From: sandell@ils.nwu.edu (Greg Sandell)
Subject: Re: What is the resolution of human hearing?
Date: 19 Jul 91 21:47:33 GMT
Message-ID: <2530@anaxagoras.ils.nwu.edu>
Organization: The Institute for the Learning Sciences



My third example was presented rather confusedly; let me try to 
improve it.

> (3)
> Sound travels (under typical atmospheric conditions) at
> 3440 meters/sec, or 344,000 millemeters a second.  A 1000 Hz
> tone has a period of 1 msec, during which the sound wave
> travels 344 millemeters.  Our ability to notice changes in
> the location of the sound is the most finely tuned aspect of
> the temporal auditory system (it's how man survived in the
> forest).  A change in location of even one millemeter in
> the 1000 Hz tone can be noticed because there is a change in
> phase relationships between the sounds that reach the two
> ears.   The portion of the 1000Hz tone that sounds in just
> a 1 millemeter stretch of time is .001sec/344 and that's
> .0000029 sec, or 2 usec.  So the one millemeter change in
> sound source location that the system detects is a temporal
> change as small as 2 usec!

This should clarify.  The physical distance traversed by one period of 
a 1000 hz. tone is 344 millemeters, and the temporal duration is
1 millesecond.  Suppose the location of the tone with respect to
a listener is directly in front of the head, so the oncoming wave
of sound reaches both ears at the same moment.  Now suppose we move
it so it gets closer to one of the ears, by a distance of 344
millemeters.  Now the waveform is reaching one ear earlier than the
other, but by exactly the distance of one period; the waveforms are
still in phase.  Now consider a smaller change which would result
in the waveforms not being in phase.  If it was only one millemeter,
then the waveform is reaching one ear earlier by (1 millesecond) *
1/344, or .0029 seconds, or around 3 usec.  If the listener detects
a change that small, and it is true that the ears measure phase
difference to detect location (that's always open to question), then
this indicates a 3 usec. resolution.

Greg Sandell
I went overboard.  Basically the idea was that the mind compares
differences in phase between frequencies received by the two ears.
 
> The human hearing system is remarkable indeed.  The poster mentioned
> the resolution of visual perception with reference to film projection
> (24 frames/sec).  This is pretty coarse (a 42 msec resolution) but 
> good enough for video, I guess.  In commercial computer music we have the 
> MIDI standard which ends up imposing a temporal resolution of about
> 10 msec in the very best conditions.  But this is much too coarse,
> even lay-listeners can notice the flaws caused by sounds not happening
> at the same time when they should be.
> 
> Greg Sandell
> sandell@ils.nwu.edu
> Greg Sandell
> sandell@ils.nwu.edu

-- 
Greg Sandell
sandell@ils.nwu.edu
Greg Sandell
sandell@ils.nwu.edu