[JeffB]

The last couple of weeks I have been demoing a pair of stand mount speakers in 2.1 mode.  I was using an AV receiver, and after much experimenting, I found that setting the speakers to small and using a 120Hz cross-over to be optimal.  A lower cross-over was not effective because it muddied up the sound of the mains.  I believe it was sound coming back through the midrange cone.  There was significantly less muddiness at 120Hz than 100Hz.  For subs I have two 15" drivers each on their own open baffle.  Baffle width is 18".  Baffle height is 48".  I have simply re-purposed my open baffle speaker to use just the bass drivers.  If I were to stay with the monitor speakers, I would like to reduce the baffle height considerably.

This setup worked extremely well.  I had always thought that a much lower cross-over point would be better.  This has been a bit of a revelation though.  If I only need my mains to work effectively at the 120Hz cross-over point, my mains can possibly be quite small.  A small monitor could afford significant cost savings.  I was thinking maybe something with a 4.5" driver.

However, since the polar response is so critical to good sound, I figure this should determine the optimal mid-range driver size.

If I keep the two 15" drivers in open baffle, and I keep the 120Hz cross-over(12db per octave), what is the ideal mid-range driver size to keep a good polar response?

The demoed speaker used a 5" long throw driver.

[*Scotty*]

If you are using this monitor for an HT application it should be able to at least hit 105 dB SPL with very low distortion to meet THX specs. The polar response of any small two-way monitor is dependent on the cross-over frequency being no higher than the wave-length that is equivalent to the emissive diameter of the speaker cone. This assumption relies on the driver behaving like a piston at the cross-over frequency. An 8in. mid-range driver as well as smaller drivers could have very good polar when used in a two-way monitor.
Here is a list of driver diameters and their associated cross-over frequencies needed for good polar response.
Bear in mind that this is a simplistic approach to answering your question.
8in. 1500Hz.
7in. 1750Hz.
6in. 2000Hz.
5in. 2500Hz.
4.5in. 2900Hz.
 Realize that crossovers don't turn-off a mid-range instantly with no overlap in their response with that of the tweeter. The tweeter's response also overlaps the mid-range drivers output.
The amount of overlap is dependent on the crossover slope. A higher order slope,say 24db/oct. will turn off the drivers much more quickly than a 6dB/oct slope. The more overlap you have the stranger the polar response graph will look because of the effects of constructive and destructive interference caused by the two drivers producing the same frequencies.  The less overlap you have between the mid-range and the tweeter,the better the polar response will look.
  In conclusion,we can see that the polar response a monitor may have is dependent upon the crossover frequency,the cross-over slope and the emissive diameter of the mid-range driver.
You might pose this question in the GR Research Circle. Danny Ritchie may have a more detailed answer to your question.
 As for your observation that a 120Hz. crossover point sounds much less muddy than a 100Hz crossover, I believe you are hearing less distortion from the mid-range driver caused by the driver exceeding it's region of linear excursion when you set the xover at 100Hz.
Scotty

[JeffB]

Thanks Scotty,
But I am interested in the mating of the 15" woofer and midrange, as oppossed to midrange and tweeter.

Actually, now that I think about it, I guess my original question makes no sense without a waveguide.
I want the directivity of the midrange at 120Hz to match the directivity of the 15" driver at 120Hz.
I guess the natural directivity of any driver smaller than 15" will be wider than the 15" driver at 120Hz.

However, I figure a 120Hz wave to be about 9.4 feet.  Perhaps that is wide enough that the polar response matching is of no concern.  I have never heard this point discussed.

[*Scotty*]

I figure a 120Hz wave to be about 9.4 feet.  Perhaps that is wide enough that the polar response matching is of no concern.

You got it. The problems come in when the wave lengths get shorter.
Scotty