Confusion abounds in this thread
The real issue with tweeters is how the hand off to the mid or bass mid is handled.
Now the things of concern about any tweeter, are is Fs, its frequency response, and especially the linearity thereof. The off axis response (dispersion) sensitivity and power handling are all important issues. The designer also has to look carefully at the intrinsic roll off of the driver and the high frequency resonance.
Now I think horns are problematic in domestic installations. Horn loaded compression drivers will have some and often a lot of response irregularity due to horn resonances. Dispersion in the domestic situation is inclined to be less than ideal. The sensitivity and efficiency is high, however unless mated with a horn loaded bass unit the efficiency can not be realized, as the high pass output has to be padded down to match the sensitivity of the woofer. In my view horns have a place in large professional installations in large spaces.
In the hey day of Klipsch the HF horns were matched to huge bass horns. In the 50s the klipschorn was an impressive speaker, and still is, but few would have room for a pair. By the way, a properly designed L-pad can be impedance neutral.
Now the composition of the tweeter dome is only partially relevant. What I mean by this is that hard domes will have a sudden break up mode and an associated peak in output. If the break up mode is close to the audible range, it gives the dome a certain artificial brightness, for some reason. The soft domes obviously do not radiate as a unified rigid surface throughout operating range. However in my view rigidity of drivers, with the exception of sub woofer drivers is a misguided obsession. I have successfully used both rigid and soft dome tweeters.
Now the free air resonance of the tweeter is very important. The crossovers have gradual roll off, and are additive to the tweeter roll off. Now the crossover point is generally determined by the woofer response and roll off. The combined roll offs of the tweeter, woofer and high and low pass filters, must result in a smooth frequency response across the crossover region. This must do the minimal violence to phase and time. Now if the tweeter receives appreciable power in its region of low frequency resonance, then that makes for a harsh sound.
One of the important tasks when designing a speaker is to select drivers that will match well with each other with the simplest crossover. What the component parts of the driver are, or its theory of operation are very secondary considerations.
I hope this sheds some light on the issue.
