I titled this “Advanced Subtractive Synthesis” but I don’t like the term “subtractive synthesis;” I think that the segregation of subtractive and additive synthesis is a false dichotomy. Using phase differences, additive synthesizers can subtract, and, as I hope to show you, adding is an essential part of advanced subtractive synthesis. I’ll be using Reason’s Subtractor, one of my favorite synthesizers, but you can follow along with any synthesizer that has two or more audio oscillators and two or more low pass filters (gain compensated and mild slopes, preferred).
First, let me explain how tonewheel organs work, for those who don’t know. Tonewheel organs were an early attempt at additive synthesis. Being that certain models are now coveted for their unique sound, I’d say that they were (conceptually) a miserable failure but you could do worse than being so highly regarded as the Hammond B3, the most coveted of them all. Tonewheel organs work by spinning tonewheels (sprockets, in essence) in front of a pickup (like an electric guitar’s) to produce a close approximation of a sine wave. A small number of tonewheels are then mixed as harmonics, using eight-position “drawbars,” to create a complex sound. In the case of the B3 and many others, these tones are, in ascending order and according to Hammond’s very strange naming convention that has everything in the wrong octave (less strange, from Hammond’s point of view – they were following pipe organ tradition), the octave below the fundamental, the fifth above the fundamental, the fundamental, the second harmonic, the third harmonic, the fourth harmonic, the fifth harmonic, the sixth harmonic, and the eighth harmonic.
But that’s not all there is to it. Not only do the tonewheels not produce pure sine waves but their signal gets distorted multiple ways en route to the output. And there’s leakage between tonewheels. Also, because the sound would otherwise be static and, therefore, musically uninteresting, tonewheel organs are almost exclusively played through rotating speakers (a particular make – Leslie – too) which further shapes the sound in ways beyond the scope of this not-as-short-as-any-of-us-would-like explanation. We won’t be synthesizing that, anyway. We will, however, have to incorporate an electronic key click and “percussion” effect.
So, let’s get started synthesizing a commonly used and thankfully simple Hammond registration (as each unique combination of drawbar settings is called), the first three drawbars (suboctave, fundamental, and fifth) at equal volume (or, 888000000). On synths that have three or more audio oscillators, this is naturally quite easy to do, but we’ll have to be clever if we want use Subtractor.
First off, we have to set the oscillators to produce the right harmonics. No one waveform will work; a saw is the only one that produces each harmonic but they’re proportions are too far off and I’m not confident in our ability to filter out the fourth. We can, however, manage this sound, if we start with two waveforms: a square, which produces the first (suboctave) and third (fifth above) harmonics and leaves a gap where the fourth should be, and a sine wave, an octave above, taking the place of the missing second harmonic (fundamental). I won’t be pitching them, an octave down but it doesn’t really matter.
We now have two of the harmonics in place, the first and second at equal volume, but the third’s still to low and there’s many more odd harmonics than there should be. Luckily, we can solve both of those problems with the filter. You can use filter resonance to pick out and reinforce harmonics. All we have to do is turn on keyboard tracking, set the 24 db/octave low pass filter cutoff to the third harmonic, and turn up the resonance.
(Subtractor’s filter cutoff increases and decreases in increments of slightly less than a semitone; with keyboard tracking at 100%, a cutoff value of 59 is approximately at the triggered key.)
Well, there’s still one problem: the second harmonic is within the resonance band and will also be boosted. We could try using the oscillator mix control to compensate for this but that will also affect the fundamental. As with elsewhere, I’ll opt for the “does it sound good?” method of calibration. It will undoubtedly be wrong (though, after comparison, I got pleasingly close) but it will at least sound good.
Having set the resonance to a value of 73, we’re left with just the key click and percussion to synthesize. The key click is a simple, bright “clicky” noise and the percussion is a short emphasis of the second or third (forth or sixth) harmonic. A crude but usable approximation of these is easily created by quickly sweeping down the filter, at the start of each note. To do this, I’ve set the filter envelope sliders to 0 and the amount to 8. Our work is now done but there’s still the matter of the rotary speaker, which is almost as much of the sound as the organ itself. There really isn’t much that Subtractor can do to synthesize its sound but there are many emulations. For a free, Reason based solution, I recommend Jiggery Pokery’s combinators.
