures 6 and 7. The first of these is 83 4211 100, the closest approximation available to a '1/n' harmonic series, while the second is 00 8030 200, an approximation to a '1/n' series with all the even harmonics missing. In other words, they are the closest a vintage Hammond can come to producing a sawtooth wave and a square wave, respectively. Clearly, we can create a huge range of tones using the nine pitches available and, way back in the mists of time, I showed how we can use nine sine-wave oscillators, nine amplifiers, a gate of some sort and a mixer to emulate a note produced by a tonewheel generator. Figure 8 (on the next page) shows an advanced version of this idea, with the oscillators' pitches fixed to the drawbars' pitch relationships, and a voltage-controlled mixer that allows you to mix the oscillators' outputs just as you would if you were clutching a fistful of drawbars. Apart from dedicated additive instruments such as the Kurzweil 150, Kawai K5 and Kawai K5000 (of which more next month), there is only one family of synths that allows you to patch Figure 8 in a cost-effective fashion. These are the more powerful of the FM synths that dominated the mid- to late-1980s. The DX7 isn't quite up to the job, but the DX5 and DX1 have a dozen freely tuneable 'operators' so, using Algorithm 32, you can program Figure 8 with three oscillators to spare. Long before the current crop of digital B3/C3 emulators, these powerful synths were responsible for some excellent Hammond impersonations. Unfortunately, there are few of the larger DXs in circulation, and you're unlikely to lay your hands on one. If you do, you'll probably pay up to £750 for a DX5, and as much as £2000 for a DX1. Oh, alright... I admit that this is not a very cost-effective solution! So let's see whether we can use a much simpler and cheaper analogue polysynth to patch an acceptable Hammond sound.
Organ-ism Back in the dim and distant 1980s, I owned two Hammond emulators: a cheap and cheerful Crumar Organiser that had cost me the grand sum of £199 in the late '70s, and a Korg BX3 that, a few years later, had cost a whole lot more. The Crumar sounded little like a Hammond, but was relatively light and portable. In contrast, the Korg sounded far more realistic, but was almost as unwieldy as the top of a split B3. As a result, I was always looking for alternatives that would sound good, but save weight and hassle. I tried everything, but — until the advent of digital emulators such as the Hammond XB2 several years later, I found that nothing improved greatly upon the 88 8000 000 organ sound that I patched on a very simple analogue polysynth. That synth was a Roland Juno 6, and given that it offered just one oscillator per voice and no sophisticated voicing capabilities, it seemed a most unlikely solution to my problem. I'll start to develop the patch by considering the Juno's single oscillator section (see Figure 9). As you can see, this offers just two waveforms — variable pulse (with pulse-width modulation) and sawtooth — plus a square-wave sub-oscillator one octave below the basic pitch. There is no way to mix the pulse and sawtooth waveforms in different amounts — they are either 'on' or 'off', although you can add as much or as little sub-oscillator as you like. I'm now going to introduce a rather unusual way to represent harmonic spectra. I haven't used this representation before, but it's particularly well-suited to depicting the output from tonewheel organs. For reasons that will soon become apparent, I will draw the harmonics' frequencies and amplitudes on logarithmic scales. I will also invert the amplitude axis so that the louder a harmonic is, the lower on the page it appears. Strange though this may seem, it mimics a visual representation of Hammond drawbars. So, for example, I can depict a spectrum comprising three sine waves lying on the first three harmonics of a given frequency (see Figure 10, below), and it is should be clear that this is a different way of representing the 88 8000 000 registration shown in Figure 11). If we now return to the Juno 6 and activate its sub-oscillator, we will (in a perfect world) obtain the spectrum shown in Figure 12 (on the next page). Clearly, this is a million miles from what we require. What's more, for a fundamental of, say, 200Hz, there are 100 harmonics within the 20Hz-20kHz audio spectrum, of which 50 have non-zero amplitude. By the way, I hope that you can now see why it's useful to plot '1/n' plots on logarithmic axes — on linear axes, this graph would have been considerably wider than this magazine, and the resulting fold-out diagram would have given SOS's printers a terrible headache! To start sculpting this into something useful, I am going to filter the sub-oscillator using the Juno's low-pass filter, with the cutoff frequency set precisely 19 semitones (one octave and a fifth) above the sub-oscillator pitch itself. The reasons for this very precise setting of the cutoff will become apparent shortly... The result appears in Figure 13 (right). As you can see, the first two partials (which are the first and third harmonics) pass through the filter unscathed, while the third (the fifth harmonic) is attenuated, and the higher harmonics are so quiet as to be almost inaudible. This