Does anyone know what cone profiles mean?

What's the point of the extended high frequency performance if the driver is beaming at that point?
The beaming woofer nicely crosses to a horn of similar dispersion (90* or less), giving an easy 2-way, avoiding a midrange driver and its related driver / network / cabinet costs, and also size and weight. The reason for popularity of the stiffer straight cones is the questionable fidelity of the resulting HF 'extension' of the curvilinear paper-based ones.
 
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I’m aware of the cross where there is a pattern match. I asked why yap about 4k extension when the pattern match is around 1k. The AE TD10 and 12m are straight cones with unparalleled accuracy. I have the TD10m with a beryllium compression driver. My issue is with thin fragile cones and weak motors that have poor low end. Most compression drivers have more distortion at the crossover than a AE driver. I still want midbass slam with my new bigger system.
 
The HF beaming is not an issue in many PA applications where cost drives the market. Many PA speakers cross much higher than the usual 600-800Hz. For example, JBL SF15 and SF25 cross the 15" M115-8A at 1.6kHz and 2kHz respectively. The same is true for the JRX115/215 models that use the same woofer.

However, the mid-level cinema models like 4622 and 4722 with straight cone drivers cross off at 630Hz.
 
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frequency_response_straight_cone_vs_exponential.png

I used to design OEM car speakers at Jensen.

A straight sided "perfectly conical" cone (blue curve above) has the most piston-like behavior and has a rising response which peaks, and then drops off immediately. Because it's the most piston-like, it has lower distortion. The deeper the cone, the more piston-like it is. It's most often used in subwoofers. The radiation pattern is more beamy in the upper end of the range.

A flared "exponential" cone (red curve above) has a more gradual transition from passband to stopband and greater bandwidth. It has higher distortion because it's more flexible, but its breakup modes are more evenly distributed. This gives it more high frequency extension. It's usually easier to design a crossover for an exponential cone because the peak followed by the sudden cutoff of the straight sided cone is difficult to deal with. The radiation pattern is less beamy in the upper end of the range. It's the most common type of cone for speakers that cover the midrange.

I'm not certain that the term "curvilinear" has an exact definition. I think it usually means exponential, which means the flare is steepest near the voice coil and gradually flattens out near the outer edge.
 
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B&C has profiles on their cones listed as radial or exponential. The driver I’m interested in is listed as radial. Earl Geddes used this driver in the original summa. It was crossed at 900hz. I’m going to be using an active crossover.

What is a radial cone?
 
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I guess in the end, the best course of action is to go by the manufacturer measurements as there are very little differences in the top end response of the exponential and radial profiles. Dr. Geddes used both profiles in his signature product to 1k hz with great success.

Thanks for the great input.
 
I guess in the end, the best course of action is to go by the manufacturer measurements as there are very little differences in the top end response of the exponential and radial profiles. Dr. Geddes used both profiles in his signature product to 1k hz with great success.

Thanks for the great input.
You can tell just by looking at a photo whether the cone is straight sided or exponential.