From: sandell@ils.nwu.edu (Greg Sandell)
Subject: Re: What is the resolution of human hearing?
Date: 19 Jul 91 04:01:30 GMT
Message-ID: <2518@anaxagoras.ils.nwu.edu>
Organization: The Institute for the Learning Sciences



In article <1991Jul18.184025.9933@milton.u.washington.edu>, dnettles@libserv1.
ic.sunysb.edu (David E Nettles) writes:
 
> What is the resolution of human hearing?
> 
> For vision I think it is 24 frames/sec.  What is it for sound?

I gather that the question intended to cover the *temporal* resolution
of hearing (not the range of audible frequencies, as the moderator
suggested).  If so, here are some facts.  (They are facts insofar as
there is empirical evidence to back it up.)

(1)
If two sounds placed close together in time, listeners will hear
only one fused sound rather than two.  But how close do they have
to be?  We can tell that two sounds have occurred when they
are as close in time as 2 msec (.002 seconds).  We need as
much as 10 msec separation to tell which sound came first.

(2)
Around the neighborhood of 2000 Hz, we get pretty good at telling
one frequency apart from another.  People can easily hear that 2000 and 
2100 Hz are different tones.  Frequency is encoded in the nervous
system by some sort of detection of the periodicity of the frequency.
The period of 2000 Hz is 500 usec (.0005 seconds) and 2100 Hz
is 472 usec.  That indicates a temporal resolution of 24 usec.

(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!

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