What is interesting about the Tone Zone is that it is one of DiMarzio's dual resonance designs. This take on pickup design was novel when DiMarzio applied for the patent in 1983. It differs from modern boutique pickups like the 57/08 that attempt to capture the magic of asymmetrically wound coils commonly found in old Gibson PAFs (the winding machines of the day were inaccurate). Most of those pickups do not have the same number of turns on each bobbin. That flaw results in better fidelity at the cost of some amount of common-mode hum rejection because humbuckers rely on a perfectly, or near perfectly balanced coils from an inductance point of view for hum cancellation. A humbucker rejects hum because the coils are reverse wound, which means that they are electrically 180 degrees out of phase, which causes picked up hum to sum to zero. The reason why the induced guitar signal is not summed to zero has to do with the magnetic part of the circuit. Not only are the coils are reverse wound, they are at also opposite magnetic polarities. As a current is induced into the coils when ferrous guitar strings cut magnetic lines of force, we have a situation where the reverse wound coil's output is the result of magnetic lines of force from the opposite polarity being cut. If we take the negative of a negative, we have a positive, resulting in both coils summing to a higher electromagnetic force while canceling hum. Dual resonance is based on winding each bobbin with the same number of turns with different wire gauges, which should give us roughtly the same amount of inductance, and it is inductance and the strength of the magnetic field, not resistance that determines a pickup's output, which is why judging pickups by their DC resistance is not recommended. What winding the coil with different wire gauges does is give us different self-capaticitance values.
A pickup circuit is known as an RLC or tuned circuit. The resonant frequency of a pickup coil is calculacted by taking its inductance and self-capactiance values and plugging them into the the following equation.
Resonant Frequency (F) = 1 / (2pi * SQUARE-ROOT(L * C)), where L is inductance in Henries and C is self-capacitance in Farads.
Anything that affects self-capacitance affects resonant requency. Wire diameter, insulation thickness, and winding pattern are going to affect self-capacitance. If we wind two coils with the same winding pattern and number of turns, but different wire gauges, the coils are going to have different self-capacitance readings.
Here is the summary from the Dual Resonance patent:
"SUMMARY OF THE INVENTION
The present invention avoids the shortcomings of prior two-coil hum-bucking pickups by winding the coils such that both coils of the pair have substantially the same number of turns but are wound with wire of different diameter or gauge. It has been found that by means of this construction, low frequency cancellation is emphasized, providing more effective elimination of 60 cycle hum without affecting the higher harmonics of the 60 cycle signal which may contribute to the desired tonal qualities. Moreover, because of the difference in impedance characteristics resulting from different diameter wire on the respective coils, overall frequency response can be selectively adjusted to provide improved tonal qualities."
The difference in impedance characteristics is the dead give away. Impedance is not a synonym for DC resistance. Impedance has reactive components; therefore, impedance changes with respect to frequency.
Formula for impedance:
Z = SQUARE-ROOT(R^2 + X^2), where the symbol "^" denotes raised to the power of, R = DC resistance, and X = reactance
X = Xl - Xc, where Xl = inductive reactance and Xc = capacitive reatance.
Xl = 2pi * F * L, where F = frequency in Hertz and L = inductance in Henries
Xc = 1 / (2pi x F * C), where F = freqency in Hertz and C = capactiance in Farads
Here, one can clearly see that Z changes with respect to frequency. That is why speakers are rated with a nominal value and rarely, if ever, measure at their rated impedance at DC. The impedance of a speaker changes with respect to the frequency being sent to it, which makes its performance non-linear. That is why most tube amps use global negative feedback. Global negative feedback is used to decouple of the output stage from the speaker's varying impedance; thereby, helping to linearize the output stage. Amps lke the Vox AC30 that do not use global negative feedback are more sensitive to the speakers used in the amp than amps that employ global negative feedback.
The resonant peak of a pickup is the frequency at which inductance reactance (Xl) and inductive capacitance (Xc) cancel each other and the circuit becomes purely resistive. It is the frequency at which a pickup is loudest. I have covered this information before, but a lot of guitarists falsely believe that the tone control on a guitar bleeds treble to ground, but this not correct because a pickup is an RLC circuit, not an RC circuit. If the tone control bled signal to ground, there would be a noticable drop in volume as the tone control is rolled down. The tone controls brings the tone capactior into the RLC circuit, which results in its value being added to the self-capacitance of the pickup. This addition causes a downward shift in the resonant peak of the circuit. A lot guitarists also falsely believe that adding a higher value volume pot adds treble back to a pickup when it does not. The "R" in the circuit controls its "Q" or quality factor. A circuit's Q determines how quickly signal amplitude drops off from the resonant peak.
Q = Xl / R, where Xl = inductive reactance and R = resistance
An overwound pickup has a lower resonant peak, so it will sound darker than a non-overwound pickup. What increasing the value of the volume pot does is lower the Q factor; thereby, flattening out a pickup's response. The pickup does not have more treble with a higher value pot. What it has is a lower resonant peak, which is results the pickup havng a smaller amplitude at a pickup's resonant frequency.