Now let’s ask ourselves a question: can this work with more complicated registrations? I think this is a question worth answering and, to that end, we’ll try synthesizing a favorite registration of mine, 006646440, which was used by one of my favorite keyboardists, Tony Banks. (He’s a very, very clever musician; I highly recommend his work.) Just to recap, this registration will have the fundamental, second harmonic, and fourth harmonic at equal volume and the third, fifth, and sixth harmonics at roughly two thirds that volume. As with before, a sawtooth wave would produce all of the harmonics we need but in grossly wrong proportions and I’m not confident in our ability to filter out the ones we don’t want, most notably, the seventh.
But I have an idea. We’ll again use oscillator one, for odd harmonics, and oscillator two, for evens but, this time, with a square and a pitched up sawtooth, respectively. The square produces its usual odd harmonics and the sawtooth, because it’s pitched up an octave, produces only evens (one becomes two, two becomes four, etc.). We now have first and second harmonics of equal volume, too weak third, forth, and sixth harmonics, and a much too weak fifth. And too strong seventh and above harmonics. And two resonant filters.
Choosing which combination of harmonics to reinforce is tricky and I wouldn’t say that there’s a wrong answer. One thing to keep in mind is that, because Subtractor’s filters are (hardwired) in series, filter one will reduce the amplitude of the harmonics passed to filter two. The first harmonic I’ll reinforce is the third (using filter one in 12 db/octave low pass mode). It needs to be reinforced more than the fourth and I generally find that fifths are more important to Hammond sounds than octaves. Additionally, it’s the percussion sound at the beginning of the note. The second and fourth harmonics are within the filter’s resonant band, which is again bad, in the case of the of the second, but good, in the case of the fourth, which needs a boost.
The second harmonic I’ll reinforce is the fifth (note: Subtractor’s second filter is always a 12 db/octave lpf). It needs to be reinforced far more than the sixth and reinforcing it, instead of the sixth, keeps the seventh harmonic out of the resonant band, if only just. The sixth harmonic (and the fourth, too) are also reinforced somewhat by the filter. Resonance is again calibrated using the “does it sound good?” method. Again, the relative amplitudes of the harmonics are surely wrong but when comparing my patch to a The Colony of Slippermen, I’m pleasently surprised by how similar it sounds (perhaps Banks used a slightly different registration than I had thought).
So, can we use subtractive synthesis to emulate tonewheel organs? Well, kind of. The key click/percussion sound in the first patch isn’t very satisfying at all. It could be improved by adding filter two but that would be wrong for the body of the note. (The key click/percussion sound for the second patch isn’t perfect either but I’ll take it.) Our organ may also be a bit too clean sounding. We can solve this by mixing in some dark noise at a just-noticeable level. For the Leslie sim I used, color and level values of 21 and 66, respectively, worked. This makes it sound a bit more organ-y. (The organ in question may need servicing but beggars can’t be choosers.) This also improves the click/percussion sound, by giving the filter more partials to sweep through.
One thing I didn’t mention is that organ harmonics use equal temperament. This is of little consequence for our 888000000 sound, as equal temperament fifths are quite close to just, but it may be holding back our 006646440 sound, which includes a third. And then there are the countless odd but important behaviors of organs that these patches don’t begin to incorporate. (For instance, percussion should only be present on the first note triggered, after all previous notes have been released.)
But, in a much less academic look at usability, how do these patches fair? Well, if I were hired as the keyboardist in a jazz B3 combo, this is NOT how I’d get my sounds. But, with a good Leslie sim (or a real Leslie) and loud bandmates, I think I might get away with using my Slippermen patch at a Genesis tribute show. I’d certainly have no qualms about using it in a demo.
But, in that case, I wouldn’t go to the trouble of trying to program an organ sound using just one device, I’d put multiple tone generators and a mixer in a Combinator and give myself proper control over the individual harmonics. Though, as of this writing, there actually isn’t a way to get a proper Hammond organ sound within Reason (no, not even Revival).
So why did I go through all the trouble to teach you this method, if I’m just going to tell you to not bother with it? Because I thought it would be an educational bit of synthesizer programming.