is closer to Figure 10, but still wins no cookies. Now I'm going to add the output from the oscillator. I'll set it up so that only the pulse wave is produced, and this has a duty cycle of 'one third'. If you recall the instalment of this series, and specifically the large box in that instalment on the nature of pulse waveforms, you'll remember that you can approximate the harmonic content of the resulting waveform if you take a sawtooth wave and remove every third harmonic. Of course, if you remember the rest of that instalment, you'll also recall that this approximation breaks down as you decrease the duty cycle — so the harmonic content of a pulse wave with a duty cycle of one-twelfth, for example, isn't much like that of a sawtooth with every 12th harmonic removed at all. But for a pulse wave with a duty cycle of one third, the approximation is reasonably sound, and the remaining partials conform almost exactly to a 1/n amplitude spectrum, as demonstrated in Figure 14 (right). The output from the pulse wave has to pass through the same filter as the sub-oscillator, so it too will be heavily filtered. However, whereas the filter cutoff frequency is set to the third harmonic of the sub-oscillator, it lies halfway between the fundamental of the pulse wave and its first overtone (which, in this case, is the second harmonic). So — to paraphrase the above — the fundamental passes through the filter unscathed, but the first overtone is attenuated and everything else is so quiet as to be almost inaudible (see Figure 15 on the next page). I'll now switch on the Juno's pulse wave and sub-oscillator simultaneously, and show the spectrum of the mixed signal by adding the partials in Figures 13 and 15. The result of this can be represented in Figure 16, also on the next page). Clearly, this is much closer to the ideal, with the leftmost partials representing the 16' and 8' drawbars fully extended, and the next two representing the 5 2/3' and 4' drawbars respectively. The only aberration is the fifth partial, which has an amplitude of about 2.5 percent. As shown by the table earlier in this article, there is no Hammond drawbar which produces the fifth harmonic, so in theory this should not be present. But in the real world, impurities in the geometry of the tonewheels and valve distortion add some fifth harmonic to the sound, so this does not overly concern me. Nonetheless, it would be nice to bring the 5 2/3' pitch to the fore because, as it stands, the sound lacks depth (if you pull out just the 16' and 8' drawbars on a Hammond, you obtain a relatively uninteresting timbre, so it's not surprising that the synthesized equivalent should be similarly lacking). Before attempting to raise the profile of the third harmonic in this way, let's check the settings for the DCO, as shown in Figure 17. Note that the sawtooth wave is 'off', that the pulse wave modulation switch is set to 'Man' (manual), and that the PWM slider is positioned so that the pulse width is a constant 33.33 percent. With practice, you can adjust this by ear... as you move the slider to the correct position, you can hear the third harmonic disappear. Note also that the sub-oscillator output is at its full amplitude, but that there is no contribution from the noise generator. Now it's time to return to that troublesome 5 2/3' drawbar. Given that we have no further control over the oscillator, how can we accentuate the third harmonic of the sub-oscillator? The secret lies in the filter which — if you remember — is tuned exactly 19 semitones above the sub-oscillator's pitch. And of course, 19 semitones above the sub-oscillator is where the third harmonic lies... If you've wondering how on Earth this helps, it should help to know that the Juno 6 has a self-oscillating filter that tracks the keyboard perfectly. If we set the filter resonance to 100 percent, the self-oscillating filter produces a sine wave at the filter cutoff frequency — in other words, 19 semitones above the fundamental. So, if the sub-oscillator produces a bottom 'C' and the pulse wave produces the 'C' an octave higher, the self-oscillating filter will produce a 'G' 1.5 octaves above the sub-oscillator. This works on the Juno because its filter is so perfectly behaved. Unfortunately, attempting this trick on most other analogue synths causes all manner of problems, including severe attenuation of the lower frequencies, and unpleasant distortion as the signal presented to the filter input 'fights' the signal generated within the filter. Oh yes... and it's unlikely that the sine wave produced by self-oscillation will track the keyboard correctly, so its pitch will wander all over the place, making the patch useless. So, if you're trying to create this sound on a lesser instrument (and that includes all the Prophets, all the Oberheim OB-series, and nearly everything else) you must reduce the resonance, leaving it high enough to amplify the third harmonic that is already present in Figure 16, but not so high as to send the filter into oscillation (see Figure 18, on the previous page). Nice though the result in Figure 18 is (especially if high resonance causes the filter to attenuate the higher harmonics further), I don't see why I should limit myself in this fashion. So I'm