When we’re designing wiring schemes for guitars, one thing we can take into account is whether certain configurations will be hum-cancelling. Of course, you know that when we select a humbucker on its own it will cancel its own hum. And you probably know that two single coils combined, where one is RWRP, will also form a hum-cancelling combination.
The trick to cancelling hum is to have two coils active, where the hum is out of phase but the guitar signal is in phase. To know how to achieve that, we’ll first look at a basic view of how a pickup works.

’59 Custom/Hybrid humbucker

Simply put, a pickup is a coil of wire and a magnetic field combined into a single package. Sometimes the pole pieces of the pickup are the magnets, and sometimes a separate magnet is used to magnetise the polepieces. The effect is the same.
Because the strings on an electric guitar are made of a magnetic material (usually steel), the strings are magnetised when they get close to the pickup, and as they move they disturb this magnetic field and induce a current in the coil. This then becomes our guitar signal. So far, so good.
However, the coil will also pick up disturbances in ambient magnetic fields around the guitar. Of course, the most common form of this interference is the infamous 60Hz hum (or 50Hz if you’re in the UK). This is the frequency of mains electricity and so is very difficult to ignore.
Let’s look at a simplified example of the signal we might get from a single-coil pickup:

Of course, the frequency of the hum would normally be lower than the frequency of the guitar signal, and the guitar signal wave would be much more complicated, but this is purely illustrative so I’ve just tried to keep it clear. The wriggly ‘actual’ line represents the combined effect of the two waves – the actual voltage change over time that finds its way to the amp.
To cancel the hum, what we need to do is get another signal, which has the hum completely out of phase with out original signal, and combine them together. So, how can we reverse that hum?
Let’s see what happens if we wind the coil in the other direction, or keep the winding the same but connect the pickup the other way round in the circuit (the effect is the same: the current flows in the opposite direction around the coil):

Hmm. We have reversed the hum, but we’ve also reversed our desired signal from the strings. If we combine this with our original pickup, we’ll cancel out everything and end up with silence!
Another thing we can try is if we keep the winding and electrical connections the same, but invert the polarity of the pickup:

As before, the signal from the strings is inverted. But the hum is not inverted! That’s because the hum isn’t induced by the magnetic field of the pickup – it comes from other magnetic fields in the surrounding environment. If we were to sum these two signals, we’d cancel our string sound out completely, but double the hum! That’s the opposite of what we want. Interesting…
In the next article, we’ll look at how we can use what we’ve learned here to combine two coils and cancel the unwanted hum.