Coil Splitting and Hum Cancelling: where is the mistake?

[Skilpad]

Hi,

When trying to work a little bit around coil splitting and other funny stuff, I found myself stuck: there is something I do not understand…

Here is what I get about hum cancelling:
  - Inverting the polarity (north/south) will invert the response to the strings motion, but not the hum.
  - Inverting the wind (inverting the direction of rotation of the wire, or the start/finish connections) will invert the response to the strings motion and the hum.
  - The two coils of a humbucker have opposite pole and wind, to have in-phase responses to strings motion, but opposite hum. This is how hum cancelling is done.

Now, here is what I understood about the humbucker conventions, and I may be totally wrong:
  - For both bridge and neck humbuckers, the coil with screws is the south pole, and the slug coil is the north pole.
  - Screw coils are set at the extreme positions: near the neck and near the bridge. Thus we basically obtain for the four coils: South-North – North-South.

So, in standard configuration, I assume that for not having phase-inverted responses from the humbuckers, south pole have the same wind.
All these data are summarized on the drawing bellow.

Now what I do not understand is this: in many sources, I found that when coil splitting, if I want to keep hum cancelling when both pickups are active, I need to keep either the two internal coils, either the two external ones… But, with what I explained before, I get that those coils have same polarity and same wind… So combining them would not cancel hum.

Please, your help will be very useful. I just cannot find my error. Did I miss something?

[Skilpad]

Well, beside the theoretical question, maybe someone can answer to more practical ones:

- If I use one single coil from the neck humbucker, and one single coil from the bridge humbucker, which coils can it be so that they work together to cancel noise?

- Now, assuming that one of those two coils is phase inverted. The hum-cancelling combinations of single coils are not the same, right?

[FELINEGUITARS]

to get inner coils or outer coils on together like PRS, Musicman, and Ibanez have managed on various guitars you need to have the magnet in one pickup reversed
That way the two inner(or outer coils) can stand a chance to be in phase and hum-cancelling)

[darkbluemurder]

- If I use one single coil from the neck humbucker, and one single coil from the bridge humbucker, which coils can it be so that they work together to cancel noise?

As Feline said you need to combine a south coil with a north coil. You have two options:
1) In the standard S-N-N-S configuration you need to make sure that one S and one N stays active. So humcancelling would work with the neck pickup screw coil plus the bridge pickup slug coil or with the neck pickup slug coil and the bridge pickup screw coil. That would work for both parallel and series wirings. Going by the standard BKP wiring the slug coil stays active in split mode so you would need to change the wiring to the pickup where you want the screw coil to be active in split mode. 
2) If you "must" have either both slug coils or both screw coils active but don't want hum, you need to flip the magnet in one of the pickups to change the polarity order to S-N-S-N (or N-S-N-S, does not matter which way round) and use the normal wiring instructions.

- Now, assuming that one of those two coils is phase inverted. The hum-cancelling combinations of single coils are not the same, right?

Correct.

Cheers Stephan

[Skilpad]

Ok. Perfect.  :D

So I shall select top or bottom coils (south-neck north-bridge, or north neck-south bridge).

And if, in addition, I invert the phase of one pickup (thus changing only its winds), coils combinations that cancel hum become the inner coils and the outer coils.

Right?
I will actually propose my own wirings, and try to cover all the optimal possibilities.

[darkbluemurder]

Yes, all correct.

Cheers Stephan