Got it, and I'm ashamed it took me so long. I didn't spot an explanation to this on the web.
Of the 91 tonewheel generators in the Hammond, numbers 49 to 91 each feed the drawbars via a series capacitor and a transformer. Apparently, the value of the capacitor and the leakage inductance of the transformer are chosen, with the inductance of the pickup coil, to make this series tuned circuit resonant at the frequency desired from the tonewheel. Some of this is written in web sites such as
http://www.stefanv.com/electronics/hammond_tonewheel_capacitors.html but the reason for needing filters isn't explained.
The reason would appear to be that the shape of tone wheel required to obtain an exact sin wave can't be made - there's always an approximation. Maths/physics-phobes may wish to move on at this point!
The EMF produced by each coil is related to the magnetic flux passing through its permanently-magnetised core (rod) by Faraday's Law of induction: E(t) = k1.dPhi(t)/dt ... where Phi is the flux and k1 is a constant (involving things like the number of turns in the pickup coil, and a negative sign). In words, the magnitude of the EMF is proportional to the rate of change of Phi.
The magnetic circuit includes a Magneto-Motive Force provided by the permanent magnetisation, other iron (high-mu) parts including the tonewheel, and an air gap between the periphery of the wheel and the end of the core. The very-low-mu of the air dominates this magnetic circuit and acts as a reluctance that varies with time, R(t). Like current in an electrical circuit, where I = EMF/R, the flux Phi(t) = k2/R(t) ... where k2 is another constant involving the MMF minus whatever leakage flux.
The magnitude of R(t) is proportional to the length of the gap so it is related to the radius of the tonewheel r(t) by some more constants: R(t) = k3 + k4.r(t) ... where k3 accounts for the minimum gap and k4 involves things like the effective area of the end of the core.
So Phi(t) = k2/{k3 + k4.r(t)}. Then E(t) = k1.d/dt[k2/{k3 + k4.r(t)}].
Re-arranging, integrating both sides, and re-arranging:
r(t) = [(k1.k2)/k4].[1/IntegralE(t).dt] - k3/k4
In order to generate a simple sine wave, E(t) = sin(wt) for which the integral is -cos(wt) which has a value of zero when wt = Pi/2, the result for r(t) goes to infinity which can't be achieved. Indeed,if E(t) is to be an alternating voltage then it must pass through zero and r(t) will 'blow up' at some point in the cycle. Indeed, whatever practical function is used for r(t), the generated voltage can't be a simple sine wave.
If r(t) = cos(wt), the simplest case: E(t) = k1.k2.[k4.sin(wt)]/[k3 + k4.cos(wt)]^2
... and the presence of the square is indicative of harmonic distortion. It could be that the profiles actually used were determined iteratively, or by a very clever man with a slide rule (in 1934). The use of BPFs rather than LPFs is probably only a matter of adding the smallest number of additional components.
Chris
. It would be embarrassing to admit how many wasted hours/days/weeks/months I have spent "decoding" the mysteries. I am finally at a point where I can just appreciate the beast for what it is- certainly greater than the sum of its parts. Though I will mention that I don't think you can underestimate the "intangibles" of the system: the hysteresis of the magnets, the imperfect wax and paper capacitors, etc, etc. etc.