going to push the Juno 6's filter all the way into self-oscillation (as shown in Figure 19), creating a pure tone at the 19th semitone, and at the same time severely attenuating all the frequencies that lie above this. The result appears in Figure 20 (below), and is exactly what we were after in Figure 10 — a very elegant result, if I say so myself! However, we need to set up the rest of the filter correctly if the sound is to work. In particular, precise adjustment of the filter envelope settings (which I have omitted from Figure 20) is vital if the cutoff frequency is to lie at the correct pitch. But why do we need to modulate the filter using the envelope? Surely it would be best to leave well alone? We all know that Hammond organs exhibit a 'spit' at the start of the note, caused by what Laurens Hammond thought were deficiencies in the keying system. Today, of course, we are rather attached to these so-called 'key-clicks', and the programmers of DSP-driven Hammond emulators spend a great deal of time imitating them as accurately as possible. Unfortunately, the Juno 6 lacks the sophistication needed to produce the clicks correctly, so I will have to resort to using the filter envelope to generate a reasonable imitation. Figures 21 and 22 (above) show how we set up the ADSR envelope generator to create a pronounced, but almost instantaneous, transient at the moment you press a key, and how this can make the VCF cutoff frequency change as you play a note. Given that the filter is oscillating, this will create a very rapid downward sweep during the Decay stage, also accentuating the pulse wave's and sub-oscillator's harmonics as it does so. The 'blip' thus produced is satisfactory for our purposes. The settings in Figure 21 may look trivial, but to apply the contour to the filter itself, you must position the 'VCF Env' switch for positive polarity and raise the 'Env' slider in the VCF section — see Figure 23 (below). You must then be very careful how you set this up, because the Sustain Level and the amount of 'Env' will together raise the cutoff frequency that you have previously tuned so carefully to the sub-oscillator's third harmonic, thus destroying all your hard work so far. So... how can you create the 'key-click' and still get the filter to produce the sound of the 5 2/3' drawbar? You solve this conundrum by taking the following steps: Set the Sustain Level in the ADSR so that you obtain the amount of 'spit' required. A high value will reduce the amount, while a low value will accentuate it, making the organ very 'clicky'. Add the correct amount of 'Env' to the filter to create the click effect that you want. Re-adjust the filter cutoff frequency ('Freq') so that the combined effects of 'Freq', 'Env' and Sustain again tune the cutoff frequency to the third harmonic. The chances are that you'll have to run through these steps a couple of times before everything is hunky dory, but it's not hard once you've got the hang of it. Personally, I find that a 'Freq' value of 'zero' is best, and that tuning the filter using the 'Env' control alone is the ideal solution. Now let's take care of the amplitude envelope. To a first approximation, this is rectangular: you press a key and the note immediately attains its maximum amplitude; you release the key and it immediately falls to silence. The Juno 6 has a neat way of achieving this; you can disconnect the VCA from the envelope generator using the switch shown in Figure 24 (right). The amplifier then responds to the gate pulse itself, being 'on' when you press a key, and 'off' when you release it. This is the mechanism we were after way back in Figure 8, and it produces the amplitude contour shown in Figure 25 (below).  Figure 26: The Juno 6 tonewheel generator patch. |
Putting It All Together We now have everything in place to allow us to emulate the tonewheel generator set to an 88 8000 000 registration, so let's combine the parts to create our final synthesized Hammond patch. Figure 26 (at the bottom of the page) does this. Note that the Key Transpose and Hold buttons are off, that the arpeggiator is off, and that there is no LFO applied in either the DCO section or the filter section, so the LFO controls themselves are irrelevant. Finally, there is no Chorus. So how does it sound? Great, huh? Well... no. It's OK, but it sounds little like a vintage B3, being more akin to one of Hammond's transistor organs from the 1970s; the sort often observed lying unloved and unused in your Auntie Maud's living room. Nevertheless, this sound is in fact not far removed from that of a Hammond's unadorned tonewheel generator — it's just that it lacks the additional treatments and effects that make the Hammond A-, B- and C-series organs the sonic marvels they are. Clearly, in order to synthesize the complete sound, it's necessary to synthesize all the parts of the instrument. I'll return to this point in a couple of months, but for now, I'll leave you with this thought, which may already have occurred to you ’Äî what if you don't have access to a Roland Juno 6? Can we make use of any of the principles we've learned this month on any other synth? Next month, we'll attempt to do just that. source: Published in SOS |
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