[impedance]

[Robert Scott]

Don Rose wrote:

>With todays technology it is *already* possible to prove that the frequence
>of the partials change with voicing and also with the changes in the
>humidity content of the sound board.


I don't think it has been proven.  A lot of well-respected people 
have certainly made their opinions known, but that does not constitute
proof.  Here is the problem:  Proponents of the view that voicing affects
inharmonicity start by measuring the inharmonicity using some means
or another.  Then they voice the hammers.  Then they measure the
inharmonicity again.  Lo and behold it is different.  But wait!
How different is it?  And what is the inherent measurement error anyway?
Isn't it possible that the "difference" in inharmonicity is actually
nothing more than the normal variation from one measurement to another?
I think the accuracy of inharmonicty measurements is vastly overrated.

If you really want to prove that voicing affects inharmonicity, here is
what you would do.  Get 5 different technicians to measure the inharmonicity
of several strings on a piano.  Allow each technician to be alone with the
piano while making the measurement.  Do not allow the 5 technicians to
compare notes until all 5 have made their measurements.  Then change
the voicing.  Then bring in 5 more technicans who have not talked with
the first group and have them make inharmonicity measurements.  Use a
variety of devices to make the measurements, both before and after
voicing (RCT, TuneLab, SAT, whatever).  When you are all done, look at
the results.  If voicing really plays a role in determining inharmonicity,
then the "before" and "after" readings should cluster into two clearly
distinguishable sets of numbers with little or no overlap.

If it is inconvenient to get 10 technicians to perform this experiment,
then perhaps it could be done by one person provided the measurement
means does not allow any biasing of the results by the one taking
the measurements.  Perhaps if you measure about 20 strings, you
will not remember the measurements when taking the readings after voicing,
so wishfull thinking won't be able to bias the result.  

If anyone can or has ever performed an experiment that is even vaguely
like what I have described, then I would be glad to entertain the notion
that voicing might be a factor.  But until then I will continue to
disbelieve the claimed results and ascribe them to random experimental
error.  The reason that I am so slow to believe these claims is that
they run counter to my understanding of resonant systems.  Extraordinary
claims require extraordinary proofs.

In the event that proof of this point does emerge, then there is one
way in which I can imagine that voicing may affect inharmonicity,
and that is through its affect on volume.  We know that the pitch of a
string is higher when it is played louder because of the increased average
tension.  And we also know that the degree to which the pitch is
raised is not the same for every partial.  Thus some partials could be
affected by volume more than others.  And voicing can affect volume.
But what this really proves is not that voicing affects inharmonicity
but that volume affects inharmonicity.  And we would have to qualify
all inharmonicity measurements in terms of the strength of the blow and
the point along the decay curve at which the measurement is taken.  If we
are to prove anything about voicing affecting inharmonicity independently
from its effect on volume, then we would have to find a way to play the
note, regardless of its voicing, so that it has the same volume level
during the inharmonicity measurement.

-Robert Scott
 Real-Time Specialties