Modeling Hammond Tonewheel Organs inside of Reaktor Primary or Core?

cs5947 Member Posts: 28 Member
edited March 2022 in Reaktor

Hi, I'm new to NI's reaktor, and I have been interested in physical modeling of virtual Hammond organs (specifically the B3 and C3) but I do not have an actual physical B3 because I can't afford it. The best alternative I could go for is to reference from really good Hammond plugins like IK Multimedia's Hammond B3-X, Acousticsamples B5 or GSi's VB3-II.

My first Hammond ensemble (now deleted) comprised of a 9-tone-per-voice model and 1 short burst of noise for the keyclick. I'm creating a new one that aims to involve a 91-tonewheel model, 9 key contacts and calculated crosstalk.

I could easily just use 91 bare sine waves but that wouldn't allow me the flexibility I need for a good Hammond replica. I want to start modeling the pickups, circuts, imperfections and all that so it actually sounds like a real Hammond without having to buy one...

but I just don't know which formula to start with. I found this one:

That's inteded for audio effects, not instruments. I'm trying to create an INSTRUMENT here.

I also found this one:

but for my knowledge it's a little hard to understand. I can only do very basic maths.

I found these two videos:

From this one I learned multiple things. 1: The drawbars are assigned to 9 key contacts, 1 drawbar for each. The highest one is the one that plays first and the lowest one plays last. 2: The Leslie speaker features 2 speakers: horn and drum.

From this video I had a bit of a revelation. I found out that the tonewheels aren't just arranged chromatically, they're actually arranged in a certain order so if one pitch leaks into another pitch we get a harmonically complementary pitch.

Now, back to the million-dollar question. Which equations do I start with to start virtually modeling the tonewheels, pickups and leslie speaker? Your cooperation is much appreciated




  • cs5947
    cs5947 Member Posts: 28 Member

    This didn't help at all.

    What I'm saying is that I need help finding methods on how to physically model the organ tonewheels for my ensemble. I don't need other Hammond ensembles that I can use, I'm creating one MYSELF.

  • colB
    colB Member Posts: 633 Guru

    If there are other Hammond ensembles, then you can look inside and try to understand how they work, seems to me like that would be a valuable resource?

    As far as the papers you posted, at least the one specifically about modelling an organ, the info is very sparse, so it's difficult to understand the maths, because there is no context or detailed explanation. I get the broad idea, but not how to link that to the equations in the paper.

    what it does have is references, one that immediately looks worth following up:

    Jussi Pekonen, Tapani Pihlajamäki, Vesa Välimäki: Computationally efficient Hammond Organ Synthesis.In: Proceedings of the 14th International Conference on Digital Audio Effects (DAFx-11), Paris(2011)

    The name Vesa Välimäki is familiar to me from other papers, so if you can get your hands on this one, maybe it will have a more detailed description.

  • cs5947
    cs5947 Member Posts: 28 Member

    Hey, thanks for your information on that. V. Välimäki sounds like a prominent name, especially in physical modeling synthesis.

  • Chet Singer
    Chet Singer Member Posts: 53 Helper
    edited March 2022

    I once built a fully-polyphonic Hammond model that contained 91 drawbars. It's here:

    It doesn't contain advanced features such as crosstalk. But it does model some other features such as foldback, so it properly maps the 91 drawbars to the busses of the 61 keys. Maybe it will be useful to you.

  • Laureano Lopez
    Laureano Lopez Member Posts: 102 Advisor

    The name Vesa Välimäki is familiar to me from other papers

    Indeed. These finnish guys do write a lot of papers 😄

  • ehdyn
    ehdyn Member Posts: 25 Helper

    Not directly related but should be a good talk on physical modeling that just came out..

  • cs5947
    cs5947 Member Posts: 28 Member

    Chet the Reaktor G.O.A.T! Thanks for your input.

    Sounds pretty useful. Thanks for your input.

  • cs5947
    cs5947 Member Posts: 28 Member

    Update: I've finally managed to come up with my own plan. I'm aware that this will be an arduous process but then again, who doesn't encounter this when modeling it like this?

