Modify gen~ crossover example

The basic trick with crossovers is that for each split, any additional channels need matching allpass filters to keep their phase relationships the same. That's why in that patch there's an additional allpass stage to keep the already-split "high" signal in phase with the newly-split "low" and "mid".

If you have the GO book there's another example of a 3-stage crossover using trapezoidal 2-pole filters, and it does the same thing.

In short:

the input goes into a 2x onepole LP sequence to get the a lowpassed version, call it L1. The same input is passed through a matched allpass filter (call it A1), and we get a high pass H1 from A1-L1. That's the first stage. Then the second stage does this all again to L1: pass L1 through 2x onepole LP to get L2, pass L1 through a matching allpass for A2, and derive a highpass M2 as A2-L2. Now M2 is our "mid" signal, because it is the highpass of the lowpassed L1. But we can't use H1 as our "high" signal because it is now out of phase with L2 and M2. So we pass H1 through another matched allpass to fix the phases, and that's our high output H2.

You can just keep cascading more of these sections -- being sure that everytime you apply a 2x lowpass onepole to a signal, you apply a matching allpass to all the other signals at that stage.

Using 2x onepole + 1x allpass isn't the only way to split the signal, often folks cascade 2x butterworth biquad filters for this for deeper crossover transitions (4 pole).