As usual, I agree with Twl. The problem has to do with two different materials properties: STIFFNESS and DAMPING. These are two entirely different things, but you would be amazed how much confusion there is about them. I have seen plenty of references to how well-damped aluminum is, for example in the Stereophile review of the Krell LAT-1. For anyone who thinks that aluminum is well-damped, do a simple experiment: go to your local musician supply store, and pick up a tuning fork. Knock it against your skull, then keep it next to your ear until you can no longer hear it ringing. Multiply the 10 seconds (or whatever) by the 420 Hz frequency (or whatever), to get the number of cycles it took to die out of audibility. Now ask yourself one simple question: "What's it made of?" Chances are, it's ALUMINUM, one of the most poorly damped materials known to man.
Sorry, but had to get that off my chest. To get back to the issue, different materials have very different combinations of stiffness and damping. Aluminum is very stiff and very poorly damped. Kevlar is still quite stiff, better damped, and lower in density as well. Plastics are generally quite flexible, and usually better damped still, but have a wide range of variability in both stiffness and damping depending on the formulation and the fillers used. Paper is typically stiffer than most plastics, and by itself is not as well damped, but when coated with the correct polymer coating achieves a very good compromise between stiffness and damping.
What you take from this is that there is no perfect material for making cones. What you would like is something with infinite stiffness and infinite internal damping, in addition to zero mass. This combination does not exist in the real world. Aluminum's advantages are very high stiffness, good formability, and relatively low cost. The price you pay is a GIANT resonant peak when the thing finally breaks up. There are two solutions: one, do what Joseph does and use a very high crossover slope to get it out of audibility, or two, do what Thiel does and push the resonant peak high enough in frequency that even a shallow-slope crossover can do a good job of removing it. (Notice the large voice coil on the 1.6? It's there to get the cantilevered length of aluminum down to a smaller value, to drive the resonant frequency up.) Kevlar is probably a better material in that its stiffness is still very good but it has much better internal damping. I believe B&W has a patent on single-layer Kevlar cones, which may be why they are "attached" to that lately. (Like a lot of patents, I'm not sure it would hold up in court, but they have enough lawyers to discourage anyone from trying.) There are many plastic formulations, some of which are quite good, usually using some type of mineral filler to add stiffness, often magnesium based in order to keep it light. The French manufacturers Audax and JMLab/Focal have experimented with all kinds of cone materials, including all kinds of exotic polymers and fiberglass and kevlar sandwich cones, but none of them have impressed me much. Eton made their living on fiberglass/honeycomb sandwich cones, which are very stiff but also have a nasty breakup peak. The only exotic construction I've seen that had some good sense behind it was the Ensemble driver from Switzerland, a sandwich of two thin layers of aluminum separated by a thick layer of EPS foam. Stiff, light, and well damped. Also very expensive to make and even harder to get good quality control due to the variability in EPS foams.
After many years of experience, I personally have come down in the camp of "make it as stiff and light as possible while still keeping very good internal damping". This, believe it or not, means coated paper cones or a very few select plastic-cone drivers.
Cdc, to answer your specific questions: Yes, ribbons eliminate this type of breakup, but they have resonant modes of their own of a different kind. Re cone "breakup", there are two separate issues. You have to distinguish between "piston mode", which is defined as the frequency range in which the cone still behaves as a piston (a flat inflexible surface), and "breakup mode", where the accelerations have gotten so high that the cone itself begins to flex and resonate in response to the drive signal. Even in "piston mode", the sound waves travel outward from the voice coil to the edge of the cone, and then reflect backwards down the cone. Note that sound waves travel MUCH faster in solids than in air, and that they will dissipate as heat if the material has good internal damping. The reflection at the edge of the cone is also highly dependent on the type of surround used; some surrounds do a much better job of absorbing this wave than others. B&W's claim in this area is that since the bidirectional Kevlar cloth they use for their cones is a non-homogeneous material (different stiffnesses in different directions across the cloth), it will do a better job of breaking up this wave. This may or may not be of much significance; I personally would much rather see a cone material with very high internal damping. In "breakup mode", where the cone is literally going crazy with internal resonances, again I would prefer a material with very high internal damping. Because you're right, you can hear cone resonance very easily, and it's not a pretty thing.