And the reason to do all this....
When you select the crossover point in the receiver, it rolls off the sub and main speaker and theoretically they should "cross" (play the same volume) at that frequency. That only happens when the levels of both are the same. When you boost the sub, it and the main speaker still roll off at the same points, but the sub has a "head start" in SPL so it continues to play louder than the main speaker above the crossover point that was set.
Pics are worth 1000 words.... Here are a few measurements I took a while back as an example that can demonstrate this. This is my left front channel only, playing the same signal for all measurements. (Smoothed 1/3 octave to make them easier to read.)
Here is a calibration corrected to the standard Reference curve (flat bass) but with the sub boosted 6 db afterward:
The black curve is the main speaker set to Large. The brown curve is the sub only--main speaker set to small, crossover set to 250 and main speaker unplugged.
As you can see, at 80 hz the sub has a 6 db head start on the main speaker in level. So when you apply an 80 hz crossover, this is what you get:
At 80 hz, the sub is still playing significantly louder than the main speaker and they don't actually "cross over" until nearly 100 hz. So the sub is playing as loud or louder nearly all the way to 100 hz. In addition to not sounding as good (setup dependent) that can also make the sub more easy to localize. Just imagine what it looks like with a 100 Hz crossover!
Contrast that with this:
Here I used the method described above to get a 6 db boost on the bottom, correcting both the main speaker and the sub to the same curve and matching the levels. As you can see, the levels are matched pretty well from about 60-140 hz. A crossover setting anywhere in there should work well and not change the shape of the overall curve--it's a matter of what sounds better at what frequencies--the sub or the speaker. When you do that you can change crossover settings and see what sounds the best without changing the overall tonal balance (which overwhelms what you hear from different crossover settings).
With an 80 hz cross over setting as an example:
The actual point at which they cross lands almost exactly on 80 hz. Right where you set it. By 100 hz, the main speaker is playing 6 db louder than the sub.
Even though the two overall response curves are nearly identical and the overall tonal balance is nearly identical, they sound quite a bit different--mostly noticeable with music. Even though my current front speakers aren't very big and don't dig very deep, they are sensitive and capable of high output--by 100 hz they are rockin'. They simply sound more "impactful" in that range than my current sub which gives a softer, smoother sound in that range.
It won't be the same answer for every system--some people will have subs that sound better than mine at higher frequencies and/or have main speakers that can't play very loudly without distortion at 100 hz...in that case the method I describe above still works just fine--just set the crossover to a higher point--100, 110 hz or whatever sounds the best.
But the biggest benefit is for those with speakers that can play well and sound good to lower frequencies (80 or lower crossover setting) at music listening volume. This allows them to set the crossover lower without removing the bottom end bass boost because it's built into the curve of the main speaker as well. If the main speaker is corrected flat with the Audyssey reference curve and the sub is boosted, lowering the crossover removes a lot of bass and probably won't sound as good. My speakers weren't the best example for this as 80 is about as low as I'd want to go with them. Mains that will maintain the target curve down to 30-40 hz (instead of falling away significantly at 60 hz) would have made for a better graphic example. I should have some of those soon......
And as said above, if both are corrected to flat bass but you boost the sub, if you have smaller surrounds, etc, they'll have WAY too much bass and won't tonally balance the main speakers. If you apply this method to all the speakers, they'll maintain a matching tonal balance even if you have to use higher crossover settings for the small ones.