On 10/06/2011 01:29, Robert Greene wrote:
Could I be permitted a mathematical comment?
There is no such thing as a linear
system (say a subwoofer) with an absolute upper frequency limit in
the actual world, only in mathematical theory.(A step function
of finite width is L2 and so it is the Fourier transform of something
else that is L2. But that is mathematics, not the real world).
Is bass directionally perceived? In practice, we almost all seem
to think so. But is this because of its higher frqeuency components?
Hmmm - there are a number of ways that this could potentially be tested. Here's
one suggestion.
Firstly, one would ideally need specially designed subs coupled into the space with _acoustic_
filtering to reduce the output into the space of speaker distortion based high frequencies. Second,
mask what is left with filtered noise from additional, evenly distributed loudspeakers. Set the
level of this such that it is high enough to mask out the, ummm, shall we call them "mathematically
generated", higher frequency components?? (belt and braces approach - I actually suspect that from
Fon's function the levels would be close to hearing thresholds anyway). Thirdly, do what Fons
suggests but in a fully controlled double blind test with lots of listeners. I think the result
would be the same - people would be able to tell exactly where the sound was coming from, provided
the space was not too small (experiment could, of course, be done outdoors)
Another suggestion - repeat the experiment with continuous tones, imposed on which are the
mathematically generated high frequency components that would have been generated from Fons'
enveloped LF. See if people swap from not being able to localise the sound to being able to.
Incidentally, the fact that speakers in rooms produce impressions of bass sounds coming from one
place or another is not really a valid determination of anything scientific to my mind. It mostly
just shows that if one likes the effect, having a bunch of subwoofers is a good idea. Plus it
illustrates the above principle.
But if the sounds consistently localise to where they should do, it shows that there are mechanisms
at work that probably _should_ be exploited if one wants to get the best out of the system.
my guess--and this is only a guess-- is that the sense of
localization of say a double bass player or contrabassoon player--and of course they are localized
fine in practice--is almost entirely a matter of higher
frequency components in a simple minded sense, not the compact support
sense I just described, and not the time of arrival of the envelope of the
fundamental either.
Strikes me that this could be proved (or disproved) by an experiment of the type
"that saved hi-fi"
http://phillokit.com/high_fidelity/experiment_that_saved_high_fidelity.html
Dave
--
These are my own views and may or may not be shared by my employer
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