Pianos are subjected to what is known as "stretched tuning",
because the "strings" used for the low notes are complex structures
with small wire wrapped around another wire to increase the linear
density. The result is that they don't vibrate like simple strings,
and the overtones occur at frequencies that are higher than those for a
simple string. When notes are sounded on the piano, most of the energy
is in the high overtones, and when notes are played together the beats
between the overtones give the sound its character. Since the
overtones become progressively sharper for the nonideal low pitch
strings, the fundamentals have to be tuned to be more and more flat
relative to the middle strings in order for combinations of overtones
to sound "pleasant". To compromise, the higher strings tend to be
tuned sharp relative to the middle, although the degree of "stretch"
for the higher strings is much smaller than for the lower strings. The
degree of "stretch" also depends on the physical size of the piano--
a 9-foot grand piano can be built with longer, more massive strings
than a small upright spinet, so the grand piano has less "stretch" than
spinet (and therefore tends to sound better). You can read about
stretch tuning in most texts on musical acoustics.
The 256 Hz "C" was something that puzzled me when I first began
teaching a musical acoustics course. While doing some background
reading in preparation for classes on construction of musical scales,
I ran across a reference to a "scientific" scale that was proposed
either late in the 19th century or early in the 20th century. The
idea is that since musical intervals (pitch differences) are defined
as frequency ratios, only one "standard" pitch needs to be defined.
Historically, this has been done with the A above middle C on the piano
having a frequency somewhere in the neighborhood of 440 Hz, although
the actual standard has varied somewhat. When (around the end of the
19th or beginning of the 20 century) it was decided to have an official
standard of pitch, one suggestion was to make all the C's have
frequencies that were multiples of 2. However, this turned out to be
too far from musical preferences of that time, because a 256 Hz middle
C puts the next A at about 431 Hz. At this time, even wind band
instruments were built to be tuned either to a 440 Hz A or a 435 Hz A
(I have one of those old instruments at home), so adopting a 256 Hz
standard for middle C would make all existing instruments very sharp.
Thus the 440 Hz A was settled on as a standard, and the scientific
scale persists only in the form of tuning forks for physics labs. (I
can't remember where I read this little history, but if anyone is
desperate for a source, I'll try to track it down.)