x-over levels for mids and tweeters

[Pete H]

Assume for the sake of this question we are dealing with speakers with a constant impedence and I am using 2nd order networks. I am currently working with passive networks but I imagine this would also apply to active networks.
I've always thought there should be a gap between the x-over points of the mid and the high but I've seen some articles with designs calling for both to be x'd-over at the same frequency.
My question:
If your cross over point is the same frequency for both mid and high, (3000hz), wouldn't the actual sound output be higher for 1 or 2 octaves above and below the x-over freqency?
Here's what I picture in my mind (I don't have the instruments to actually test and measure this). Let's say enough power is applied to the system to produce 100db. The sound pressure level at one octave from the x-over point is 12db lower for both mid and high. This means that at 1500 hz the mid produces 100db and the high produces 88db. Likewise at 6000hz the high is producing 100db and the mid is producing 88db. In my mind this would mean that from 1500hz through 6000hz there should be a significant rise in the sound output. I am assuming the output from both speakers would combine to produce this higher output.
Next question:
If this is true then can this be caculated so one may arrive at the correct x-over 'gap'?

[BobEllis]

It all depends on your crossover Q. A 2nd order Butterworth crossover will have a 3 dB rise in total outut at the crossover point, extending several octaves, just as you thought. this assumes that the acoustic centers of the drivers are perfectly aligned relative to the listening position

One solution is a Linkwitz-Reilly XO. With a L-R crossover the output of each driver is down 6 db at the XO point, resulting in flat summed amplititude response. If you look for the -3 dB points, you'll find a spread.

There is a spreadsheet somewhere that does (and may be named) driver offset response calculation. It lets you visualize the effects of spreading the XO frequencies and moving the drivers.

[Pete H]

I have been using Butterworth x-overs in the past. I just recently read about the 3db rise at the x-over frequency. I am now experimenting with 2nd order Bessel x-overs because the article said they did not have this 3db rise. It's intersting that with relatively high outputs from each speaker one full octave away from the x-over frequency that the rise is only 3db for the Butterworth. I would have expected more. But this is all new to me. I've been playing with these things for years but have just recently had my eyes open to the details of how these things work. I had now idea the interactions between stereo system components could be so complex. I'll run a search for that spread sheet you referenced.

[Pete H]

Well, nothing turned up in my search. I also did a search of Google and Yahoo and didn't come up with any hits.
So I suppose the bottom line is the x-over point should be set the same for both the mid and high? And using a Bessel 2nd order network should eliminate the 3db rise in sound level.

[BobEllis]

Here is the spreadsheet - I wish I could remember where I got it to give proper credit. Whoever wrote it, thanks.

[Pete H]

Thanks for posting the spreadsheet.