A 440 Standard

[James Ellis]

Hi Don:

Thanks for your excellent post.  You are right on target.  I know you have
done extensive research on pitch-vs-string temperature, because that's what
your "Self-Tuning" piano is based upon.  And you are right that it can't be
reduced to a simple relationship of temperature and pitch when it comes to
a real piano in a real-world situation.  There are too many other things
going on, too many unknowns.  For example, when the temperature is
changing, no two parts of the piano's structure will be at the same
temperature, and we can't be sure where the soundboard will carry the
bridge while these changes are taking place.  And as you say, shiny
surfaces reflect more radient energy, and dull black surfaces absorb more.
In my previous post, I was speaking in generalities to piano technicians.

The demonstration that I did at the Conventions in 1994 and 1995 used a
monochord mock-up of a piano.  The "plate" was a five-foot section of
strictural steel channel, not cast iron.  However, the expansion
coefficient was close enough to that of cast iron that it was OK for the
demonstration.  The hair dryer that I used to warm the string, to which Wim
referred, was one of those antique low-wattage jobs - air just warm, not
much of that, and used at a distance to simulate the heat coming on in a
room.  As I said, it was a demonstration to make a point, not a precise
measurement.

Back in the shop, I measured the change in pitch as a function of change in
ambient temperature, and it came out as -0.56 cents per degree F.  But then
the "plate" thermometer showed a 2-degree increase while the ambient air
thermometer showed 8 degrees.  That's not all:  The string temperature
lagged behind that of the air; the air thermometer lagged behind the actual
temperature; and the "plate" thermometer lagged behind the actual
temperature of the plate.  How much?  Don't know!  This demonstration was
as well controlled as I could make it, but even then, it had a host of
unknowns.  In a real piano, there would have been many more unknowns.  The
point of that part of the demo was to show what happens in a piano when the
temperature is changing.

Don, your calculated value for pitch-vs-temperature of a string looks
reasonable to me.  Oh, by the way:  I know there is a square root
relationship between tension and pitch of a taut string.  That was a part
of my demonstration too.  That's why I used a string length-vs-pitch that
would put the string at about the same stress it would be under at middle C
of a concert grand.  Obviously, at a lower tension, the effect of
temperature change on pitch would be exaggerated.

Jim Ellis