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Beaming
Copyright 2016 © Troels Gravesen

As a rule of thumb, speaker drivers will start beaming a frequency having a wavelength equal to the diameter of the radiating cone. Just a few comments here to illustrate the problem as I've had to explain this many times from mails coming in.

Having an 8" driver with a cone diameter of 17 cm, beaming will start at 34400/17 = 2023 Hz (speed of sound in cm/diameter in cm). This may prove an 8" well suited for a 2-way with a point of crossover around 2 kHz, but it's not as simple as that. As can be seen from the graphs below, an 8" starts losing off-axis response already at 1 kHz being some 7-8 dB down on 60 deg off-axis compared to on-axis response, the  Discovery being 8 dB down. Despite differences in cone geometry, this figures are fairly constant. Cone geometry may to some extent impact dispersion, but it's not a major factor in overcoming the problem. Some old-time soft-cones may be less prone to beaming as only the part of the cone around the voice coil will generate sound in upper-mid/lower treble as the cone breaks up and the outer part of the cone not generate high frequencies at all. Manufacturers have called this "controlled" break-up to cover the fact the cones break up and smear detail as different parts of the cone move in opposite direction and cause phase shifts, which sometimes can seriously distress the ear and cause listening fatigue at loud levels. I rush to say that at moderate levels this can be very good indeed like the old Vifa C17 cone having a fairly soft and thin coated paper cone.

Now, put you hands around your mouth and say something nice to your wife. Not only she, but yourself will notice the sound becomes honky and directional. The same thing happens to the sound from a speaker driver the higher in frequency it goes, and more noticeable the larger the cone diameter.

Bass notes are omnidirectional, hence the phenomenon room-gain. The room augments (amplifies) deep bass due to bass notes having long wavelength. They disperse in all direction and are reflected back from front and side walls, the floor and ceiling. The higher in frequency we go, the less room-gain, but obviously higher frequencies will hit walls, floor and ceiling in front of the speaker depending on the driver's dispersion pattern.
Listening on-axis (at a reasonable distance) we have almost the same distance to the cone, where listening off-axis we have different distances to the various parts of the cone causing interferences (lobing) at higher frequencies causing reduction in overall response, hence beaming. You can see this from the 60 deg. curves below where we at different frequencies have a strong suck-out, e.g. 4 kHz for the 5", 3 kHz for the 6", 2800 Hz for the 8" and 1900 and 3100 for the 13". 

As can been seen from the ScanSpeak graphs above, at low frequencies we have the same response in all directions. The bigger the driver, the sooner we start seeing a decline in off-axis response, the 5" being pretty good all the way up to 2kHz, the 6" being only 3 dB down at 2 kHz/60deg. The 8" is already down 7 dB/2kHz/60deg and the 13" starts loosing off-axis response already at 6-700 Hz.

click image to view large

Above three 8" drivers from the various range of drivers from ScanSpeak, Illuminator, Classic and Discovery. Despite different cones and cone shape, they display almost the same loss of response at 60 deg off-axis, 7-8 dB.

Now to the good question of what we can get away with! Should we make a 2-way from an 8" and a dome tweeter? Well, it all depends.
It depends on the actual 8" driver and we have to listen to different drivers because they're not equally bad despite same cone diameter and - on paper - same dispersion pattern. I launched a small study some years ago on two-ways from an 8" + dome tweeter. One of the drivers actually did quite well and the other didn't and I couldn't pin it down to a specific feature of one of the drivers over the other. My feeling is that that polyprop cone due to an usually smooth response and roll-off profile made the best match.
The thing is that mating the right 8" and finding a tweeter going down to 1.5 kHz may be possible, but in the end it still sounds like an 8+1 speaker! It has a distinct character due to the large driver having to handle everything up to 1.5 kHz. The dispersion pattern may look exactly as good as a 3-way, but the sound is very, very different. At higher frequencies the 8" driver cone also acts as a waveguide and this may count for some of the distinct sound.
Crossing over at 1.5 kHz is challenge and few dome tweeter like this - and some even require a steep 4th order filter to save it from voice coil burning. Most dome tweeters start having serious distortion when we get down below 1.5 kHz. My own solution to this in the TQWT and DTQWT constructions is to use a large dome fitted with a waveguide, a soft-cone 8" driver and a shallow slope crossover around 2 kHz. This way the dome helps the 8" in upper-mid and provides adequate dispersion in this critical range. For most domes we need 4th order filters so they don't "help" the 8" in its upper frequency band.

One way or the other, an 8" + dome is a compromise - as any other loudspeaker construction. Previously we saw numerous brands taking advantage of the 8+1, like Snell. But Snell used a very benign coated soft-cone Vifa driver. It had its strengths and weaknesses, but provided at lot of good sound for a modest price.
As you may know, I love the classic 3-way and so far, 4 constructions have been made. Adding a small 3-5 inch midrange solves the issue of dispersion in upper-mid and it doesn't cost much. End of story.