    [1 - Tonewheels]

    It'll model 91 'tonewheels,' each is a macro with an in port (for example, voicing) and an out port that goes into a 'pickup' (see [Pickups]) The first 2 tonewheels will be square waves with a LP filter for the bass pedals, and parabol waves for the rest of the organ. Parabolic waves are chosen over sines because they have a subtle amount of complexity and dirtiness to their wave.

    [2 - Pickups]

    The individual pickups will be modeled as macros with 17 inputs, 16 for the crosstalk and 1 for the fundemental tone. I mean that as in 'Eight going one way, eight going the other way.' The pickups will be 'triggered' or 'amplified' by the notes and drawbar layers, but this is where I run into multiple problems (see [Problems])

    [3 - Problems]

    Warning: this is mostly me just rambling like a lunatic looking for an answer

    Okay, here's the big question I need some of you to answer for me - how should I implement this? I mean, I could model the foldback with a selector with 61 inputs, right!? No. Selectors only support 40 inputs. And they only interpolate stuff too, how would that react with multiple notes going into an AVC, thus converting it into a mono signal?

    What I have right now is this system:

    if [notePitch] -> AVC = 60 then C3Amp = 1

    if [notePitch] -> AVC = 62 then C#3Amp = 1

    if [notePitch] -> AVC = 64 then D3Amp = 1

    and so on. Is this an efficient and correct system? Am I ordering it correctly? Will it take up a lot of CPU? Where do I go from here?

  • colB
    colB Member Posts: 633 Guru

    iirc the strength of a magnetic field drops with the square of the distance, so I really don't think you need to go eight steps in either direction for the parasitics from other tonewheels,,, probably one or two in each direction would be enough? even the bleed from the nearest ones will be very low level, only the bleed form the other wheel on the same cog will maybe be really noticeable which is why that is chose to be harmonically related on the real deals....?

    I'm just rambling too, but it's interesting.

    Best would be to get recordings of each tone wheel, build a sample map, and use some wavetable oscillators.

    definitely don't need full polyphony... even for mashing the keyboard with both hands... how many poly notes do you really need?

  • colB
    colB Member Posts: 633 Guru
    edited March 2022

    it would be useful to get info about the gearing ratios, so you can model the parasitic amplitude modulation correctly... it should be at the frequency the tonewheels rotate, but they are in pair on differently geared cogs, so they go at different speeds... so the AM modulations are a different frequencies for different tonewheel pairs

    maybe you can get this info from a service manual? might find that online.

    service manuals can be really useful when trying to model old tech, because back in the day they did include a lot of very useful information about how the thing works in the service docs.

  • cs5947
    cs5947 Member Posts: 28 Member
    edited March 2022

    Idek what gearing ratios are, I'm just beginning to learn about the Hammond organ. Should I stick to the default sine oscillators or a more complex algorithm to model them?

  • colB
    colB Member Posts: 633 Guru

    You know more than I do about Hammonds - unless you've done literally no research :)

    I did skim a page about the tonewheels that had some pics and an explanation of the cogs/gears... also that paper I suggested you find, it seems pretty informative.

    I would guess (definitely just guessing) that the accuracy gain you get by linking 8 extra tonewheels to each pickup will be way less than what you would get by modelling the waveforms of thetonewheels more exactly - I think sine will be much too clean, and I'm not sure there's any point in just picking some waveform with arbitrary harmonics... should at least try to get something like the original...

    Like I said, service manuals are good. This one has 73 pages! a lot of it is only useful for fixing a real Hammond, but in amongst it, there is detailed descriptions of how it works, and lots of info about which drawbars work which partials... also lists of all the gearing tooth counts... just lots of useful technical info to absorb!

    good luck!

  • cs5947
    cs5947 Member Posts: 28 Member

    I thought the gearing ratios determined the tuning? Because I asked about this on Reddit and someone said it determines the tuning (more specifically, how fast the wheels rotate) because Hammonds aren’t tuned in exactly 12-TET.

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