One of the greats in the audio world, Siegfried Linkwitz, died today, age 82.
https://en.wikipedia.org/wiki/Siegfried_Linkwitz
He, along with Russ Riley, invented the Linkwitz-Riley filter, widely used in audio crossovers. The term Linkwitz-Riley filter is often spoken of, but it's interesting to read why it became important. See
https://en.wikipedia.org/wiki/Linkwitz–Riley_filter
"Linkwitz-Riley filters are usually designed by cascading two Butterworth filters, each of which has −3
dB gain at the cut-off frequency. The resulting L-R filter has a −6 dB gain at the cutoff frequency. This means that summing the low-pass and high-pass outputs, the gain at the crossover frequency will be 0 dB, so the crossover behaves like an all-pass filter, having a flat amplitude response with a smoothly changing phase response."
The illustration shows the response from a 2nd order L-R crossover filter, but 4th order L-R crossovers (LR4) are probably today's most commonly used type of audio crossover. Dennis Murphy prefers using them. Perhaps he can comment more about why he so prefers the LR4.