Sub-woofer fast enough for Horns?

When people refer to "fast and slow" in relation to a speaker, they are referring to the dynamic speaker driver's ability to respond instantaneously and accurately to the signal provided at any exact moment in time.

How well it performs in this regard is largely determined by the mass of teh cone. All cone movements are affected by inertia and therefore must have some amount of temporal delay in responding to the signal at any particular instant as a result. That tendency in general can be described as "slowness". Larger, more massive drivers, like those in subwoofers, will be the most affected compared to to others. Smaller low mass cones, like those used generally in tweeters and midrange drivers, are less effected by inertia and hence tend to be inherently "faster".

Other factors of speaker design and tolerances may come into play, like damping factor, but I think size and mass of teh cone and relationship to inertia is the main one. Planars, electrostatic, ribbon type drivers tend to suffer less from effects of mass and inertia and tend to sound "fast" in that they are able to respond to signal changes more instantaneously in general than most dynamic drivers.

Another exception might be a transmission line style Walsh dynamic driver, where much of the sound is produced via "wave bending" principles as described by the original designer, Lincoln Walsh, rather than pistonic type driver movements, where the mass of teh speker normally comes more into play I would think.

Tweeters and midrange drivers tend to have low mass compared to woofers and subwoofers in particular. HEnce the perceived difference possible when using a sub with speakers that are relatively "fast" in of themselves.

Compression drivers used often in horns are generally also very low mass and inherently "fast", so matching subs with those in particular to get coherent sound top to bottom might be a somewhat more difficult challenge.

Speaker systems that are "fast" may or may not sound "coherent" top to bottom as well, in that other factors like crossover design and performance come into play there as well.

If you have a speaker that is both "fast" and "coherent", then I would say you really have something special that might also possibly sound particularly "musical" compared to others! Make it "full range" to-boot, and bingo!

The advantage of field coil or em type driver motors is these can be made more powerful than natural magnets and make for a faster drive when needed, almost always for large bass drivers.

An alternate approach are very light but rigid drivers like the paper drivers in triangle titus monitors, which are often praised for their "speed", but they are small and have limited extension. Scaling to larger drivers for more bass this way is a challenge.

No doubt the room acoustics is the biggest and often hardest factor to get a handle on in regards to bass and overall sound quality. Even more so in teh case of "full range" sound. Optimal placement of a sub or better yet multiple subs makes a big difference, as does how well the sub(s) are sonically integrated with the mains. "speed" or any sonic artifacts that might be attributed to that, even with most decent large subs or bass drivers, are a distant second and practically may not matter much at all if components are selected and set up well in any particular room to start with.

Not sure how it works exactly but Rhythmik direct servo technology is a unique advertised feature that at a glance sounds like it should make some difference. Looks like a kind of negative feedback associated with the built in amp maybe? Not sure what makes theirs so special in that most power amps use negative feedback, but surely not all NF is created equal.