You know, in the case of the infinities, it just might be that the reason they happened to use a tweeter with signficant output above 20 kHz had to do with entirely different reasons such as its behavior in the audible region of the audio spectrum as well as how it mated with everything else.
As for the Tannoy SuperTweeter, we have the following from their website regarding the crossover...
Quote:
Frequency 14kHz, 16kHz or 18kHz adjustable
Type 3rd order compensated high pass
Level 89dB, 90.5dB, 92dB, 93.5dB or 95dB adjustable
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Again, we're dealing with some audible output given the crossover points so I'd expect it to have an effect. As to whether it actually results in a better sounding speaker if you add it to yours, all I can say is that it's certainly a tendency for people to assign positive benefits to a change. Especially when they cost around $1000!
Quote:
The SuperTweeter is designed to provide the extended high frequency response demanded by modern programme material and sources. It not only resolves fine detail of high frequency notes but also effectively enhances the listening experience even at lower frequencies.
Extending the frequency response by two octaves corrects time and phase response within the bandwidth of normal human hearing.
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I tend to read stuff like the above a little differently. I'd imagine if you're no longer listening to vinyl and have speakers that lack signficant HF output, then this product might be of benefit (costly though!). Further, even if the phase errors are corrected this begs the question were they even audible to begin with? After all, we have all the phase errors from the microphones, the mixing consoles, the wiring that might've been hooked up improperly, the phase errors introduced by your player, preamp, and amp. The audiophile business is infamous for creating to solutions to problems that aren't in fact problems.