Perceivable time differences [was Re: PSA: Clock drift and pkgin]

[Mouse <mouse%Rodents-Montreal.ORG@localhost>]

> ? If I remember right, anything less than 200ms is immediate response
> for a human brain.

"Response"?  For some purposes, it is.  But under the right conditions
humans can easily discern time deltas in the sub-200ms range.

I just did a little psychoacoustics experiment on myself.

First, I generated (44.1kHz) soundfiles containing two single-sample
ticks separated by N samples for N being 1, 101, 201, 401, 801, and
going up by 800 from there to 6401, with a second of silence before and
after (see notes below for the commands used):

for d in 0 100 200 400 800 1600 2400 3200 4000 4800 5600 6400
do
	(count from 0 to 44100 | sed -e "s/.*/0 0 0 0/"
	echo 0 128 0 128
	count from 0 to $d | sed -e "s/.*/0 0 0 0/"
	echo 0 128 0 128
	count from 0 to 44100 | sed -e "s/.*/0 0 0 0/"
	) | code-to-char > zz.$d
done

I don't know stock NetBSD analogs for count and code-to-char.  count,
as used here, just counts as the command line indicates; given what
count's output is piped into, the details don't matter much.
code-to-char converts numbers 0..255 into single bytes with the same
values, with non-digits ignored except that they serve to separate
numbers.  (The time delta between the beginnings of the two ticks is of
course one more than the number of samples between the two ticks.)

After listening to them, I picked the 800 and 1600 files and did the
test.  I grabbed 128 bits from /dev/urandom and used them to play,
randomly, either one file or the other, letting me guess which one it
was in each case:

dd if=/dev/urandom bs=1 count=16 |
  char-to-code |
  cvtbase -m8 d b |
  sed -e 's/./& /g' -e 's/ $//' -e 's/0/800/g' -e 's/1/1600/g' |
  tr \  \\n |
  ( exec 3>zz.list 4>zz.guess 5</dev/tty
    stty -f /dev/tty min 1 time 0 -icanon
    while read n
    do
	echo $n 1>&3
	audioplay -f -c 2 -e slinear_le -P 16 -s 44100 < zz.$n
	skipcat 0 1 0<&5 1>&4
    done
  )

char-to-code is the inverse of code-to-char: for each byte of input, it
produces one line of output containing the ASCII decimal for that
byte's value, 0..255.  cvtbase -m8 d b converts decimal to binary,
generating a minimum of 8 "digits" (bits) of output for each input
number.  skipcat, as used here, has the I/O behaviour of "dd bs=1
count=1" but without the blather on stderr: it skips no bytes and
copies one byte, then exits.  (The use of /dev/urandom is to ensure
that I have no a priori hint which file is being played which time.)

I then typed "s" when I thought it was a short-gap file and "l" when I
thought it was a long-gap file.  I got tired of it after 83 data
samples and killed it.  I then postprocessed zz.guess and compared it
to zz.list:

< zz.guess sed -e 's/s/800 /g' -e 's/l/1600 /g' | tr \  \\n | diff -u zz.list -

I got exactly two wrong out of 83 (and the stats are about evenly
balanced, 39 short files played and 44 long).  So I think it's fair to
say that, in the right context (an important caveat!), a time
difference as short as (1602-802)/44.1=18.14+ milliseconds is clearly
discernible to me.

This is, of course, a situation designed to perceive a very small
difference.  I'm sure there are plenty of contexts in which I would
fail to notice even 200ms of delay.

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