Randolph Herr wrote, in regard to the effect of the sustain pedal on
volume:  "It seems to me that he is saying the volume is the same (the
height of the curve) but it is perceived louder because of the longer
sustain.  I do not think that the area under the curves is of paramount
importance since the heights are the same.  Furthermore, the total area
under the curve measures the tone over time-people hear only an instant
at a time, and piano notes are the classic example of tones starting at
their loudest and going down from there."

Don't get the two values, "volume" and "loudness", mixed up.  The ear
perceives volume.  A dB meter perceives loudness.  Loudness is what a
dB meter measures.  Volume is what the ear measures.  Volume is the
loudness integrated or summed up over a given amount of time, but
_defined_ to have a cutoff point down to a certain percentage of the
maximum loudness (the ear doesn't retain it forever).  Volume is also
determined by how many notes are playing down at the same time, not
just a single note.

For instance, on large, powerful chords played on any pneumatic player,
you will notice the vacuum drop tremendously, and yet the piano is very
powerful for an instant.  The reason is volume, not loudness.  The number
of notes played, although perhaps only at 15" or so, equates to the ear
as a triple forte.  And the hands and arms of the artist react the same
way, so it's realistic.

"The second thing is that I disagree with Craig Brougher's explanation
on sound curves (assuming that I understand it correctly).  Craig is
saying that if you graphed the power of a played note with and without
the sustain, the height of the curve in both cases would be the same,
but the decay time of the sustained note would be longer when the loud
pedal is on, so the area under the curve is a little greater and the
tendency of the ear to integrate that effect tells it the note is
louder, rather than equal but of longer duration (equally loud and
slower decay)."

Stop and think about it a minute, Randolph.  Whether I have the loud
pedal on or off makes no difference at all when I play a note, does it?
Because when I play a note, the key itself raises the damper, too.
So however I strike the note -- with or without the pedal -- I get
exactly the same thing: the same power, the same loudness.  The only
difference then is how long I leave the damper off the string.
Therefore, the loudness of the initial strike would measure exactly the
same on a dB meter, with or without the sustain pedal.

Craig Brougher