Sub-woofer fast enough for Horns?

Not enough info, as others have said.

Regarding "fast", there is no such thing as "fast" 60hz, or 50hz, or 40hz, etc. They all travel at the speed of sound and have periods (the time for one wavelength) equalling the reciprocal of the frequency.

Many "perceive" speed or lack thereof based on distortion. High second order distortion at lower frequencies is the bane of many loudspeakers and subwoofers. Adjustability is a real plus in a crossover. The key is getting a low distortion subwoofer with a crossover that is steep enough for your main speakers to not have a bump in the upper bass where they overlap, which will also cause you, I think, to say the bass is "slow".

Vapor, I think we're not taking about horns being faster than a diaphragm but high frequency being faster than low.

Timing is timing: if this user is finding the timing is disconnected or does not match his horn loudspeaker it seems that there is a disconnect. I recommended a front firing sub placed forward in the set up if possible works like magic.

Horns are faster in the sense that they can increase both the dynamic range and spl by as much as 5db making them seem faster as they are often more in your face.

Q

Sorry guys, my horn is Cessaro Chopin. Their smallest model. I think it goes down to around 30Hz on paper. I am very happy with most music but not enough for electronic and heavy rock. I had Thiels 3.6 before and I think the Thiels has stronger bass.

Technically subwoofers don't need to be fast as the frequencies they do are relatively slow. As far as the mass argument, it's more the ability to stop than go. Rythmik uses a servo system that allows the driver to be a bit lighter but, usually, heavier means more extension and larger means more for less excursion, where too much leads to distortion.

A sealed sub will have a fraction the group delay of a ported or PR sub but sacrifice deep bass with an earlier, shallower rolloff. Not usually a big concern for music and subs 12" and over, considering room gain. For the HT bass fanatics, it's another story.

Have you considered an active crossover, one that has a high pass for the main speakers? Maybe something like a Paradigm X30, Reckhorn S-1 or miniDSP. Maybe even a Harrison labs FMOD inline passive. How about a DSPeaker Antimode?