Speakers for leading edge, transients, speed and big sound

"If the woofer can reproduce 40Hz with low distortion, how fast the woofer starts is almost irrelevant (within reason of course). It only needs to accelerate fast enough to match the rise time of 40Hz at the fastest point along a 40Hz sine wave. If the woofer can do that, it is going as fast as it needs to in order to be as fast as fast can be -- at 40Hz."

This may be fine if you are just listening to sine waves.  But what about a square wave or sawtooth wave where the woofer has to pop out to its maximum travel instantaneously?  And please don’t say there are no square waves used in music.

In fact, there is not a sine wave anywhere to be found on a MiniMoog.

I’ll second the Legacy speakers. I had the original Focus and now have the Aeris with the Wavelet processor. The speakers are biamped, each with a 700-watt built-in woofer/subwoofer amp. They are not horn-loaded, but they do use custom-designed dual air motion tweeters and super tweeters. The Wavelet II is an electronic crossover, DAC, equalizer/processor, and preamp.  It’s a phenomenal sounding system—dynamic, with an amazing soundstage, and has some of the tightest, best bass (in my opinion) I’ve heard in any home speaker system. It’s also incredibly efficient. Bill Dudleston is an amazing speaker-designer. You could buy the Aeris speakers with the Wavelet II processor new and stay within your budget.

@faustuss 

Interestingly, you have to keep a supply of ionized gas around which in effect acts as the diaphragm as the plasma excites the atoms of whatever gas it is producing sound. When the gas floats away or is dissipated though, no more sound. Not very practical or I would assume, cheap.  

In reality, no one has ever improved on the good old dynamic driver which people in the know are always coming up with new ways to configure and implement this legacy technology to achieve whatever sonic milestone they desire for less money and hassle and what the market will rationally except.

They use a pulsating plasma flame to excite the air itself. No need for an external gas supply.

They're lifespan is extremely long, since there are no moving parts. 

Another company that uses ION tweeters, which I like even better than Acapelle, is Lansche audio. I heard their speakers at T.H.E. SHow last year. 

Their ION tweeter, if it needs to be replaced, is less expensive than other high end speaker's tweeters. 

fffffffffffffffffffffff

Yes they are placement and need a big room (but what you're looking for in sound rather implies that); yes they need a LOT of amp power to function their best, yes they tall (but thin) but there's nothing faster than Magnepans. I think there is no better sounding speaker in any price bracket. And all the experts seem to live them and they crush the competition if you care about value. Demo them or they let you try at home for 30d for full refund if you don't like. 

For some ionic tweeters, like the Hill Plasmatronic, a chemically inert gas was injected around the electrode to prevent it from corroding in the highly reactive environment of an ionized plasma.  Even with such gas protecting the electrode, it would get eaten up by that harsh environment.