Organ Tone Wheel development.

You guys need to forget about the idea that the tonewheels are all phase aligned. Here's a vid of a guy momentarily stopping a tonewheel with his finger and letting it go again, you can see the clutch mechanism in action, and you can imagine over years of use, dirt, getting moved around that it is extremely unlikely that a real Hammond will ever have phase alignment between the different tonewheels.

You can see how the tonewheel he touches stop, but the others keep on moving, then when he releases it, it starts up again. There is only phase alignment between the stopped tonewheel and it's single partner, not even the other octaves of the same note.

That's why we need to know which partials are partnered up together! They should be phase aligned, and the rest should be randomised.

Can you post the un-separated version please

here is un-separated version

Yeah, that's true, but in reality I don't think it matters. I don't think we can actually detect a change in phase of a single note.

You are correct, phase of a single isolated partial is not detectable to humans, but you are misunderstanding the point I'm making.

…So playing a low note with a strong 2nd harmonic will sound fine no matter what the phase is but if you play an octave higher along with, the fundamental of the octave higher can cancel or add to volume on the second harmonic emitted by the lower note. As long as they add together every time you play it's not a problem.

That would be a problem if we were using separate oscillators for each partial of each active note, and stopping and starting them with every note played, but I don't think anyone is suggesting that.

The point here is more subtle. Relating to correlation or lack thereof between the phases of different octave partials.

In your example, you play a note with a strong second harmonic, and also play the octave above. Then the second harmonic of the low note and the fundamental of the higher note will use the same tonewheel, and just sum it (there will be some loss in the hardware but not much (google "hammond organ loudness robbing" for details). So that particular partial ring out nice and loud… great. (In my current model that's exactly what happens, in the earlier version, they used different sine oscillators, but they were phase aligned so the result was identical).

That's not the issue here, in the same example, it's more about the way that shared partial interferes with the fundamental of the lower note and with the upper harmonic of the higher note. That interaction will be somewhat arbitrary and depend on the tonewheel phase offsets for that particular hammond organ. It doesn't make much different to the volume or the timbre, but the effect is there. Seems most noticeable to me in terms of how full the bass or mids sound, but it is very subtle. Sometimes it even gives a phsycho-acoustic effect that can make a note sound very slightly sharper or flatter…

The tonewheels are mounted in pairs. Each pair is two partials four octaves apart and those two partials are physically connected and so phase locked (maybe aligned, maybe not!). However, their connection to the drive train is via a damping spring and a clutch, so they are not and cannot be reliably phase aligned to any of the other tonewheels, even the other octaves of that particular note.

The result is that any two partials an octave apart can have a completely arbitrary phase offset. As Andrew pointed out, it is unlikely that the relative phase will be drifting or modulating, but the initial phase offset between any two different tonewheels that are one, two ore three octaves apart will be fixed (maybe?), but arbitrary/random.

It's possible that in an older instrument, the relative phase alignment changes a tiny bit every time the unit is power cycled and the motor spins up/down, due to slight movement in all those clutches due to inertia vs friction. Even just stiction with dirt and old oil in the spring damping mechanism might be enough. Consider the higher frequencies: one tonewheel with 128 teeth, a clutch slip of just 1.4 degrees will throw the waveform 180degrees out of phase. So over months and years, infinitesimal changes could accumulate to be significant.

Anyway… the point is that the idea of using a single sinewave base note and multiplying up to create all the octaves is great from an efficiency and simplicity/elegance POV, but will not give an accurate result, because all those octave partials will be phase aligned and locked. It might not make a big difference to the sound, it might not even be perceptible, but on the other hand, it might be an important ingredient to the overall sound soup. With the model I'm using it only costs a single addition, and when the whole thing gets to a point where I'm satisfied with it, I can try removing it and see if it makes a difference. Then simplify the model if not.

The motivation is that every Hammond model I've heard including this one is way too clean. What's missing is the cumulative effect of all these subtle quirks that each add just the right kind of distortion or modulation or noise or colour that sum together into that big juicy sound. Unless you know exactly which parts are important and which are not (and if you did you would have built an exact model already), then you first have to just brute force the thing by making everything as accurate as possible. Then when it sounds right, try removing different details one by one to optimise the cpu requirements.

There is one tonewheel per partial

To save space and gears, they are arranged in a particular way.

There are a bunch of drive gears along the main motor spindle. Each drive gear drives two driven gears, each driven gear drives a pair of tonewheels that are four octaves apart.

A generator consists of multiple sets of four tonewheels, arranged in two pairs - one drive gear, two driven gears, and four tonewheels all in an enclosure.

These are harmonically related (they must be to some degree because they share gearing). Each of these arrangements of four is electromagnetically isolated from the rest of the generator by a steel enclosure. There is some crosstalk between the four, particularly between the pairs due to their proximity.

FWIW, all this information is readily available online. Google is your friend. There are many sites covering hammond technicalities in a lot of detail with diagrams and photos!

Maybe apply some filtered noise to the gain of the partials. Noise is so erratic it could simulate a bit of character and not be noticeable like a fixed repetitious pattern.

I really wish simulating the character of vintage hardware was as simple as modulating some parameters with filtered noise, that would be awesome! Unfortunately, the only time that is ever useful is when the 'character' being simulated is that of filtered noise, in which case you just mix it into the signal chain, no need for anything fancy. And yes, that is a thing here, Hammonds produce broadband noise. if you look in the structure, you will see that there is noise being mixed in… low hanging fruit and all that ;)

as far as the whole phase coherence thing i would think the thing to do is generate a corresponding cosine with every sine that way you could easily randomize a static phase offset per partial